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Edge of entanglement in nonergodic states: A complexity parameter formulation
Devanshu Shekhar1, Pragya Shukla1
1Indian Institute of Technology, Department of Physics, Kharagpur 721302, West Bengal, India.
Physical Review. E
|September 16, 2025
Summary
This study reveals infinite universality classes for nonergodic pure states, where entanglement entropy scales universally with subsystem size. A complexity parameter helps identify critical regimes in these complex quantum systems.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
- Statistical Mechanics
Background:
- Nonergodic pure states exhibit complex entanglement properties.
- Understanding entanglement entropy scaling is crucial for characterizing quantum states.
- Gaussian ensembles of complex matrices model various quantum systems.
Purpose of the Study:
- To analyze the subsystem size scaling of entanglement entropy in nonergodic pure states.
- To identify universality classes governing local complexity.
- To establish a method for identifying critical regimes in these states.
Main Methods:
- Analysis of entanglement entropy scaling with subsystem size.
- Utilizing a multiparametric Gaussian ensemble of complex matrices.
- Characterization of states within a bipartite basis.
Main Results:
- Identified an infinite number of universality classes for local complexity.
- Demonstrated universal entanglement entropy scaling with subsystem size for these classes.
- Introduced a complexity parameter to characterize these universality classes.
Conclusions:
- The complexity parameter is key to understanding entanglement entropy scaling.
- A rescaling of the complexity parameter identifies critical regimes.
- This framework applies to a broad range of pure nonergodic states.
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