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We developed a new method to study quantum many-body systems, exploring thermalization and spectral properties of spin chains without direct time evolution simulations.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory
  • Computational Physics

Background:

  • Investigating spectral properties and thermalization in quantum many-body systems is computationally challenging.
  • Traditional methods often struggle with the exponential scaling of Hilbert space with system size.
  • Efficiently probing thermalization and density of states is crucial for understanding complex quantum phenomena.

Purpose of the Study:

  • To present a novel computational method combining matrix product operators and Chebyshev polynomial expansions.
  • To demonstrate the method's capability in exploring spectral properties of quantum many-body Hamiltonians.
  • To apply the method for probing thermalization and computing densities of states in large spin chains.

Main Methods:

  • Utilizing matrix product operator (MPO) techniques.
  • Employing Chebyshev polynomial expansions for spectral analysis.
  • Applying the combined method to Ising and PXP spin chains.

Main Results:

  • The method successfully probes thermalization in large spin chains without explicit time evolution.
  • Full and local densities of states were computed efficiently.
  • Findings for the non-integrable Ising chain corroborate thermalization for various initial states, extending previous simulation capabilities.

Conclusions:

  • The developed MPO-Chebyshev method offers a powerful approach for studying spectral properties and thermalization in quantum many-body systems.
  • This technique overcomes limitations of direct time-dependent simulations for large systems.
  • The results provide significant insights into the thermalization dynamics of spin chains.