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DOE OSTI · 2422068

Extracting the Quantum Hall Conductance from a Single Bulk Wave Function

Fan, Ruihua·Sahay, Rahul·Vishwanath, Ashvin
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Abstract

In this work, we propose a new formula that extracts the quantum Hall conductance from a single (2+1)⁢ D gapped wave function. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow, i.e., unitary dynamics generated from the entanglement structure of the wave function. The formula is shown to satisfy all formal properties of the Hall conductance: it is odd under time reversal and reflection, even under charge conjugation, universal and topologically rigid in the thermodynamic limit. Further evidence for relating the formula to the Hall conductance is obtained from conformal field theory arguments. Finally, we numerically check the formula by applying it to a noninteracting Chern band where excellent agreement is obtained.

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2-dimensional systems75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITYConformal field theoryLattice models in condensed matterPhysicsQuantum Hall effectQuantum entanglementQuantum many-body systemsStrongly correlated systemsSymmetries in condensed matterTopological materialsTopological phases of matter

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Fan, Ruihua, Sahay, Rahul, Vishwanath, Ashvin. 2023-11-01. Extracting the Quantum Hall Conductance from a Single Bulk Wave Function. https://doi.org/10.1103/physrevlett.131.186301

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