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Entanglement Hamiltonians for Chiral Fermions with Zero Modes.
Israel Klich1, Diana Vaman1, Gabriel Wong1
1Department of Physics, University of Virginia, Box 400714, Charlottesville, Virginia 22904, USA.
Physical Review Letters
|January 18, 2018
Summary
Topological zero modes impact entanglement Hamiltonians and entropy for chiral fermions. The study derives exact expressions, revealing nonlocal contributions from zero modes to entanglement.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Topological Physics
Background:
- Entanglement entropy quantifies quantum correlations in many-body systems.
- Topological zero modes are unique states in topological phases of matter.
- Chiral fermions in (1+1) dimensions exhibit distinct topological properties.
Purpose of the Study:
- To investigate the influence of topological zero modes on entanglement Hamiltonians.
- To derive exact expressions for entanglement entropy in the presence of zero modes.
- To analyze the structure of entanglement Hamiltonians for free chiral fermions.
Main Methods:
- Utilizing Riemann-Hilbert solutions for exact calculations.
- Applying finite rank perturbation theory to analyze Hamiltonians.
- Examining systems with and without topological zero modes.
Main Results:
- Entanglement Hamiltonians are found to contain local and bilocal terms.
- A zero mode introduces an additional nonlocal contribution to the entanglement Hamiltonian.
- Exact expressions for this nonlocal term and the change in entanglement entropy are derived.
Conclusions:
- Topological zero modes significantly alter the nature of entanglement Hamiltonians.
- The presence of zero modes leads to nonlocal features in entanglement.
- This work provides a precise method for calculating entanglement properties in topological systems.
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