Many-body systems with spurious modular commutators

TL;DR

This paper demonstrates that the proposed link between chiral central charge and the modular commutator in quantum many-body systems is not universal, providing counterexamples with nonzero modular commutator but zero chiral central charge.

Contribution

It introduces explicit lattice examples showing the modular commutator can be nonzero even when the chiral central charge is zero, challenging previous assumptions.

Findings

Counterexamples with zero chiral central charge and nonzero modular commutator

Examples based on cluster states generating nonlocal modular Hamiltonians

The modular commutator is not a universal indicator of chiral central charge

Abstract

Recently, it was proposed that the chiral central charge of a gapped, two-dimensional quantum many-body system is proportional to a bulk ground state entanglement measure known as the modular commutator. While there is significant evidence to support this relation, we show in this paper that it is not universal. We give examples of lattice systems that have vanishing chiral central charge which nevertheless give nonzero "spurious" values for the modular commutator for arbitrarily large system sizes, in both one and two dimensions. Our examples are based on cluster states and utilize the fact that they can generate nonlocal modular Hamiltonians.