| 1. |
- Ahari, Mostafa Tanhayi, et al.
(författare)
-
Partons as unique ground states of quantum Hall parent Hamiltonians : The case of Fibonacci anyons
- 2023
-
Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 15:2
-
Tidskriftsartikel (refereegranskat)abstract
- We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor ν = 2/3. The emergent Entangled Pauli Principle (EPP), introduced in Phys. Rev. B 98, 161118(R) (2018) and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body M-clustering property within any given number of Landau levels, that is, wave functions with Mth-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the M = 3 case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of Phys. Rev. X 1, 021015 (2011) to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.
|
|
| 2. |
- Baiguera, Stefano, et al.
(författare)
-
Conformal Carroll scalars with boosts
- 2023
-
Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 14:4
-
Tidskriftsartikel (refereegranskat)abstract
- We construct two distinct actions for scalar fields that are invariant under local Carroll boosts and Weyl transformations. Conformal Carroll field theories were recently argued to be related to the celestial holography description of asymptotically flat spacetimes. However, only few explicit examples of such theories are known, and they lack local Carroll boost symmetry on a generic curved background. We derive two types of conformal Carroll scalar actions with boost symmetry on a curved background in any dimension and compute their energy-momentum tensors, which are traceless. In the first type of theories, time derivatives dominate and spatial derivatives are suppressed. In the second type, spatial derivatives dominate, and constraints are present to ensure local boost invariance. By integrating out these constraints, we show that the spatial conformal Carroll theories can be reduced to lower-dimensional Euclidean CFTs, which is reminiscent of the embedding space construction.
|
|
| 3. |
- Bhardwaj, Lakshya, et al.
(författare)
-
Non-invertible higher-categorical symmetries
- 2023
-
Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 14:1
-
Tidskriftsartikel (refereegranskat)abstract
- We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also discuss fusions of topological defects, which involve condensations/gaugings of higher-categorical symmetries localized on the worldvolumes of topological defects. Recently some fusions of topological defects were discussed in the literature where the dimension of topological defects seems to jump under fusion. This is not possible in the standard description of higher-categories. We explain that the dimension-changing fusions are understood as higher-morphisms of the higher-category describing the symmetry. We also discuss how a 0-form sub-symmetry of a higher-categorical symmetry can be gauged and describe the higher-categorical symmetry of the theory obtained after gauging. This provides a procedure for constructing non-invertible higher-categorical symmetries starting from invertible higher-form or higher-group symmetries and gauging a 0-form symmetry. We illustrate this procedure by constructing non-invertible 2-categorical symmetries in 4d gauge theories and non-invertible 3-categorical symmetries in 5d and 6d theories. We check some of the results obtained using our approach against the results obtained using a recently proposed approach based on’t Hooft anomalies.
|
|
| 4. |
- Bhardwaj, Lakshya, et al.
(författare)
-
Non-invertible symmetry webs
- 2023
-
Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 15:4
-
Tidskriftsartikel (refereegranskat)abstract
- Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with G 0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [1]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups G, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions.
|
|
| 5. |
- Bhardwaj, Lakshya, et al.
(författare)
-
Unifying constructions of non-invertible symmetries
- 2023
-
Ingår i: SciPost Physics. - : SciPost Foundation. - 2542-4653. ; 15:3
-
Tidskriftsartikel (refereegranskat)abstract
- In the past year several constructions of non-invertible symmetries in Quantum Field Theory in d ≥ 3 have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta defects, which generalize the notion of theta-angles, and allow the construction of universal and non-universal topological symmetry defects. We complement this physical analysis by proposing a mathematical framework (based on higher-fusion categories) that converts the physical construction of non-invertible symmetries into a concrete computational scheme.
|
|
| 6. |
- Bissi, Agnese, et al.
(författare)
-
Positivity, low twist dominance and CSDR for CFTs
- 2023
-
Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 14:4
-
Tidskriftsartikel (refereegranskat)abstract
- We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correla-tion with identical scalar operators, which is manifestly symmetric under the cross-ratios u, v interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around u = v = 1/4, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of phi 1,2 operators in 2d minimal models as a test-bed. When 1 the dimension of the external scalar operator ( increment sigma) is less than 2 , the CSDR gets con-tribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of increment sigma, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in 4 - epsilon dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.
|
|
| 7. |
- Bramberger, Max, et al.
(författare)
-
Formation of CuO2 sublattices by suppression of interlattice correlations in tetragonal CuO
- 2023
-
Ingår i: SciPost Physics. - 2542-4653. ; 14:1
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate the tetragonal phase of the binary transition metal oxide CuO (t-CuO) within the context of cellular dynamical mean-field theory. Due to its strong antiferromagnetic correlations and simple structure, analysing the physics of t-CuO is of high interest as it may pave the way towards a more complete understanding of high-temperature superconductivity in hole-doped antiferromagnets. In this work we give a formal justification for the weak-coupling assumption that has previously been made for the interconnected sublattices within a single layer of t-CuO by studying the non-local self-energies of the system. We compute momentum-resolved spectral functions using a Matrix Product State (MPS)-based impurity solver directly on the real axis, which does not require any numerically ill-conditioned analytic continuation. The agreement with photoemission spectroscopy indicates that a single-band Hubbard model is sufficient to capture the material’s low energy physics. We perform calculations on a range of different temperatures, finding two magnetic regimes, for which we identify the driving mechanism behind their respective insulating state. Finally, we show that in the hole-doped regime the sublattice structure of t-CuO has interesting consequences on the symmetry of the superconducting state.
|
|
| 8. |
- Datta, Shouvik, et al.
(författare)
-
Marginal quenches and drives in Tomonaga-Luttinger liquids
- 2023
-
Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 14:5
-
Tidskriftsartikel (refereegranskat)abstract
- We study Tomonaga-Luttinger liquids thrown out of equilibrium by marginal deformations in the form of interaction modulations. This is modeled by quenching or periodically driving the Luttinger parameter or, equivalently, the compactification radius of the free boson conformal field theory between two different values. We obtain exact analytical results for the evolution of the Loschmidt echo and observables such as the particle and energy densities. Starting from generic initial states, the quench dynamics are shown to exhibit revivals and temporal orthogonalities. For the periodic drive, we show stability or instability of time-evolved physical quantities dependent on the drive parameters. We also compare the corresponding marginally deformed thermal density matrices by non-perturbatively evaluating their Rényi divergence as a Euclidean quench. All the dynamics are shown to be crucially dependent on the ratio of the Luttinger parameters, which corresponds to the Zamolodchikov distance in the space of marginal deformations. Our setup is equivalently interpreted as the dynamics of the bosonic string upon instantaneous changes of the target-space radius.
|
|
| 9. |
- Day, Isidora Araya, et al.
(författare)
-
Pfaffian invariant identifies magnetic obstructed atomic insulators
- 2023
-
Ingår i: SciPost Physics. - 2542-4653. ; 15:3
-
Tidskriftsartikel (refereegranskat)abstract
- We derive a Z4 topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a C4T symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four C4T-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a C4T-symmetric model that interpolates between them. The phase diagram shows that C4T insulators allow ±1 and 2 changes of the invariant, where the latter is overlooked by symmetry indicators.
|
|
| 10. |
- Del Monte, Fabrizio, et al.
(författare)
-
The threefold way to quantum periods : WKB, TBA equations and q-Painlevé
- 2023
-
Ingår i: SciPost Physics. - : SCIPOST FOUNDATION. - 2542-4653. ; 15:3
-
Tidskriftsartikel (refereegranskat)abstract
- We show that TBA equations defined by the BPS spectrum of 5d N = 1 SU(2) Yang-Mills on S1 x R4 encode the q-Painleve III3 equation. We find a fine-tuned stratum in the physical moduli space of the theory where solutions to TBA equations can be obtained exactly, and verify that they agree with the algebraic solutions to q-Painleve. Switching from the physical moduli space to that of stability conditions, we identify two one-parameter deformations of the fine-tuned stratum, where the general solution of the q-Painleve equation in terms of dual instanton partition functions continues to provide explicit TBA solutions. Motivated by these observations, we propose a further extensions of the range of validity of this correspondence, under a suitable identification of moduli. As further checks of our proposal, we study the behavior of exact WKB quantum periods for the quantum curve of local P1 x P1.
|
|
