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)

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
• Typology: 1.02 - Review Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2021
• Number of pages: Str. 025003-1-025003-71
• Numbering: Vol. 93, iss. 2
• PID: 20.500.12556/RUL-126996
• UDC: 530.145
• ISSN on article: 0034-6861
• DOI: 10.1103/RevModPhys.93.025003
• COBISS.SI-ID: 62716675
• Publication date in RUL: 12.05.2021

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

Secondary language

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