Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

Abstract

We study the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach. We exhibit a family of (non-equilibrium) product states for which we are able to describe exactly the full relaxation dynamics. We use this to prove that finite subsystems relax to a one-parameter family of Gibbs states. We also consider inhomogeneous quenches. Specifically, we show that when the two halves of the system are prepared in two different solvable states, finite subsystems at finite distance from the centre eventually relax to the non-equilibrium steady state (NESS) predicted by generalised hydrodynamics. To the best of our knowledge, this is the first exact description of the relaxation to a NESS in an interacting system and, therefore, the first independent confirmation of generalised hydrodynamics for an inhomogeneous quench.

Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

“…This is the second of two papers dedicated to this task. While in the first part of our work [36], which in the following we will refer to as "Paper I", we focussed on the dynamics of local observables, here we consider the evolution of the entanglement. The extension that we present bares a remarkable physical significance.…”

Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

“…This is the second of two papers dedicated to this task. While in the first part of our work [39], which in the following we will refer to as "Paper I", we focussed on the dynamics of local observables, here we consider the evolution of the entanglement. The extension that we present bares a remarkable physical significance.…”

Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality

“…The IM approach offers an alternative route to the evolution of local observables, relevant for studying thermalization and transport in strongly interacting quantum many-body systems. Unlike previous proposals [5][6][7][8][9][10][11][12][13], this approach does not involve ad hoc truncation of non-local quantum information, and possibly circumvents the exponential wall of quantum many-body dynamics whenever the scaling of TE entropy with evolution time is sublinear -which has been demonstrated in several physically distinct regimes [17,[21][22][23][24][25]28]. The generic greater efficiency of the "transverse contraction and folding" MPS algorithm was empirically observed in early applications (see Refs.…”

“…Based on this, we formulated the influence matrix (IM) approach to study dynamics in quantum circuits [16,17] (see also [18,19]). Recent insights on the IM structure of generic [16,20] and solvable [21][22][23][24][25] models suggest that this approach can be efficient in regimes inaccessible to other methods.…”

“…Since fast relaxation to equilibrium is associated with fast decay of temporal correlations, TE is expected to scale favorably with evolution time in thermalizing systems, suggesting an efficient MPS representation [16]. While quantitative predictions of TE scaling for general systems are currently lacking, a slow sublinear scaling of TE with evolution time has been shown numerically and analytically in several cases [17,[21][22][23][24][25]28].…”