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Entanglement Patterns of Quantum Chaotic Hamiltonians with a Scalar U(1) Charge
Christopher M Langlett1, Joaquin F Rodriguez-Nieva1
1Texas A&M University, Department of Physics & Astronomy, College Station, Texas 77843, USA.
Physical Review Letters
|June 27, 2025
Summary
This study introduces constrained random states to model quantum chaos in many-body systems, capturing finer details beyond random matrix theory (RMT). The approach accurately describes eigenstate entanglement, including spatial locality effects.
Area of Science:
- Quantum physics
- Statistical mechanics
- Condensed matter theory
Background:
- Quantum chaos in many-body systems is often described by random matrix theory (RMT).
- RMT successfully explains coarse features like Wigner-Dyson statistics and volume-law entanglement entropy.
- Describing finer features, especially those related to spatial locality, remains a challenge.
Purpose of the Study:
- To develop a method for accurately describing statistical behavior of eigenstates in many-body quantum systems.
- To capture finer details of quantum chaos beyond RMT predictions, incorporating spatial locality and symmetries.
- To analyze entanglement patterns of mid-spectrum eigenstates, including corrections and fluctuations.
Main Methods:
- Utilizing pure random states with physical constraints that reflect Hamiltonian properties (spatial locality, symmetries).
- Applying the method to local spin Hamiltonians with scalar U(1) charge.
- Constructing constrained random state ensembles considering commuting scalar charges (energy, magnetization).
Main Results:
- Accurate statistical description of eigenstate ensembles in many-body Hamiltonians.
- Detailed description of mid-spectrum eigenstate entanglement beyond average volume-law behavior.
- Analytical and numerical confirmation of O(1) corrections and fluctuations in entanglement patterns.
Conclusions:
- Constrained random states provide a powerful tool for understanding quantum chaos in many-body systems.
- Spatial locality plays a crucial role in universal features of quantum chaotic eigenstates, extending beyond volume-law behavior.
- The approach offers a more refined description of quantum chaotic eigenstates compared to traditional RMT.
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