# Absence of energy currents in an equilibrium state and chiral anomalies

## TL;DR

This paper proves that in equilibrium states of lattice and non-relativistic particle systems with finite-range interactions, both particle and energy currents vanish, impacting the understanding of chiral anomalies and conformal field theories.

## Contribution

It introduces an alternative proof for the vanishing of energy currents in equilibrium, extending Bloch's argument beyond particle currents.

## Key findings

- Energy currents vanish in equilibrium states of lattice systems.
- Energy currents vanish in equilibrium states of non-relativistic particles.
- 1D systems cannot flow to a CFT with unequal left and right central charges.

## 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.