| 1. |
- Ardonne, Eddy, et al.
(författare)
-
Classification of Metaplectic Fusion Categories
- 2021
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Ingår i: Symmetry. - : MDPI AG. - 2073-8994. ; 13:11
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for so(2p+1)2. These categories describe non-abelian anyons dubbed ‘metaplectic anyons’. We obtain explicit expressions for all the F- and R-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes.
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| 2. |
- Ardonne, Eddy, et al.
(författare)
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Classification of metaplectic modular categories
- 2016
-
Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 466, s. 141-146
-
Tidskriftsartikel (refereegranskat)abstract
- We obtain a classification of metaplectic modular categories: every metaplectic modular category is a gauging of the particle hole symmetry of a cyclic modular category. Our classification suggests a conjecture that every weakly-integral modular category can be obtained by gauging a symmetry (including the fermion parity) of a pointed (super-)modular category.
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| 3. |
- Ardonne, Eddy, et al.
(författare)
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Degeneracy of non-Abelian quantum Hall states on the torus : domain walls and conformal field theory
- 2008
-
Ingår i: Journal of Statistical Mechanics. - 1742-5468. ; , s. P04016-
-
Tidskriftsartikel (refereegranskat)abstract
- We analyze the non-Abelian Read–Rezayi quantum Hall states on the torus, where it is natural to employ a mapping of the many-body problem onto a one-dimensional lattice model. On the thin torus—the Tao–Thouless (TT) limit—the interacting many-body problem is exactly solvable. The Read–Rezayi states at filling ν = k/(kM+2) are known to be exact ground states of a local repulsive k+1-body interaction, and in the TT limit this is manifested in that all states in the ground state manifold have exactly k particles on any kM+2 consecutive sites. For M \neq 0 the two-body correlations of these states also imply that there is no more than one particle on M adjacent sites. The fractionally charged quasiparticles and quasiholes appear as domain walls between the ground states, and we show that the number of distinct domain wall patterns gives rise to the nontrivial degeneracies, required by the non-Abelian statistics of these states. In the second part of the paper we consider the quasihole degeneracies from a conformal field theory (CFT) perspective, and show that the counting of the domain wall patterns maps one to one on the CFT counting via the fusion rules. Moreover we extend the CFT analysis to topologies of higher genus
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| 4. |
- Budich, Jan Carl, et al.
(författare)
-
Equivalent topological invariants for one-dimensional Majorana wires in symmetry class D
- 2013
-
Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:7, s. 075419-
-
Tidskriftsartikel (refereegranskat)abstract
- Topological superconductors in one spatial dimension exhibiting a single Majorana bound state at each end are distinguished from trivial gapped systems by aZ(2) topological invariant. Originally, this invariant was calculated by Kitaev in terms of the Pfaffian of the Majorana representation of the Hamiltonian: The sign of this Pfaffian divides the set of all gapped quadratic forms of Majorana fermions into two inequivalent classes. In the more familiar Bogoliubov de Gennes mean-field description of superconductivity, an emergent particle-hole symmetry gives rise to a quantized Zak-Berry phase, the value of which is also a topological invariant. In this work, we explicitly show the equivalence of these two formulations by relating both of them to the phase winding of the transformation matrix that brings the Majorana representation matrix of the Hamiltonian into its Jordan normal form.
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| 5. |
- Budich, Jan Carl, et al.
(författare)
-
Fractional topological phase in one-dimensional flat bands with nontrivial topology
- 2013
-
Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:3, s. 035139-
-
Tidskriftsartikel (refereegranskat)abstract
- We consider a topologically nontrivial flat-band structure in one spatial dimension in the presence of nearest-and next-nearest-neighbor Hubbard interaction. The noninteracting band structure is characterized by a symmetry-protected topologically quantized Berry phase. At certain fractional fillings, a gapped phase with a filling-dependent ground-state degeneracy and fractionally charged quasiparticles emerges. At filling 1/3, the ground states carry a fractional Berry phase in the momentum basis. These features at first glance suggest a certain analogy to the fractional quantum Hall scenario in two dimensions. We solve the interacting model analytically in the physically relevant limit of a large band gap in the underlying band structure, the analog of a lowest Landau level projection. Our solution affords a simple physical understanding of the properties of the gapped interacting phase. We pinpoint crucial differences to the fractional quantum Hall case by studying the Berry phase and the entanglement entropy associated with the degenerate ground states. In particular, we conclude that the fractional topological phase in one-dimensional flat bands is not a one-dimensional analog of the two-dimensional fractional quantum Hall states, but rather a charge density wave with a nontrivial Berry phase. Finally, the symmetry-protected nature of the Berry phase of the interacting phase is demonstrated by explicitly constructing a gapped interpolation to a state with a trivial Berry phase.
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| 6. |
- Budich, Jan Carl, et al.
(författare)
-
Topological invariant for generic one-dimensional time-reversal-symmetric superconductors in class DIII
- 2013
-
Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:13, s. 134523-
-
Tidskriftsartikel (refereegranskat)abstract
- A one-dimensional time-reversal-symmetric topological superconductor (symmetry class DIII) features a single Kramers pair of Majorana bound states at each of its ends. These holographic quasiparticles are non-Abelian anyons that obey Ising-type braiding statistics. In the special case where an additional U (1) spin rotation symmetry is present, this state can be understood as two copies of a Majorana wire in symmetry class D, one copy for each spin block. We present a manifestly gauge invariant construction of the topological invariant for the generic case, i.e., in the absence of any additional symmetries like spin rotation symmetry. Furthermore, we show how the presence of inversion symmetry simplifies the calculation of the topological invariant. The proposed scheme is suitable for the classification of both interacting and disordered systems and allows for a straightforward numerical evaluation of the invariant since it does not rely on fixing a continuous phase relation between Bloch functions. Finally, we apply our method to compute the topological phase diagram of a Rashba wire with competing s-wave and p-wave superconducting pairing terms.
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| 7. |
- Davenport, Simon C., et al.
(författare)
-
Spin-singlet Gaffnian wave function for fractional quantum Hall systems
- 2013
-
Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 87:4, s. 045310-
-
Tidskriftsartikel (refereegranskat)abstract
- We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave functions, namely the non-Abelian spin-singlet state and the nonunitary Gaffnian wave function. This is a spin-singlet generalization of the spin-polarized Gaffnian, which we call the "spin-singlet Gaffnian" (SSG). In this paper we present evidence demonstrating that the SSG corresponds to the ground state of a certain local Hamiltonian, which we explicitly construct, and, further, we provide a relatively simple analytic expression for the unique ground-state wave functions, which we define as the zero energy eigenstates of that local Hamiltonian. In addition, we have determined a certain nonunitary, rational conformal field theory which provides an underlying description of the SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit. In order to verify our construction, we implement two recently proposed techniques for the analysis of fractional quantum Hall trial states: The "spin dressed squeezing algorithm," and the "generalized Pauli principle."
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| 8. |
- Edvardsson, Elisabet, et al.
(författare)
-
Sensitivity of non-Hermitian systems
- 2022
-
Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 106:11
-
Tidskriftsartikel (refereegranskat)abstract
- Understanding the extreme sensitivity of the eigenvalues of non-Hermitian Hamiltonians to the boundary conditions is of great importance when analyzing non-Hermitian systems, as it appears generically and is intimately connected to the skin effect and the breakdown of the conventional bulk boundary correspondence. Here we describe a method to find the eigenvalues of one-dimensional one-band models with arbitrary boundary conditions. We use this method on several systems to find analytical expressions for the eigenvalues, which give us conditions on the parameter values in the system for when we can expect the spectrum to be insensitive to a change in boundary conditions. By stacking one-dimensional chains, we use the derived results to find corresponding conditions for insensitivity for some two-dimensional systems with periodic boundary conditions in one direction. This would be hard by using other methods to detect skin effect, such as the winding of the determinant of the Bloch Hamiltonian. Finally, we use these results to make predictions about the (dis)appearance of the skin effect in purely two-dimensional systems with open boundary conditions in both directions.
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| 9. |
- Gils, C., et al.
(författare)
-
Anyonic quantum spin chains : Spin-1 generalizations and topological stability
- 2013
-
Ingår i: Physical Review B. Condensed Matter and Materials Physics. - : American Physical Society. - 1098-0121 .- 1550-235X. ; 87:23, s. 235120-
-
Tidskriftsartikel (refereegranskat)abstract
- There are many interesting parallels between systems of interacting non-Abelian anyons and quantum magnetism occurring in ordinary SU(2) quantum magnets. Here we consider theories of so-called SU(2)(k) anyons, well-known deformations of SU(2), in which only the first k + 1 angular momenta of SU(2) occur. In this paper, we discuss in particular anyonic generalizations of ordinary SU(2) spin chains with an emphasis on anyonic spin S = 1 chains. We find that the overall phase diagrams for these anyonic spin-1 chains closely mirror the phase diagram of the ordinary bilinear-biquadratic spin-1 chain including anyonic generalizations of the Haldane phase, the AKLT construction, and supersymmetric quantum critical points. A novel feature of the anyonic spin-1 chains is an additional topological symmetry that protects the gapless phases. Distinctions further arise in the form of an even/odd effect in the deformation parameter k when considering su(2)(k) anyonic theories with k >= 5, as well as for the special case of the su(2)(4) theory for which the spin-1 representation plays a special role. We also address anyonic generalizations of spin-1/2 chains with a focus on the topological protection provided for their gapless ground states. Finally, we put our results into the context of earlier generalizations of SU(2) quantum spin chains, in particular so-called (fused) Temperley-Lieb chains.
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| 10. |
- Kjäll, Jonas, et al.
(författare)
-
Matrix product state representation of quasielectron wave functions
- 2018
-
Ingår i: Journal of Statistical Mechanics-Theory and Experiment. - : IOP Publishing. - 1742-5468.
-
Tidskriftsartikel (refereegranskat)abstract
- Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.
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| 11. |
- Lahtinen, V., et al.
(författare)
-
Hierarchy of exactly solvable spin- 1 2 chains with s o (N) 1 critical points
- 2014
-
Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 89:1, s. 014409-
-
Tidskriftsartikel (refereegranskat)abstract
- We construct a hierarchy of exactly solvable spin-1/2 chains with so(N)1 critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples N transverse field Ising chains such that the resulting theory is critical and described by the so(N)1 conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary N into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. For odd N our models generalize the phase diagram of the transverse field Ising chain, the simplest model in our hierarchy. For even N the models can be viewed as longer ranger generalizations of the XY chain, the next model in the hierarchy. We also demonstrate that our method of constructing spin chains with given critical points goes beyond exactly solvable models. Applying the same strategy to the Blume-Capel model, a spin-1 generalization of the Ising chain in a generic magnetic field, we construct another critical spin-1 chain with the predicted conformal field theory (CFT) describing the criticality.
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| 12. |
- Lahtinen, Ville, et al.
(författare)
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Realizing All so(N)1 Quantum Criticalities in Symmetry Protected Cluster Models
- 2015
-
Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 115:23
-
Tidskriftsartikel (refereegranskat)abstract
- We show that all so(N)(1) universality class quantum criticalities emerge when one-dimensional generalized cluster models are perturbed with Ising or Zeeman terms. Each critical point is described by a low-energy theory of N linearly dispersing fermions, whose spectrum we show to precisely match the prediction by so(N)(1) conformal field theory. Furthermore, by an explicit construction we show that all the cluster models are dual to nonlocally coupled transverse field Ising chains, with the universality of the so(N)(1) criticality manifesting itself as N of these chains becoming critical. This duality also reveals that the symmetry protection of cluster models arises from the underlying Ising symmetries and it enables the identification of local representations for the primary fields of the so(N)(1) conformal field theories. For the simplest and experimentally most realistic case that corresponds to the original one-dimensional cluster model with local three-spin interactions, our results show that the su(2)(2) similar or equal to so(3)(1) Wess-Zumino-Witten model can emerge in a local, translationally invariant, and Jordan-Wigner solvable spin-1/2 model.
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| 13. |
- Mahyaeh, Iman
(författare)
-
Edge Modes of Zn Symmetric Chains
- 2017
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this Licentiate Thesis we will study the topological phases of Z2 and Z3 symmetric chains. We will present the Kitaev chain, a Z2 symmetric model of spinless fermions, and obtain all the eigenstates of the model with an open boundary condition which hosts Majorana zero modes in the topological phase. We will also present zero modes of the Kitaev chain with phase gradient in the pairing term and longer range couplings. This model could host Majorana zero modes as well as a 'one-sided' zero energy fermionic state. We will study the role of interactions on the topological phase by considering a special model for which one can obtain the ground states exactly. Similarly, for the Z3 case, we will present a 3-state clock model as well as a solvable model for which the ground states are obtained exactly. We will briefly address the presence of edge modes in these models as well.
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| 14. |
- Mahyaeh, Iman, et al.
(författare)
-
Exact results for a Z(3)-clock-type model and some close relatives
- 2018
-
Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 98:24
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we generalized the Peschel-Emery line of the interacting transverse field Ising model to a model based on three-state clock variables. Along this line, the model has exactly degenerate ground states, which can be written as product states. In addition, we present operators that transform these ground states into each other. Such operators are also presented for the Peschel-Emery case. We numerically show that the generalized model is gapped. Furthermore, we study the spin-S generalization of interacting Ising model and show that along a Peschel-Emery line they also have degenerate ground states. We discuss some examples of excited states that can be obtained exactly for all these models.
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| 15. |
- Mahyaeh, Iman, et al.
(författare)
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Study of the phase diagram of the Kitaev-Hubbard chain
- 2020
-
Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 101:8
-
Tidskriftsartikel (refereegranskat)abstract
- We present a detailed study of the phase diagram of the Kitaev-Hubbard chain, that is the Kitaev chain in the presence of a nearest-neighbor density-density interaction, using both analytical techniques as well as DMRG. In the case of a moderate attractive interaction, the model has the same phases as the noninteracting chain, a trivial and a topological phase. For repulsive interactions, the phase diagram is more interesting. Apart from the previously observed topological, incommensurate, and charge density wave phases, we identify the excited state charge density wave phase. In this phase, the ground state resembles an excited state of an ordinary charge density phase, but is lower in energy due to the frustrated nature of the model. We find that the dynamical critical exponent takes the value z similar or equal to 1.8. Interestingly, this phase only appears for even system sizes, and is sensitive to the chemical potential on the edges of the chain. For the topological phase, we present an argument that excludes the presence of a strong zero mode for a large part of the topological phase. For the remaining region, we study the time dependence of the edge magnetization (using the bosonic incarnation of the model). These results further expand the region where a strong zero mode does not occur.
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| 16. |
- Mahyaeh, Iman, 1990-
(författare)
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Study of the phase diagram of Zn symmetric chains
- 2020
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study the phase diagrams of Zn symmetric chains. We start with investigating the topological phases of the Kitaev chain, a Z2 symmetric model, with long range couplings and a phase gradient. Then we go beyond the free fermion classification of topological phases and consider the effect of interactions by studying the Kitaev-Hubbard chain, incorporating a density-density interaction. Next we move on to the Z3 symmetric models and present a frustration free model with an exact three-fold degenerate ground state. In the end we present the phase diagram of a hopping model of Z3 Fock parafermions, the generalization of polarized Dirac fermions which could host at most two particles per site. The model has a pairwise hopping which is forbidden for fermions. In our studies we use analytical methods like the Lieb-Schultz-Mattis method, bosonization and conformal field theory, as well as numerical ones like exact diagonalization and the density matrix renormalization group.
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| 17. |
- Mahyaeh, Iman, et al.
(författare)
-
Zero modes of the Kitaev chain with phase-gradients and longer range couplings
- 2018
-
Ingår i: Journal of Physics Communications. - : IOP Publishing. - 2399-6528. ; 2:4
-
Tidskriftsartikel (refereegranskat)abstract
- We present an analytical solution for the full spectrum of Kitaev's one-dimensional p-wave superconductor with arbitrary hopping, pairing amplitude and chemical potential in the case of an open chain. We also discuss the structure of the zero-modes in the presence of both phase gradients and next nearest neighbor hopping and pairing terms. As observed by Sticlet et al, one feature of such models is that in a part of the phase diagram, zero-modes are present at one end of the system, while there are none on the other side. We explain the presence of this feature analytically, and show that it requires some fine-tuning of the parameters in the model. Thus as expected, these 'one-sided' zero-modes are neither protected by topology, nor by symmetry.
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| 18. |
- Majidzadeh Garjani, Babak, 1973-, et al.
(författare)
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Anyon chains with pairing terms
- 2017
-
Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 50:13
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce a one-dimensional model of $su(2)_k$ anyons in which the number of anyons can uctuate by means of a pairing term. The model can be tuned to a point at which one can determine the exact zero-energy ground states, in close analogy to the spin-1 AKLT model. We also determine the points at which the model is integrable and determine the behavior of the model at these integrable points.
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| 19. |
- Majidzadeh Garjani, Babak, 1973-
(författare)
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On Aspects of Anyons and Quantum Graphs
- 2017
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of two distinct parts. The first part, based on the first two accompanied papers, is in the field of topological phases of matter and the second part, based on the third accompanied paper, looks at a problem in the field of quantum graphs, a rapidly growing field of mathematical physics.First, we investigate the entanglement property of the Laughlin state by looking at the rank of the reduced density operator when particles are divided into two groups. We show that the problem of determining this rank translates itself into a question about symmetric polynomials, namely, one has to determine the lower bound for the degree in each variable of the symmetric polynomials that vanish under a transformation that clusters the particles into groups of equal size and then brings the particles in each group together. Although we were not able to prove this, but we were able to determine the lower bound for the total degree of symmetric polynomials that vanish under the transformation described. Moreover, we were able to characterize all symmetric polynomials that vanish under this transformation.In the second paper, we introduce a one-dimensional model of interacting su(2)k anyons. The specific feature of this model is that, through pairing terms present in the Hamiltonian, the number of anyons of the chain can fluctuate. We also take into account the possibility that anyons hop to empty neighboring sites. We investigate the model in five different points of the parameter space. At one of these points, the Hamiltonian of the model becomes a sum of projectors and we determine the explicit form of all the zero-energy ground states for odd values of k. At the other four points, the system is integrable and we determine the behavior of the model at these integrable points. In particular, we show that the system is critical and determine the CFT describing the system at these points.It is known that there are non-Hermitian Hamiltonians whose spectra are entirely real. This property can be understood in terms of a certain symmetry of these Hamiltonians, known as PT-symmetry. It is also known that the spectrum of a non-Hermitian PT-symmetric Hamiltonian has reflection symmetry with respect to the real axis. We then ask the reverse question whether or not the reflection symmetry of a non-Hermitian Hamiltonian necessarily implies that the Hamiltonian is PT-symmetric. In the context of quantum graphs, we introduce a model for which the answer to this question is positive.
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| 20. |
- Majidzadeh Garjani, Babak, et al.
(författare)
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On the particle entanglement spectrum of the Laughlin states
- 2015
-
Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 48:28
-
Tidskriftsartikel (refereegranskat)abstract
- The study of the entanglement entropy and entanglement spectrum has proven to be very fruitful in identifying topological phases of matter. Typically, one performs numerical studies of finite-size systems. However, there are few rigorous results in this regard. We revisit the problem of determining the rank of the 'particle entanglement spectrum' (PES) of the Laughlin states. We reformulate the problem into a problem concerning the ideal of symmetric polynomials that vanish under the formation of several clusters of particles. We introduce an explicit generating set of this ideal, and we prove that polynomials in this ideal have a total degree that is bounded from below. We discuss the difficulty in proving the same bound on the degree of any of the variables, which is necessary to determine the rank of the PES.
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| 21. |
- Moosavi, Per
(författare)
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Interacting fermions and non-equilibrium properties of one-dimensional many-body systems
- 2016
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recent experimental progress on ultracold atomic gases have opened up the possibility to simulate many-body systems out of equilibrium. We consider such a system described by the Luttinger model, which is a model of interacting fermions in one spatial dimension.It is well known that the Luttinger model is exactly solvable using bosonization. This also remains true for certain extensions of the model, e.g., where, in addition, the fermions are coupled to phonons. We give a self-contained account of bosonization, together with complete proofs, and show how this can be used to solve the Luttinger model and the above fermion-phonon model rigorously.The main focus is on non-equilibrium properties of the Luttinger model. We use the exact solution of the Luttinger model, with non-local interactions, to study the evolution starting from a non-uniform initial state with a position-dependent chemical potential. The system is shown to reach a current-carrying final steady state, in which the universal value of the electrical conductance, known from near-to-equilibrium settings, is recovered. We also study the effects of suddenly changing the interactions and show that the final state has memory of the initial state, which is, e.g., manifested by non- equilibrium exponents in its fermion two-point correlation functions.
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| 22. |
- Månsson, Teresia, et al.
(författare)
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Condensate-induced transitions and critical spin chains
- 2013
-
Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:4, s. 041403-
-
Tidskriftsartikel (refereegranskat)abstract
- We show that condensate-induced transitions between two-dimensional topological phases provide a general framework to relate one-dimensional spin models at their critical points. We demonstrate this using two examples. First, we show that two well-known spin chains, namely, the XY chain and the transverse field Ising chain with only next-nearest-neighbor interactions, differ at their critical points only by a nonlocal boundary term and can be related via an exact mapping. The boundary term constrains the set of possible boundary conditions of the transverse field Ising chain, reducing the number of primary fields in the conformal field theory that describes its critical behavior. We argue that the reduction of the field content is equivalent to the confinement of a set of primary fields, in precise analogy to the confinement of quasiparticles resulting from a condensation of a boson in a topological phase. As the second example we show that when a similar confining boundary term is applied to the XY chain with only next-nearest-neighbor interactions, the resulting system can be mapped to a local spin chain with the u(1)(2) x u(1)(2) critical behavior predicted by the condensation framework.
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| 23. |
- Nardin, Alberto, et al.
(författare)
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Spin-statistics relation for quantum Hall states
- 2023
-
Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 108:4
-
Tidskriftsartikel (refereegranskat)abstract
- We prove a generic spin-statistics relation for the fractional quasiparticles that appear in Abelian quantum Hall states on the disk. The proof is based on an efficient way for computing the Berry phase acquired by a generic quasiparticle translated in the plane along a circular path, and on the crucial fact that once the gauge-invariant generator of rotations is projected onto a Landau level, it fractionalizes among the quasiparticles and the edge. Using these results we define a measurable quasiparticle fractional spin that satisfies the spin-statistics relation. As an application, we predict the value of the spin of the composite-fermion quasielectron proposed by Jain; our numerical simulations agree with that value. We also show that Laughlin's quasielectrons satisfy the spin-statistics relation, but carry the wrong spin to be the antianyons of Laughlin's quasiholes. We continue by highlighting the fact that the statistical angle between two quasiparticles can be obtained by measuring the angular momentum while merging the two quasiparticles. Finally, we show that our arguments carry over to the non-Abelian case by discussing explicitly the Moore-Read wave function.
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| 24. |
- Niemi, Antti, et al.
(författare)
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Nobel Symposium 148 : Graphene and quantum matter
- 2012
-
Ingår i: Physica scripta. T. - 0281-1847. ; :T146
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- The 2010 Nobel Symposium on Graphene and Quantum Matter, was held at the Grand Hotel in Saltsjöbaden south of Stockholm on 27-31 May. The main theme of the meeting was graphene, and the symposium turned out to be very timely: two of the participants, Andre Geim and Kanstantin Novoselov returned to Stockholm less then six months later to receive the 2010 Nobel Prize in Physics. In these proceedings leading experts give up-to-date, historical, experimental, theoretical and technological perspectives on the remarkable material graphene, and several papers also make connections to other states of quantum matter. Saltsjöbaden is beautifully situated in the inner archipelago of Stockholm. It provided a pleasant setting for the talks and the ensuing discussions that took place in an enthusiastic and friendly atmosphere. The social programme included a boat trip in the light summer night and a dinner at the renowned Grand Hotel. These proceedings are ordered thematically, starting with historical overviews, followed by first experimental and then theoretical papers on the physics of graphene. Next are several papers addressing more general topics in quantum matter and finally contributions on the technological applications of graphene. We hope that this volume will serve as a source of knowledge and inspiration for any physicist interested in graphene, and at the same time provide a snapshot of a young field of research that is developing at very high speed. We are grateful to Marja Fahlander for excellent administrative support, and to the Nobel Foundation who funded the symposium.
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| 25. |
- Nissinen, Jaakko, et al.
(författare)
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Local height probabilities in a composite Andrews-Baxter-Forrester model
- 2012
-
Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 45:43, s. 435001-
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Tidskriftsartikel (refereegranskat)abstract
- We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two- and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behavior of the composite height model, the critical behavior of the anyonic chains is established as well. Depending on the overall sign of the Hamiltonian, this critical behavior is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.
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