Abstract

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.

Highlights

  • Random-matrix theory plays a central role in the understanding of chaotic quantum systems [1]

  • We show that quantum dynamics in this system exhibits a range of features that are expected to be characteristic of ergodic many-body quantum systems: Correlators of local observables decay rapidly in time, and quantum information spreads ballistically, in the sense that the bipartite entanglement of an initial product state grows linearly in time, and the out-of-time-order correlator [14,15] (OTOC) shows the “butterfly” effect

  • We seek a minimal model for quantum chaos in a spatially extended many-body system with local interactions

Read more

Summary

Introduction

Random-matrix theory plays a central role in the understanding of chaotic quantum systems [1]. Diffusive transport in weakly disordered conductors is such an example for single-particle systems, and spreading of quantum information is a counterpart for many-body systems. It is natural to attempt to combine the simplifying features of randommatrix theory with extended spatial structure. For diffusive conductors, this goal is achieved in Wegner’s n-orbital model [2] in which hopping between sites of a tightbinding system is governed by n × n random matrices, and disorder-averaged properties can be calculated exactly in the limit n → ∞. Our aim in this paper is to establish a comparable simplification for spatially extended manybody systems

Methods
Results
Conclusion
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call