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Finite-temperature transport in one-dimensional quantum lattice models
Bertini, Bruno (Author), Heidrich-Meisner, Fabian (Author), Karrasch, Christoph (Author), Prosen, Tomaž (Author), Steinigeweg, R. (Author), Žnidarič, Marko (Author)

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Abstract
Over the last decade impressive progress has been made in the theoretical understanding of transport properties of clean, one-dimensional quantum lattice systems. Many physically relevant models in one dimension are Bethe-ansatz integrable, including the anisotropic spin-1/2 Heisenberg (also called the spin-1/2 XXZ chain) and the Fermi-Hubbard model. Nevertheless, practical computations of correlation functions and transport coefficients pose hard problems from both the conceptual and technical points of view. Only because of recent progress in the theory of integrable systems, on the one hand, and the development of numerical methods, on the other hand, has it become possible to compute their finite-temperature and nonequilibrium transport properties quantitatively. Owing to the discovery of a novel class of quasilocal conserved quantities, there is now a qualitative understanding of the origin of ballistic finite-temperature transport, and even diffusive or superdiffusive subleading corrections, in integrable lattice models. The current understanding of transport in one-dimensional lattice models, in particular, in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, is reviewed, as well as state-of-the-art theoretical methods, including both analytical and computational approaches. Among other novel techniques, matrix-product-state-based simulation methods, dynamical typicality, and, in particular, generalized hydrodynamics are covered. The close and fruitful connection between theoretical models and recent experiments is discussed, with examples given from the realms of both quantum magnets and ultracold quantum gases in optical lattices.

Language:English
Keywords:condensed matter physics, quantum mechanics, quantum transport
Work type:Article (dk_c)
Tipology:1.02 - Review Article
Organization:FMF - Faculty of Mathematics and Physics
Year:2021
Number of pages:Str. 025003-1-025003-71
Numbering:Vol. 93, iss. 2
UDC:530.145
ISSN on article:0034-6861
DOI:10.1103/RevModPhys.93.025003 This link opens in a new window
COBISS.SI-ID:62716675 This link opens in a new window
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Record is a part of a journal

Title:Reviews of modern physics
Shortened title:Rev. mod. phys.
Publisher:American Physical Society
ISSN:0034-6861
COBISS.SI-ID:26281984 This link opens in a new window

Document is financed by a project

Funder:EC - European Commission
Funding Programme:H2020
Project no.:694544
Name:Open Many-body Non-Equilibrium Systems
Acronym:OMNES

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:P1-0402
Name:Matematična fizika

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:J1-7279
Name:Termodinamika disipativnih nanosistemov

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:J1-1698
Name:Načrtovanje večdelčnega transporta

Secondary language

Language:Slovenian
Keywords:fizika kondenzirane snovi, kvantna mehanika, kvantni transport

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