Integrable Many-Body Quantum Floquet-Thouless Pumps

Friedman, Aaron J.; Gopalakrishnan, Sarang; Vasseur, Romain

doi:10.1103/physrevlett.123.170603

Cited by 60 publications

(119 citation statements)

References 119 publications

(157 reference statements)

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“…Following recent developments in the hydrodynamic description of integrable systems [23,31,46,[46][47][48][49][50][51], the transformation R as well as other transport matrices such as A, B, and G can be computed exactly. In integrable systems normal modes are stable quasi-particle excitations that fully describe the thermodynamics and hydrodynamics of the system [52,53]. An expression for the L i j matrix has been found in [31] by exploiting integrability techniques.…”

Section: Diffusion In Integrable Systemsmentioning

confidence: 99%

Diffusion from convection

2020

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We introduce non-trivial contributions to diffusion constants in generic many-body systems with Hamiltonian dynamics arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in terms of powers of local and quasi-local conserved quantities. We show that only the second-order terms in this expansion carry a finite contribution to diffusive spreading. Our formalism implies that whenever there are at least two coupled modes with degenerate group velocities the system behaves super-diffusively, in accordance with non-linear fluctuating hydrodynamics. Finally, we show that our expression saturates the exact diffusion constants in quantum and classical interacting integrable systems, providing a general framework to derive these expressions.

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Section: Diffusion In Integrable Systemsmentioning

confidence: 99%

Diffusion from convection

2020

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“…In the case of RCA54, the condition for a site to flip is identical to that of the classical Fredrickson-Andersen (FA) KCM [6,9,11]. For this reason RCA54 is sometimes called Floquet-FA [35][36][37]. In the case of RCA201, the local condition for spin flips coincides with that of the PXP model [14,15,42].…”

Section: Introductionmentioning

confidence: 99%

“…If deterministic, they can either be reversible or not, where the former (RCA [1], see also [30]) can be considered as a model of classical many-body Hamiltonian (or symplectic) dynamics. The RCA201/Floquet-PXP is a deterministic RCA, closely related to the now much studied RCA54/Floquet-FA [27,[31][32][33][34][35][36][37][38][39][40][41]. Just like the RCA54, the RCA201 (see detailed definitions below) is a one-dimensional lattice of binary variables with local three-site gates applied simultaneously to two halves (of even/odd indexed sites) of the lattice in two successive half time-steps.…”

Section: Introductionmentioning

confidence: 99%

Exact solution of the Floquet-PXP cellular automaton

et al. 2020

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We study the dynamics of a bulk deterministic Floquet model, the Rule 201 synchronous onedimensional reversible cellular automaton (RCA201). The system corresponds to a deterministic, reversible, and discrete version of the PXP model, whereby a site flips only if both its nearest neighbours are unexcited. We show that the RCA201/Floquet-PXP model exhibits ballistic propagation of interacting quasiparticles -or solitons -corresponding to the domain walls between non-trivial three-fold vacuum states. Starting from the quasiparticle picture, we find the exact matrix product state form of the non-equilibrium stationary state for a range of boundary conditions, including both periodic and stochastic. We discuss further implications of the integrability of the model. I.

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“…al. in [24] 1 and studied extensively in the last years, both in classical [27][28][29][30][31][32] and in quantum setting [33][34][35][36]. In particular, dynamical structure factor of this model has been computed exactly [31] and shown to exhibit diffusive transport.…”

mentioning

confidence: 99%

Space-like dynamics in a reversible cellular automaton

Klobas

Prosen

2020

SciPost Phys. Core

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In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on the dynamics of quasi-particles and follows from an exhaustive check of all the relevant time configurations, while the second one relies on purely algebraic considerations based on the circuit representation of the dynamics. Additionally, we use the properties of the local space evolution maps to provide an alternative derivation of the matrix product representation of multi-time correlation functions of local observables positioned at the same spatial coordinate.

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Integrable Many-Body Quantum Floquet-Thouless Pumps

Cited by 60 publications

References 119 publications

Diffusion from convection

Diffusion from convection

Exact solution of the Floquet-PXP cellular automaton

Space-like dynamics in a reversible cellular automaton

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