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Spectral crossovers in non-Hermitian spin chains: Comparison with random matrix theory
Ayana Sarkar1, Sunidhi Sen1, Santosh Kumar1
1Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, Uttar Pradesh-201314, India.
Physical Review. E
|December 20, 2023
Summary
We studied spectral fluctuations in non-Hermitian spin chains using complex spacing ratios (CSRs). Quantum chaotic behavior emerges with random fields, showing a crossover from Poisson to Ginibre unitary ensemble (GinUE) statistics.
Area of Science:
- Condensed matter physics
- Quantum chaos
- Non-Hermitian systems
Background:
- The one-dimensional anisotropic XY model is a standard model in condensed matter physics.
- Its Hermitian counterpart is exactly solvable and widely used.
- Non-Hermitian Hamiltonians with rotation-time (RT) symmetry are of recent interest.
Purpose of the Study:
- Investigate short-range spectral fluctuation properties of non-Hermitian spin chains.
- Analyze the impact of random fields on integrability and RT-symmetry.
- Examine spectral crossovers using complex spacing ratios (CSRs).
Main Methods:
- Systematic investigation of three non-Hermitian spin-chain Hamiltonians.
- Utilized complex spacing ratios (CSRs) to analyze spectral fluctuations.
- Employed phenomenological random matrix models for 1D and 2D Poisson to Ginibre unitary ensemble (GinUE) crossovers.
Main Results:
- Random fields along x and z directions break integrability and RT-symmetry.
- Emergence of quantum chaotic behavior evidenced by spectral crossovers.
- Observed crossover from Poissonian to Ginibre unitary ensemble (GinUE) statistics.
Conclusions:
- Spectral fluctuations in non-Hermitian spin chains exhibit transitions similar to random matrix theory predictions.
- CSRs effectively capture spectral behavior in these systems.
- The study provides insights into quantum chaos in non-Hermitian systems.
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