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Detecting Quantum Anomalies in Open Systems.

Yunlong Zang1, Yingfei Gu2, Shenghan Jiang1

  • 1<a href="https://ror.org/01kv3wg35">Kavli Institute for Theoretical Sciences</a>, <a href="https://ror.org/05qbk4x57">University of Chinese Academy of Sciences</a>, Beijing 100190, China.

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This summary is machine-generated.

This study reveals how quantum anomalies, specifically the mixed 't Hooft anomaly, can be detected in open quantum systems. Half-integer spin chains exhibit unique topological phenomena detectable through specific measurements.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • High Energy Physics

Background:

  • Symmetries and quantum anomalies are key to understanding quantum many-body systems.
  • Their application has been limited to closed quantum systems, excluding open systems described by density matrices.

Purpose of the Study:

  • To introduce a novel, experimentally feasible method for detecting quantum anomalies in open quantum systems.
  • To demonstrate that the mixed 't Hooft anomaly distinguishes between half-integer and integer spin chains in open systems.

Main Methods:

  • Utilizing measurements of exp(iθS_{tot}^{z}) as a function of θ for spin chains coupled to an environment.
  • Developing a lattice-level spacetime rotation for analysis.
  • Employing matrix product density operator and transfer matrix formalism.

Main Results:

  • The mixed 't Hooft anomaly between spin rotation and lattice translation symmetries provides distinct signatures for half-integer and integer spin chains.
  • Half-integer spin chains show a topological phenomenon analogous to 'level crossing' in closed systems.
  • Analytical and numerical methods confirm singular behavior of exp(iθS_{tot}^{z}) for half-integer spin chains.

Conclusions:

  • This work extends the discussion of quantum anomalies to open quantum systems.
  • It provides a framework for analyzing concepts like spectral flow and flux threading in systems without a Hamiltonian.
  • The findings offer a new avenue for probing quantum phenomena in realistic, open systems.