Conformal field theory out of equilibrium: a review

By D. Bernard, B. Doyon. 2016

171 citations recorded by the source corpus.

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/27b08231e9378368d057c5a63bab94db4796c4f9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Pasquale Calabrese
2. B. Doyon
3. J. Cardy
4. M. Fagotti
5. F. Essler
6. J. Dubail
7. J. Caux
8. E. Tonni

In Statistical and Nonlinear Physics

1. Pasquale Calabrese
2. B. Doyon
3. J. Cardy
4. M. Fagotti
5. J. Caux
6. F. Essler
7. J. Dubail
8. T. Yoshimura

Citations in the corpus

• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases (2016, background): “5 Conclusion Inhomogeneous 1D quantum systems are difficult to tackle and this is motivating an enormous activity in order to provide exact results in some regimes, as for example the recently developed integrable hydrodynamics [49,50] (anticipated in [47]) which may have important ramifications int”
• Quantum quenches in 1  +  1 dimensional conformal field theories (2016, background): “1), where there are non-zero energy currents, or to the steady state currents set up by a non-zero temperature gradient (see [190] and [191]).”
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization (2016, background): “That requires consideration of a genuinely non-equilibrium situation, and we focus on the popular [20, 21, 22, 23, 24] geometry shown in Figure 1.”
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts (2016, background): “In particular, it provides striking results in the context of quantum transport far from equilibrium [10–17] (see also the review [18]).”
• Lecture notes on Generalised Hydrodynamics (2019, background): “In more general contexts it is sometimes referred to as the “partitioning protocol" [51–53], see the reviews [54, 55], as well as [56] for a more general discussion of transport in quantum models.”
• Emergent hydrodynamics in integrable quantum systems out of equilibrium (2016, background): “Similarly, one can show [28] (see Appendix A) that there exists a function gβ”
• The Quench Action (2016, background): “The link with outof-equilibrium conformal field theory (see the accompanying papers [159, 160]) and Luttinger physics (see [161]) could also be explored further.”
• Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, background): “144 A. De Luca, J. Viti, D. Bernard, and B. Doyon, Nonequilibrium thermal transport in the quantum Ising chain, Phys.”
• Introduction to ‘Quantum Integrability in Out of Equilibrium Systems’ (2016, background): “Bernard and Doyon [17] review the transport properties of conformal field theories both in one and higher dimensions.”