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Related Experiment Video

Updated: May 7, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: June 8, 2018

Many-Body Systems with Spurious Modular Commutators.

Julian Gass¹, Michael Levin¹

¹Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA.

Physical Review Letters

|January 3, 2025

Summary

The chiral central charge is not always proportional to the modular commutator in quantum systems. This study demonstrates lattice systems with zero chiral charge exhibit non-zero modular commutators, challenging universality claims.

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Area of Science:

Condensed Matter Physics
Quantum Information Theory
Many-Body Systems

Background:

A proposed relationship links the chiral central charge of gapped 2D quantum systems to the modular commutator, a bulk entanglement measure.
This connection is supported by significant evidence, suggesting a universal link between topological order and entanglement properties.

Purpose of the Study:

To investigate the universality of the proposed relationship between chiral central charge and the modular commutator.
To identify potential counterexamples or limitations to this proposed universal relationship in quantum many-body systems.

Main Methods:

Analysis of lattice quantum many-body systems in one and two dimensions.
Construction of examples utilizing cluster states.
Exploitation of the nonlocal nature of modular Hamiltonians generated by cluster states.

Main Results:

Demonstrated that the relationship between chiral central charge and modular commutator is not universal.
Presented lattice systems with vanishing chiral central charge that yield nonzero 'spurious' modular commutator values.
These findings hold for arbitrarily large system sizes in both one and two dimensions.

Conclusions:

The modular commutator is not a universally reliable measure for the chiral central charge in all gapped quantum systems.
The use of cluster states and nonlocal modular Hamiltonians provides a mechanism for generating these non-universal behaviors.
Further research is needed to understand the precise conditions under which the proposed relationship holds.