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Researchers propose a new framework using entanglement Hamiltonians to find conserved quantities for generalized Gibbs ensembles (GGE). This non-Abelian GGE more accurately predicts relaxation in quantum systems like free fermions and hardcore bosons.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Relaxed quantum systems with conservation laws are often approximated by generalized Gibbs ensembles (GGE).
  • GGE incorporates conserved quantities that act as integrals of motion.
  • The origin and natural set of these conserved quantities remain an active area of research.

Purpose of the Study:

  • To propose a novel framework, the entanglement Hamiltonian superdensity matrix (EHSM), for deriving conserved quantities in GGE.
  • To demonstrate the framework's efficacy for models of free fermions.
  • To investigate the properties and predictive power of the derived conserved quantities.

Main Methods:

  • Drawing an analogy between eigenstate reduced density matrices and GGE.
  • Utilizing the entanglement Hamiltonian superdensity matrix (EHSM) framework.
  • Identifying conserved quantities as linear superpositions of eigenstate entanglement Hamiltonians.

Main Results:

  • A natural set of conserved quantities for GGE emerges from reduced density matrices within the EHSM framework.
  • Explicit demonstration for models mappable to free fermions.
  • The derived conserved quantities lead to a non-Abelian GGE for 1D free fermions and hardcore bosons.
  • The non-Abelian GGE shows improved accuracy in predicting the relaxation of fermion and boson bilinears compared to the conventional Abelian GGE.

Conclusions:

  • The EHSM framework provides a method for identifying relevant conserved quantities for GGE.
  • The non-Abelian GGE offers a more accurate description of relaxation dynamics in certain quantum systems.
  • Generalization of this framework may offer new numerical approaches for studying quantum integrability.