Abnormalities of Chaotic Systems found in the Entanglement States of Quantum Scars
By Victoria
Ergodicity, or the ability of a system to explore all accessible phase states, is a fundamental assumption in statistical mechanics, particularly in the thermodynamic representations of many-body systems. However, not all many-body systems are ergodic. Quantum many-body scars are a recently discovered class of non-thermal eigenstates embedded within otherwise thermalizing chaotic systems found to weakly violate ergodicity. In this paper, we numerically investigate the entanglement properties of scarred eigenstates in the PXP model, a paradigmatic example of quantum scars. By comparing entanglement entropy to Page’s theoretical prediction for random states and highlighting low-entropy eigenstates with large overlap with the period-2 charge density wave state ($\ket{Z_2}$), we observe distinct violations of ergodicity and uncover the unique structure of scars. Our findings support recent theoretical work proposing the universality and robustness of quantum scars and suggest future directions in using scarred states to preserve quantum coherence.
Files and Resources
"Average Entropy of a Subsystem" Paper
A 1993 paper by Don N. Page deriving an approximation for calculating the average entropy (information) for a quantum system of Hilbert space dimension mn. This project would aim to confirm and compare entropy calculations of many-body systems with the approximation derived in this paper.
"Ballistic Spreading of Entanglement in a Diffusive Nonintegrable System" Paper
A 2013 paper by Hyungwon Kim and David A. Huse introducing a spin-1/2 Ising chain as a Hamiltonian to investigate the spread of entanglement. This project chooses an eigenstate in the middle of the spectrum of this paper's Ising chain Hamiltonian to verify patterns in our calculations of entanglement entropy.
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