Localization and entanglement entropy in the Discrete Non-Linear Schrödinger Equation

• URL: http://arxiv.org/abs/2503.14364v1
• Date: Tue, 18 Mar 2025 15:47:50 GMT
• Title: Localization and entanglement entropy in the Discrete Non-Linear Schrödinger Equation
• Authors: Martina Giachello, Stefano Iubini, Roberto Livi, Giacomo Gradenigo,
• Abstract summary: A numerical sampling of the microcanonical ensemble done by means of Hamiltonian dynamics reveals a new and subtle relation between the localized phase and a non-trivial behaviour of entanglement entropy.<n>Our finding that the entanglement entropy grows as $S_textent(N) sim log(N)$ beautifully encodes the lack of additivity in the DNLSE non-thermal localized phase.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work we perform an accurate numerical study of the very peculiar thermodynamic properties of the localized high-energy phase of the Discrete Non-Linear Schr\"odinger Equation (DNLSE). A numerical sampling of the microcanonical ensemble done by means of Hamiltonian dynamics reveals a new and subtle relation between the presence of the localized phase and a non-trivial behaviour of entanglement entropy. Our finding that the entanglement entropy grows as $S_{\text{ent}}(N) \sim \log(N)$ beautifully encodes the lack of additivity in the DNLSE non-thermal localized phase and reveals how a property so far believed peculiar of purely quantum systems may characterize even certain classical frameworks.

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