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Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis.

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Area of Science:

  • Quantum Many-Body Physics
  • Statistical Mechanics

Background:

  • The eigenstate thermalization hypothesis (ETH) explains thermalization in isolated quantum systems.
  • Understanding systems that violate ETH is crucial for a complete picture of quantum thermodynamics.

Purpose of the Study:

  • To develop a general method for embedding target quantum states as energy eigenstates within the spectrum of a many-body Hamiltonian.
  • To construct and analyze a Hamiltonian that violates ETH for specific states but exhibits thermalization.

Main Methods:

  • Analytical derivation of a method to embed target states.
  • Construction of a translationally invariant, local Hamiltonian lacking local conserved quantities.
  • Numerical simulations to verify the absence of ETH for target states and its presence in other eigenstates.
  • Quench dynamics analysis.

Main Results:

  • A general method for embedding target states into the energy spectrum was successfully developed.
  • A novel Hamiltonian was constructed that does not satisfy the eigenstate thermalization hypothesis for the embedded target states.
  • Analytical and numerical evidence confirmed the absence of ETH for target states.
  • Numerical calculations demonstrated that other energy eigenstates do exhibit ETH.

Conclusions:

  • The constructed models can thermalize after a quantum quench, despite not fully satisfying the eigenstate thermalization hypothesis.
  • This work provides insights into quantum thermalization in systems with unusual spectral properties.
  • The findings challenge the universality of ETH as the sole mechanism for thermalization.