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Topologically Protected Negative Entanglement.

Wen-Tan Xue1, Ching Hua Lee1

  • 1Department of Physics, National University of Singapore, Singapore, 117542, Singapore.

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Summary
This summary is machine-generated.

Negative entanglement entropy in quantum systems arises from topological edge states in non-Hermitian settings. This study reveals robustly negative entanglement in gapped systems and a novel quadratic scaling in gapless systems due to non-Hermitian critical skin compression (nHCSC).

Keywords:
negative entanglement entropynon‐Hermitian physicstopological flat bandsunconventional entanglement scaling

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Area of Science:

  • Quantum Many-Body Physics
  • Topological Phases of Matter
  • Non-Hermitian Systems

Background:

  • Entanglement entropy characterizes quantum systems but is complex in non-Hermitian settings due to non-orthogonal eigenstates.
  • Previous work linked negative entanglement to gapless exceptional points.

Purpose of the Study:

  • Investigate the origin of negative entanglement entropy in non-Hermitian systems.
  • Explore entanglement behavior in gapped and gapless non-Hermitian systems, particularly flat-band edge states.
  • Introduce and analyze the novel non-Hermitian critical skin compression (nHCSC) mechanism.

Main Methods:

  • Analysis of free fermion systems with topologically protected edge states.
  • Theoretical investigation of entanglement scaling in 2D flat-band edge states.
  • Characterization of entanglement eigenstates and their properties across system cuts.

Main Results:

  • Negative biorthogonal entanglement generically arises from topologically protected non-orthogonal edge states.
  • Robustly negative entanglement is demonstrated in gapped systems, challenging prior assumptions.
  • Gapless 2D flat-band edge states exhibit a novel entanglement scaling of SA ~ -1/2 Ly2 log L due to nHCSC.
  • nHCSC involves a hierarchy of probability non-conserving entanglement eigenstates.

Conclusions:

  • Topological edge states are a key source of negative entanglement in non-Hermitian systems.
  • Negative entanglement is not limited to gapless systems with exceptional points.
  • nHCSC provides a new mechanism for understanding extreme negative entanglement scaling and its connection to topology and non-Hermitian localization.