Bruno Bertini (Author), F. Heidrich-Meisner (Author), C. Karrasch (Author), Tomaž Prosen (Author), R. Steinigeweg (Author), Marko Žnidarič (Author)

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.

Keywords

fizika kondenzirane snovi;kvantna mehanika;kvantni transport;condensed matter physics;quantum mechanics;quantum transport;

Data

Language: English
Year of publishing:
Typology: 1.02 - Review Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 530.145
COBISS: 62716675 Link will open in a new window
ISSN: 0034-6861
Views: 321
Downloads: 441
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Other data

Secondary language: Slovenian
Secondary keywords: fizika kondenzirane snovi;kvantna mehanika;kvantni transport;
Type (COBISS): Article
Pages: str. 025003-1-025003-71
Volume: ǂVol. ǂ93
Issue: ǂiss. ǂ2
Chronology: 2021
DOI: 10.1103/RevModPhys.93.025003
ID: 12887518