| 1. |
- Bollmark, Gunnar, et al.
(författare)
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Solving 2D and 3D lattice models of correlated fermions : combining matrix product states with mean-field theory
- 2023
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Ingår i: Physical Review X. - : American Physical Society. - 2160-3308. ; 13:1
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Tidskriftsartikel (refereegranskat)abstract
- Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature Tc for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work, we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: two- and three-dimensional materials comprised of weakly coupled correlated 1D fermions. This MPS+MF framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute Tc for superconductivity in 3D arrays of weakly coupled, doped, and repulsive Hubbard ladders. The MPS+MF framework thus enables the quantitative study of USC and high-Tc superconductivity—and potentially many more correlated phases—in fermionic Q1D systems based directly on their microscopic parameters, in ways inaccessible to previous methods. This approach further allows one to treat competing macroscopic orders, such as superconducting and insulating ones, on an equal footing. Benchmarks of the framework using auxiliary-field quantum Monte Carlo techniques show that the overestimation of, e.g., Tc due to its mean-field component, is near constant in microscopic parameters. These features of the MPS+MF approach to correlated fermions open up the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.
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| 2. |
- Dolfi, Michele, et al.
(författare)
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Matrix Product State applications for the ALPS project
- 2014
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Ingår i: Computer Physics Communications. - : Elsevier BV. - 0010-4655 .- 1879-2944. ; 185:12, s. 3430-3440
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Tidskriftsartikel (refereegranskat)abstract
- The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as part of the ALPS package, that provide an efficient and flexible implementation of these methods based on a matrix product state (MPS) representation. Our applications implement, within the same framework, algorithms to variationally find the ground state and low-lying excited states as well as simulate the time evolution of arbitrary one-dimensional and two-dimensional models. Implementing the conservation of quantum numbers for generic Abelian symmetries, we achieve performance competitive with the best codes in the community. Example results are provided for (i) a model of itinerant fermions in one dimension and (ii) a model of quantum magnetism. PROGRAM SUMMARY Program title: ALPS MPS Catalogue identifier: AEUL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Use of ‘mps optim’, ‘mps tevol’, ‘mps meas’ or ‘mps overlap’ requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. No. of lines in distributed program, including test data, etc.: 373799 No. of bytes in distributed program, including test data, etc.: 2019043 Distribution format: tar.gz Programming language: C++, OpenMP for parallelization. Computer: PC, HPC cluster. Operating system: Any, tested on Linux, Mac OS X and Windows. Has the code been vectorized or parallelized?: Parallelized using OpenMP 1 to 24 processors used. RAM: 100 MB–100 GB. Classification: 7.7. External routines: ALPS [1, 2], BLAS/LAPACK, HDF5. Nature of problem: Solution of quantum many-body systems is generally a hard problem. The many-body Hilbert space grows exponentially with the system size which limits exact diagonalization results to only 20–40 spins, and the fermionic negative sign problem limits the Quantum Monte Carlo methods to a few special cases. Solution method: The matrix product states ansatz provides a controllable truncation of the Hilbert space which makes it currently the method of choice to investigate low-dimensional systems in condensed matter physics. Our implementation allows simulation of arbitrary one-dimensional and two-dimensional models and achieves performance competitive with the best codes in the community. We implement conservation of quantum numbers for generic Abelian symmetries. Running time: 10 s–8h per sweep. References: [1] B. Bauer, et al. (ALPS Collaboration), The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. 2011 (05) (2011) P05001. http://dx.doi.org/10.1088/1742-5468/2011/05/P05001. [2] http://alps.comp-phys.org.
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| 3. |
- Faure, Quentin, et al.
(författare)
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Tomonaga-Luttinger Liquid Spin Dynamics in the Quasi-One-Dimensional Ising-Like Antiferromagnet BaCo2V2O8
- 2019
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Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 123:2
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Tidskriftsartikel (refereegranskat)abstract
- Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo2V2O8 in a longitudinal magnetic field. This material shows a quantum phase transition from a Neel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.
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| 4. |
- Faure, Quentin, et al.
(författare)
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Topological quantum phase transition in the Ising-like antiferromagnetic spin chain BaCo2V2O8
- 2018
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Ingår i: Nature Physics. - : Nature Publishing Group. - 1745-2473 .- 1745-2481. ; 14:7, s. 716-722
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Tidskriftsartikel (refereegranskat)abstract
- Since the seminal ideas of Berezinskii, Kosterlitz and Thouless, topological excitations have been at the heart of our understanding of a whole novel class of phase transitions. In most cases, those transitions are controlled by a single type of topological objects. There are, however, some situations, still poorly understood, where two dual topological excitations fight to control the phase diagram and the transition. Finding experimental realizations of such cases is thus of considerable interest. We show here that this situation occurs in BaCo2V2O8, a spin-1/2 Ising-like quasi-one-dimensional antiferromagnet, when subjected to a uniform magnetic field transverse to the Ising axis. Using neutron scattering experiments, we measure a drastic modification of the quantum excitations beyond a critical value of the magnetic field. This quantum phase transition is identified, through a comparison with theoretical calculations, to be a transition between two different types of solitonic topological object, which are captured by different components of the dynamical structure factor.
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| 5. |
- Fukuhara, Takeshi, et al.
(författare)
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Quantum dynamics of a mobile spin impurity
- 2013
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Ingår i: Nature Physics. - : Nature Publishing Group. - 1745-2473 .- 1745-2481. ; 9:4, s. 235-241
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Tidskriftsartikel (refereegranskat)abstract
- One of the elementary processes in quantum magnetism is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, the quantum-coherent propagation of a magnetic excitation in the Heisenberg model can be observed using a post-selection technique. Extending the study to the superfluid regime of the bath, we quantitatively determine how the bath affects the motion of the impurity, showing evidence of polaronic behaviour. The experimental data agree with theoretical predictions, allowing us to determine the effect of temperature on the impurity motion. Our results provide a new approach to studying quantum magnetism, mobile impurities in quantum fluids and polarons in lattice systems.
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| 6. |
- Kamar, Naushad Ahmad, et al.
(författare)
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Dynamics of a mobile impurity in a two-leg bosonic ladder
- 2019
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : AMER PHYSICAL SOC. - 2469-9926 .- 2469-9934. ; 100:2
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the behavior of a mobile quantum impurity, restricted to a one-dimensional motion, in a bath formed by a two-leg bosonic ladder through a combination of field theory [Tomonaga-Luttinger liquid (TLL)] and numerical (density-matrix renormalization group) techniques. We compute the Green's function of the impurity as a function of time at different momenta. We find a power-law decay at zero momentum, which signals the breakdown of a quasiparticle description of the impurity motion. We compute the exponent both for the limits of weak and strong impurity-bath interactions. At small impurity-bath interaction, the impurity experiences the ladder as a single channel one-dimensional bath, but with an effective coupling reduced by a factor of root 2. We compare the numerical results for the exponent at zero momentum with a semianalytical expression, initially established for the chain, and find excellent agreement without adjustable parameters. We find an increase of the exponent with increasing transverse tunneling in the bath. At small tunneling, the exponent is compatible with the TLL prediction, while larger tunneling shows strong deviations. Finally, we show that, as a function of the momentum of the impurity, two different regimes of decay of the Green's function exist, similar to the single chain case. The power-law regime occurs for small momentum, while at large momentum the Green's function shows a faster decay, corresponding to the one expected in a polaronic regime. In this last regime, we compute the lifetime of the polaron numerically. We compute the critical momentum marking the transition between these two regimes. We compare with analytical predictions based on the structure factor of the bath and find good agreement with the numerical results. Finally, we discuss the consequences of our results for cold atomic experiments.
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| 7. |
- Knap, Michael, et al.
(författare)
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Probing Real-Space and Time-Resolved Correlation Functions with Many-Body Ramsey Interferometry
- 2013
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Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 111:14
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Tidskriftsartikel (refereegranskat)abstract
- We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.
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