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Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
1Department of Physics, University of Seoul, Seoul 02504, Korea.
Physical Review. E
|February 17, 2023
Summary
We studied the spin-1/2 XXZ model and found it follows the eigenstate thermalization hypothesis. This quantum physics principle was confirmed even within subspaces with conserved total spin.
Area of Science:
- Quantum Many-Body Physics
- Condensed Matter Theory
- Statistical Mechanics
Background:
- The eigenstate thermalization hypothesis (ETH) is a cornerstone for understanding thermalization in isolated quantum systems.
- The spin-1/2 XXZ model is a fundamental model in condensed matter physics, exhibiting rich quantum phenomena.
Purpose of the Study:
- To investigate the validity of the eigenstate thermalization hypothesis (ETH) in the two-dimensional spin-1/2 XXZ model.
- To explore thermalization properties in a realistic lattice model with tunable interactions.
Main Methods:
- Exact diagonalization of the Hamiltonian for the two-dimensional XXZ model on rectangular lattices.
- Numerical analysis of energy spectra and Hamiltonian matrix elements in the eigenstate basis.
- Exploitation of lattice symmetries to enable larger system size studies.
Main Results:
- Numerical evidence strongly supports that the two-dimensional XXZ model adheres to the eigenstate thermalization hypothesis.
- The ETH was confirmed to hold within subspaces characterized by conserved total spin, even when SU(2) symmetry is present.
- System sizes up to 4x7 (eigenvalues) and 4x6 (eigenstates) were studied.
Conclusions:
- The two-dimensional XXZ model provides a concrete example supporting the eigenstate thermalization hypothesis.
- ETH is robust and holds even in the presence of symmetries like SU(2) and conserved total spin.
- This work contributes to the fundamental understanding of thermalization in quantum many-body systems.
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