Absence of energy currents in an equilibrium state and chiral anomalies

Abstract

A long time ago F. Bloch showed that in a system of interacting non-relativistic particles the net particle-number current must vanish in any equilibrium state. Bloch's argument does not generalize easily to the energy current. We devise an alternative argument which proves the vanishing of the net energy currents in equilibrium states of lattice systems as well as systems of non-relativistic particles with finite-range potential interactions. We discuss some applications of these results. In particular, we show that neither a 1d lattice system nor a 1d system of non-relativistic particles with finite-range potential interactions can flow to a Conformal Field Theory with unequal left-moving and right-moving central charges.

arXiv comment6 pages. Shortened and streamlined version published in Physical Review Letters

References in corpus (5)

• Anyons in an exactly solved model and beyond
• Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field
• Energy Magnetization and Thermal Hall Effect
• Non-equilibrium steady-states in conformal field theory
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• Collisionless dynamics of general non-Fermi liquids from hydrodynamics of emergent conserved quantities
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Microscopic formulas for thermoelectric transport coefficients in lattice systems
• Vanishing and non-vanishing persistent currents of various conserved quantities
• Nernst and Ettingshausen effects in gapped quantum materials
• Spatial Decay of Kubo's Canonical Correlation Function
• The Bloch theorem in the presence of an additional conserved charge
• Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering