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.
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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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.
An updated survey of methods to generate absolutely maximally entangled states, with new analyses of reduced-state entanglement, GHZ superpositions, orthogonal frequency square representations, and local unitary equivalence classes.
citing papers explorer
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Graph restricted tensors: building blocks for holographic networks
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.
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Exact large deviations and emergent long-range correlations in sequential quantum East circuits
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.
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Quantum many-body operator cascade as a route to chaos
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.
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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.
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Entanglement structure for finite system under dual-unitary dynamics
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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Absolutely maximally entangled pure states of multipartite quantum systems
An updated survey of methods to generate absolutely maximally entangled states, with new analyses of reduced-state entanglement, GHZ superpositions, orthogonal frequency square representations, and local unitary equivalence classes.