Solution of a Minimal Model for Many-Body Quantum Chaos
By Amos Chan, Andrea De Luca, J. Chalker. Physical Review X, 2017
323 citations recorded by the source corpus.
We solve a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a $q$-dimensional Hilbert space and time evolution for a pair of sites is generated by a $q^2\times q^2$ random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. We show how dynamical behaviour averaged over realisations of the random matrices can be evaluated using diagrammatic techniques, and how this approach leads to exact expressions in the large-$q$ limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth and operator spreading.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/b52f10e06c9d269f784c1659572264129c8fc6ee
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Citations in the corpus
- Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “For some dynamical quantities, for example the spectral form factor, pairings that are non-local in time play a role [11, 33, 77].”
- Emergent statistical mechanics of entanglement in random unitary circuits (2018, background): “The above shows that different Rényi entropies grow at different rates following a quench (see also [44]).”
- Unitary designs from statistical mechanics in random quantum circuits. (2019, background): “Furthermore, there has been recent interest in other random circuit models with conservation laws [40,41], local symmetries including time-reversal symmetry [42], and Floquet random circuits [43,44].”
- A semiclassical ramp in SYK and in gravity (2018, background): “Cyclic permutations have also played a central role in recent work deriving the ramp for Floquet many-body system [36, 43, 44, 38] .”
- A Universal Operator Growth Hypothesis (2018, background): “Recent work has shifted focus from states to operator growth in many-body systems [6–11].”
- Random Quantum Circuits (2022, methodology): “2 we will review the incorporation of global symmetries (92, 93) or time translation symmetry (94, 95) into the random circuit.”
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, result): “We briefly discuss the outlook for an analytical description of the dynamical transition that we find, making connections with recent results for random unitary circuits [9,18,25,26] and random tensor network states [27,28].”
- Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos (2018, unknown): “Examples range from conformal invariant systems [15,33], to nonintegrable closed systems [43], from random in time [50–52], to periodically driven [55] random unitary circuits.”
- Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, methodology): “by either a time-independent Hamiltonian[19, 21–24, 29– 39], or by Floquet dynamics[40, 41], or by a random unitary circuit [18, 42–46].”
- Measurement-driven entanglement transition in hybrid quantum circuits (2019, background): “As for unitary Hamiltonian dynamics, there is a notion of chaos in such Floquet circuits, as diagnosed by the entanglement growth [49, 50], the operator growth (and butterfly effect in out-of-time-order correlator) [51], the level spacing statistics and the spectral form factor [45, 46, 48, 52], etc”