Solution of a Minimal Model for Many-Body Quantum Chaos

We solve a minimal model for an ergodic phase in a spatially extended quantum many-body system. The model consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution. Quantum states at each site span aq-dimensional Hilbert space, and time evolution for a pair of sites is...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. X 2018-11, Vol.8 (4), p.041019, Article 041019
Main Authors: Chan, Amos, De Luca, Andrea, Chalker, J. T.
Format: Article
Language:English
Subjects:
Chaos theory
Circuits
Couplings
Evolution
Form factors
Hilbert space
Initial conditions
Mathematical analysis
Operators (mathematics)
Quantum computing
Quantum entanglement
Quantum phenomena
Qubits (quantum computing)
Statistical mechanics
Time dependence
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We solve a minimal model for an ergodic phase in a spatially extended quantum many-body system. The model consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution. Quantum states at each site span aq-dimensional Hilbert space, and time evolution for a pair of sites is generated by aq2×q2random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbor on one side during the first half of the evolution period and to its neighbor on the other side during the second half of the period. We show how dynamical behavior averaged over realizations of the random matrices can be evaluated using diagrammatic techniques and how this approach leads to exact expressions in the large-qlimit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth, and operator spreading.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.8.041019