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Reviving the Lieb-Schultz-Mattis theorem in open quantum systems.

Yi-Neng Zhou1, Xingyu Li1, Hui Zhai1,2

  • 1Institute for Advanced Study, Tsinghua University, Beijing 100084, China.

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Summary
This summary is machine-generated.

The Lieb-Schultz-Mattis (LSM) theorem

Keywords:
Lieb–Schultz–Mattis theorementanglement Hamiltonianopen quantum system

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory

Background:

  • The Lieb-Schultz-Mattis (LSM) theorem prohibits non-degenerate gapped ground states in 1D half-integer spin chains.
  • System interaction with a bath can break energy conservation, limiting the theorem's applicability.

Purpose of the Study:

  • To investigate the revival of the LSM theorem in entanglement Hamiltonians for open quantum systems.
  • To explore the role of short-range correlations induced by bath coupling.

Main Methods:

  • Theoretical analysis of entanglement Hamiltonians in open quantum systems.
  • Numerical simulations of a spin-1/2 system coupled to a spin-1/2 bath.

Main Results:

  • The LSM theorem can be revived in the entanglement Hamiltonian for short-range correlated systems.
  • Entanglement spectra in these systems cannot possess a non-degenerate, gapped minimum.
  • UV data and topological constraints significantly influence entanglement in open systems.

Conclusions:

  • The study extends the applicability of the LSM theorem to open quantum many-body systems.
  • Entanglement properties are shaped by both UV data and topological constraints, not just UV-IR correspondence.