Emergent irreversibility and entanglement spectrum statistics

Francesco Buscemi

Claudio Chamon, Alioscia Hamma, Eduardo R. Mucciolo

We study the problem of irreversibility when the dynamical evolution of a many-body system is described by a stochastic quantum circuit. Such evolution is more general than a Hamiltonian one, and since energy levels are not well defined, the well-established connection between the statistical fluctuations of the energy spectrum and irreversibility cannot be made. We show that the entanglement spectrum provides a more general connection. Irreversibility is marked by a failure of a disentangling algorithm and is preceded by the appearance of Wigner-Dyson statistical fluctuations in the entanglement spectrum. This analysis can be done at the wave-function level and offers an alternative route to study quantum chaos and quantum integrability.

Daniel Shaffer, Claudio Chamon, Alioscia Hamma +1 more

We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner–Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner–Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.

William Arveson

Richard Berkovits

Statistical properties of the low‐lying states of the entanglement spectrum of a one‐dimensional interacting disordered system are studied in order to understand the localized to extended transition as function of interaction strength and excitation number expected from the many‐body localization transition. It is shown that such a transition is observed in the statistics of the level‐spacing of the entanglement spectrum. For an intermediate range of excitation numbers and strong interaction strength where the entanglement spectrum shows a clear extended behavior, a signature of non‐ergodic behavior also emerges. We interpret this as evidence for a non‐ergodic‐extended phase suggested by previous studies.

A. Vidiella-Barranco