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arXiv:1911.11175 · Physical review. B./Physical review. B

Exact dynamics in dual-unitary quantum circuits

Lorenzo Piroli, Bruno Bertini, J. I. Cirac, Tomaž Prosen

Published Mar 9, 2020• 203 citations
arXivHTMLPDF

Abstract

Recently, random unitary quantum circuits have received increasing attention as minimal models for the chaotic quantum many-body dynamics, since they allow for exact computation of quantities that are notoriously hard to study in traditional Hamiltonian systems. A natural question is whether nonrandom quantum circuits exist, also allowing for the derivation of analytic results. The answer is provided in this work, where the authors exhibit a class of interacting quantum circuits for which they are able to compute exactly for an infinite family of initial configurations the dynamics of correlation functions and entanglement.

DOI
10.1103/physrevb.101.094304

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Recently, random unitary quantum circuits have received increasing attention as minimal models for the chaotic quantum many-body dynamics, since they allow for exact computation of quantities that are notoriously hard to study in traditional Hamiltonian systems. A natural question is whether nonrandom quantum circuits exist, also allowing for the derivation of analytic results. The answer is provided in this work, where the authors exhibit a class of interacting quantum circuits for which they are able to compute exactly for an infinite family of initial configurations the dynamics of correlation functions and entanglement.
Dual-unitary circuits have emerged as a minimal model for chaotic quantum many-body dynamics in which the dynamics of correlations and entanglement remains tractable. Simultaneously, there has been intense interest in the effect of measurements on the dynamics of quantum information in many-body systems. In this work we introduce a class of models combining dual-unitary circuits with particular projective measurements that allow the exact computation of dynamical correlations of local observables, entanglement growth, and steady-state entanglement. We identify a symmetry preventing a measurement-induced phase transition and present exact results for the intermediate critical purification phase.
The entanglement in operator space is a well established measure for the complexity of quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study the dynamics of local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quantum circuits that we recently introduced. We identify a class of ``completely chaotic" dual-unitary circuits where the local-operator entanglement grows linearly and we provide a conjecture for its asymptotic behaviour which is in excellent agreement with the numerical results. Interestingly, our conjecture also predicts a ``phase transition" in the slope of the local-operator entanglement when varying the parameters of the circuits.
The entanglement in operator space is a well established measure for the complexity of quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study the dynamics of local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quantum circuits that we recently introduced. We identify a class of ``completely chaotic" dual-unitary circuits where the local-operator entanglement grows linearly and we provide a conjecture for its asymptotic behaviour which is in excellent agreement with the numerical results. Interestingly, our conjecture also predicts a ``phase transition" in the slope of the local-operator entanglement when varying the parameters of the circuits.
The entanglement in operator space is a well established measure for the complexity of the quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and dynamics. For systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study local-operator entanglement in dual-unitary quantum circuits, a class of statistically solvable quantum circuits that we recently introduced. We identify a class of completely chaotic dual-unitary circuits where the local-operator entanglement grows linearly and we provide a conjecture for its asymptotic behaviour which is in excellent agreement with the numerical results. Interestingly, our conjecture also predicts a phase transition in the slope of the local-operator entanglement when varying the parameters of the circuits.
Bipartite entanglement entropy is one of the most useful characterizations of universal properties in a many-body quantum system. Far from equilibrium, there exist two highly effective theories describing its dynamics -- the quasiparticle and membrane pictures. In this work we investigate entanglement dynamics, and these two complementary approaches, in a quantum circuit model perturbed by an impurity. In particular, we consider a dual unitary quantum circuit containing a spatially fixed, non-dual-unitary impurity gate, allowing for differing local Hilbert space dimensions to either side. We compute the entanglement entropy for both a semi-infinite and a finite subsystem within a finite distance of the impurity, comparing exact results to predictions of the effective theories. We find that for a semi-infinite subsystem, both theories agree with each other and the exact calculation. For a finite subsystem, however, both theories qualitatively differ, with the quasiparticle picture predicting a non-monotonic growth in contrast to the membrane picture. We show that such non-monotonic behavior can arise even in random chaotic circuits, shedding light on the range of validity of the membrane picture in such systems.
Recent years have seen significant advances, both theoretical and experimental, in our understanding of quantum many-body dynamics. Given this problem's high complexity, it is surprising that a substantial amount of this progress can be ascribed to exact analytical results. Here we review dual-unitary circuits as a particular setting leading to exact results in quantum many-body dynamics. Dual-unitary circuits constitute minimal models in which space and time are treated on an equal footings, yielding exactly solvable yet possibly chaotic evolution. They were the first in which current notions of quantum chaos could be analytically quantified, allow for a full characterisation of the dynamics of thermalisation, scrambling, and entanglement (among others), and can be experimentally realised in current quantum simulators. Dual-unitarity is a specific fruitful implementation of the more general idea of space-time duality in which the roles of space and time are exchanged to access relevant dynamical properties of quantum many-body systems.