Sebastian Leontica

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Finding suitable characterizations of quantum chaos is a major challenge in many-body physics. Many choices, such as spectral statistics or operator growth offered significant progress, but not without shortcomings. There is always some level of ambiguity due to arbitrary thresholds in diagnostic criteria, and establishing a connection to the classical notion of chaos is difficult for systems without clear classical analogues. We attempt to overcome this difficulty by noticing that matrix product states offer an approximate classical description of quantum systems in 1D. The time-dependent variational principle (TDVP) produces non-linear classical Hamiltonian dynamics on the manifold, allowing the direct application of traditional Lyapunov spectrum based characterization of chaos. While the exact connection to standard quantum chaos signatures is unknown, we prove analytical bounds showing a deep connection between the classical Kolmogorov-Sinai entropy and the linear rate of entanglement growth in the system. A possible interpretation is to see local tensor fluctuations as emergent quasi-particles, driven by classical dynamics. Their propagation leads to the squeezing of wave packets on the MPS manifold, analogous to phase-space diffusion in classical chaotic systems, which simultaneously drives entanglement growth following the Cardy–Calabrese mechanism. This rigorously establishes the physical significance of the projected Lyapunov spectrum, suggesting it as an alternative method of characterizing chaos in quantum many-body systems that more closely resembles the classical chaos framework.

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University College London
0.03
Contact: Silvia Pappalardi