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Eigenstate thermalization in the two-dimensional transverse field Ising model.

Rubem Mondaini1,2, Keith R Fratus3, Mark Srednicki3

  • 1Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.

Physical Review. E
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Summary
This summary is machine-generated.

We investigated quantum chaos and thermalization in the two-dimensional transverse field Ising model (2D-TFIM). Our findings indicate these phenomena occur when fields are present but not excessively strong.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • The two-dimensional transverse field Ising model (2D-TFIM) is a fundamental model in condensed matter physics, exhibiting rich phase transitions and quantum phenomena.
  • Eigenstate thermalization is a key concept explaining how isolated quantum systems can exhibit thermal behavior in the thermodynamic limit.

Purpose of the Study:

  • To investigate the onset of eigenstate thermalization in the 2D-TFIM.
  • To analyze the influence of ferromagnetic and antiferromagnetic interactions under a longitudinal field on quantum chaos and thermalization.
  • To determine the conditions under which these phenomena manifest in the 2D-TFIM.

Main Methods:

  • Full exact diagonalization was employed to study the system's eigenstates.
  • Quantum chaos indicators were analyzed.
  • Diagonal matrix elements of relevant operators within the eigenstates were examined.
  • Finite size scaling analysis was performed to understand system size effects.

Main Results:

  • Both ferromagnetic and antiferromagnetic 2D-TFIM, in the presence of a uniform longitudinal field, exhibit indicators of quantum chaos and eigenstate thermalization.
  • These phenomena are observed when the applied fields are nonvanishing.
  • There is a critical range for the field strength; excessively large fields can suppress quantum chaos and thermalization.

Conclusions:

  • The 2D-TFIM demonstrates eigenstate thermalization and quantum chaos under specific field conditions.
  • The presence of a longitudinal field is crucial for observing these effects.
  • The study provides insights into the boundary between integrable and chaotic regimes in quantum many-body systems.