Thermal transport, geometry, and anomalies

Abstract

The relation between thermal transport and gravity was highlighted in the seminal work by Luttinger in 1964, and has been extensively developed to understand thermal transport, most notably the thermal Hall effect. Here we review the novel concepts that relate thermal transport, the geometry of space-time and quantum field theory anomalies. We give emphasis to the cross-pollination between emergent ideas in condensed matter, notably Weyl and Dirac semimetals, and the understanding of gravitational and scale anomalies stemming from high-energy physics. We finish by relating to recent experimental advances and presenting a perspective of several open problems.

68 pages, 13 figures; comments welcome!

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Cited by in corpus (42)

• New developments in relativistic magnetohydrodynamics
• Revealing Quantum Geometry in Nonlinear Quantum Materials
• Nonlinear magnetoconductivity in Weyl and multi-Weyl semimetal in quantizing magnetic field
• Quantum Field Theory Anomalies in Condensed Matter Physics
• Quantum kinetic theory of nonlinear thermal current
• Partitioning Dense Graphs with Hardware Accelerators
• Effective electromagnetic actions for Lorentz violating theories exhibiting the axial anomaly
• Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity
• Nonlinear magnetotransport in Weyl semimetal
• Lorentz invariance violation and the CPT-odd electromagnetic response of a tilted anisotropic Weyl semimetal
• Parity-Odd 3-Point Functions from CFT in Momentum Space and the Chiral Anomaly
• Torsion-induced chiral magnetic current in equilibrium
• Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
• Gravitational anomaly in the ferrimagnetic topological Weyl semimetal NdAlSi
• Chiral Anomaly in Euler Fluid and Beltrami Flow
• Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ
• Aharonov-Bohm electrodynamics in material media: a scalar e.m. field cannot cause dissipation in a medium
• Dynamical chiral magnetic current and instability in Weyl semimetals
• Coherent Plasma in a Lattice
• Intrinsic Spin Nernst Effect and Chiral Edge Modes in van der Waals Ferromagnetic Insulators: Dzyaloshinskii-Moriya vs. Kitaev Interactions
• Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches
• Chiral anomalies in black hole spacetimes
• Effective lagrangian for the macroscopic motion of fermionic matter
• Chiral current induced by torsional Weyl anomaly
• Unconventional thermoelectric transport in tilted Weyl semimetals
• Gravito-thermal transports, Onsager reciprocal relation and gravitational Wiedemann-Franz law
• Thermal and thermoelectric transport in flat bands with non-trivial quantum geometry
• Helical Separation Effect and helical heat transport for Dirac fermions
• Quantum transport phenomena induced by time-dependent fields
• Strain-induced collapse of Landau Levels in real Weyl semimetals
• Non-Hermitian chiral anomalies in interacting systems
• Quantum Field Theory and its Anomalies for Topological Matter
• Linear response in a charged gas in curved spacetime and covariant heat equation
• Study on axial fields in the dynamically assisted Schwinger effect
• Dirac Electrons in AC-Magnetic Fields: $\pi$-Landau Levels and Chiral Anomaly-Induced Homodyne Effect
• Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations
• Searching for quantum non-thermodynamic phenomena
• Gravitational coupling of QED and QCD: 3- and 4- point functions in momentum space
• Conformal anomaly transport induced by dark photon
• Thermal response of the Nieh-Yan term