Constructs staggered finite-range dual-unitary Floquet models whose entanglement entropies are exactly the sum of independent sublattice contributions for all times and all Rényi indices.
Exactly solvable many-body dynamics from space-time duality
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abstract
Recent years have seen significant advances, both theoretical and experimental, in our understanding of quantum many-body dynamics. Given this problem's high complexity, it is surprising that a substantial amount of this progress can be ascribed to exact analytical results. Here we review dual-unitary circuits as a particular setting leading to exact results in quantum many-body dynamics. Dual-unitary circuits constitute minimal models in which space and time are treated on an equal footings, yielding exactly solvable yet possibly chaotic evolution. They were the first in which current notions of quantum chaos could be analytically quantified, allow for a full characterisation of the dynamics of thermalisation, scrambling, and entanglement (among others), and can be experimentally realised in current quantum simulators. Dual-unitarity is a specific fruitful implementation of the more general idea of space-time duality in which the roles of space and time are exchanged to access relevant dynamical properties of quantum many-body systems.
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Graph-restricted tensors generalize 1-uniform states, dual-unitary operators and AME states, with exact analytic solutions for new examples motivated by holographic lattice models.
Conditioning on rare boundary measurement outcomes in a quantum East circuit generates states with finite two-point correlations at arbitrary distances and an underlying Sierpiński-triangle fractal structure.
Local operators in quantum chaotic systems cascade toward non-local fractal structures whose dimension is tied by unitarity to the decay rate of local correlations, demonstrated exactly in dual-unitary circuits and numerically in others.
Generic ergodic Hamiltonian dynamics in quantum Ising chains exhibits a long mesoscopic regime in temporal entanglement that deviates from random-circuit universality, suggesting slow spectral reorganization of the influence functional.
Dual-unitary circuits with specific two-body operators and pair-product initial states produce states approaching the multipartite entanglement bounds of absolutely maximally entangled states.
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Exact Entanglement Dynamics Beyond Nearest-Neighbor Dual-Unitary Floquet Systems
Constructs staggered finite-range dual-unitary Floquet models whose entanglement entropies are exactly the sum of independent sublattice contributions for all times and all Rényi indices.
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Mesoscopic Regimes of Temporal Entanglement in Ergodic Quantum Systems
Generic ergodic Hamiltonian dynamics in quantum Ising chains exhibits a long mesoscopic regime in temporal entanglement that deviates from random-circuit universality, suggesting slow spectral reorganization of the influence functional.