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Entanglement entropy and out-of-time-order correlator in the long-range Aubry-André-Harper model
Nilanjan Roy1,2, Auditya Sharma1
1Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462066, India.
Summary
We studied quantum entanglement and chaos in the Aubry-André-Harper model with long-range hopping. Our findings reveal distinct signatures in entanglement entropy and out-of-time-order correlators (OTOC) to differentiate quantum phases.
Area of Science:
- Condensed Matter Physics
- Quantum Dynamics
- Disordered Systems
Background:
- The Aubry-André-Harper (AAH) model describes quasiperiodic systems.
- Understanding quantum phase transitions and dynamics is crucial in condensed matter.
- Noninteracting fermions provide a tractable model for complex quantum phenomena.
Purpose of the Study:
- To distinguish delocalized, multifractal, localized, and mixed phases in the AAH model.
- To investigate the nonequilibrium dynamics of entanglement entropy and OTOC.
- To explore the impact of long-range hopping on these dynamics.
Main Methods:
- Analysis of entanglement entropy and out-of-time-order correlators (OTOC).
- Study of noninteracting fermions at half-filling starting from a product state.
- Inclusion of long-range hopping in the quasiperiodic AAH model.
Main Results:
- Entanglement entropy exhibits power-law and secondary logarithmic behaviors, varying across phases.
- Saturation of entanglement entropy scales linearly with system size in delocalized/mixed phases, but not in localized phases.
- OTOC shows distinct early-time growth and late-time decay power-law exponents, differing between phases and hopping ranges.
- Spatial profiles of OTOC reveal unique characteristics for distinguishing phases, including distance-dependent behaviors and fluctuations in mixed/multifractal states.
Conclusions:
- Entanglement entropy and OTOC serve as effective probes for phase transitions in the AAH model.
- Long-range hopping introduces novel behaviors in entanglement entropy and OTOC dynamics.
- The spatial and system-size dependence of OTOC provides robust signatures for phase identification.
Keywords:
entanglement entropylong-range Aubry–André–Harper modelout-of-time-order correlatorquantum dynamicsMore Related Videos
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