Extracting the Quantum Hall Conductance from a Single Bulk Wave Function

Journal Article · 01 November 2023 · Physical Review Letters

DOI: https://doi.org/10.1103/physrevlett.131.186301 · OSTI ID:2422068

Fan, Ruihua ^[1]; Sahay, Rahul  ^[2]; Vishwanath, Ashvin ^[2]

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1. Harvard University, Cambridge, MA (United States); OSTI
2. Harvard University, Cambridge, MA (United States)

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.

• Research Organization: Krell Institute, Ames, IA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); Simons Foundation; Defense Advanced Research Projects Agency (DARPA); Gordon and Betty Moore Foundation
• Grant/Contract Number: SC0022158
• OSTI ID: 2422068
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 18 Vol. 131; ISSN 0031-9007
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English