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Extracting the Quantum Hall Conductance from a Single Bulk Wave Function.

Ruihua Fan1, Rahul Sahay1, Ashvin Vishwanath1

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

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|November 17, 2023
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Summary
This summary is machine-generated.

We introduce a novel formula to calculate quantum Hall conductance using wave functions. This method, based on modular flow, works for many-body systems and aligns with theoretical predictions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Topological Phases of Matter

Background:

  • The quantum Hall effect (QHE) is a key phenomenon in condensed matter physics, observed in 2D electron systems subjected to strong magnetic fields.
  • Calculating QHE in complex many-body systems remains a challenge.
  • Topological properties of wave functions are crucial for understanding QHE.

Purpose of the Study:

  • To develop a new, general formula for extracting quantum Hall conductance.
  • To utilize the concept of modular flow, derived from entanglement structure, for this calculation.
  • To verify the formula's validity and applicability to various physical systems.

Main Methods:

  • Formulating a new analytical expression for quantum Hall conductance.
  • Employing modular flow, defined by unitary dynamics from entanglement, as the core principle.
  • Leveraging conformal field theory arguments for theoretical validation.
  • Numerical verification using a noninteracting Chern band model.

Main Results:

  • The proposed formula successfully extracts quantum Hall conductance from a single (2+1)D gapped wave function.
  • The formula satisfies key properties: odd under time reversal/reflection, even under charge conjugation.
  • Results demonstrate universality and topological rigidity in the thermodynamic limit.
  • Excellent agreement was achieved between the formula's predictions and numerical calculations.

Conclusions:

  • The new formula provides a powerful tool for calculating quantum Hall conductance in diverse systems.
  • Modular flow offers a robust framework for understanding topological invariants from wave function properties.
  • The findings bridge theoretical concepts with numerical simulations, advancing the study of topological phases.