Chiral central charge from a single bulk wave function

TL;DR

This paper derives a formula linking the chiral central charge of a 2+1D gapped quantum system to its bulk ground state wave function, revealing topological obstructions related to chirality.

Contribution

It provides a novel bulk wave function-based formula for the chiral central charge, connecting edge properties to bulk wave function characteristics.

Findings

Nonzero chiral central charge causes a topological obstruction to real-valued ground states.

The formula is analogous to topological entanglement entropy, but for chiral central charge.

Ground state wave functions encode information about edge chiral properties.

Abstract

A $(2+1)$-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity associated with the effective field theory of the edge. We derive a formula for the chiral central charge that, akin to the topological entanglement entropy, is completely determined by the many-body ground state wave function in the bulk. According to our formula, nonzero chiral central charge gives rise to a topological obstruction that prevents the ground state wave function from being real-valued in any local product basis.