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How universal is the entanglement spectrum?

Anushya Chandran1, Vedika Khemani2, S L Sondhi2

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA and Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, Ontario N2L 2Y5, Canada.

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Summary

The ground state entanglement spectrum (ES) does not always reveal universal phase characteristics. The entanglement Hamiltonian can have quantum phase transitions, altering the ES and potentially misleading analysis of physical systems.

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Area of Science:

  • Quantum Information Theory
  • Condensed Matter Physics

Background:

  • The ground state entanglement spectrum (ES) is widely believed to display universal features indicative of a quantum phase.
  • This assumption is crucial for characterizing complex quantum systems.

Purpose of the Study:

  • To challenge the prevailing belief about the universality of the ground state entanglement spectrum.
  • To investigate the behavior of the entanglement Hamiltonian and its spectrum during quantum phase transitions.

Main Methods:

  • Analysis of the entanglement Hamiltonian's ground state and low-energy spectrum.
  • Investigation of quantum phase transitions within the entanglement Hamiltonian itself.

Main Results:

  • Demonstrated that the ground state entanglement spectrum (ES) does not generally exhibit universal phase characteristics.
  • Showed that the entanglement Hamiltonian can undergo quantum phase transitions.
  • These transitions cause singular changes in the ES, even when the physical system remains in the same phase.

Conclusions:

  • The low-energy ES and Rényi entropies can be misleading for broken symmetry systems.
  • The entanglement spectrum in quantum Hall systems contains less universal information than previously assumed.
  • Rethinking the interpretation of entanglement spectra for phase characterization is necessary.