The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with  a minimal set of charges

Zadnik, Lenart; Bidzhiev, Kemal; Fagotti, Maurizio

doi:10.21468/scipostphys.10.5.099

Cited by 54 publications

(84 citation statements)

References 49 publications

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“…The first, v n (λ), is naturally identified with the velocity of the excitations -accessible in TBA [85] -while the second, s n (λ), can be fixed by imposing the equality between the entanglement and the thermodynamic entropy in the stationary state [5]. All this is particularly simple for excitations on the stationary states (35) in Rule 54. Indeed, on these states there is only one species of excitations and λ can take only two values (λ ∈ {±}) (for further details see Paper I, the Supplemental Material of Ref.…”

Section: Von Neumann Entropy: Exact Confirmation Of the Quasiparticle Picturementioning

confidence: 99%

“…which means that the quasiparticles cannot be though of as excitations on the stationary state (35), i.e. the state describing the expectation values of local observables at infinite times after the quench.…”

Section: Now We Note Thatmentioning

confidence: 99%

“…The situation changed recently, when Ref. [31] presented an exact characterisation of the growth of entanglement in the quantum cellular automaton Rule 54, which can be considered one of the simplest examples of interacting integrable models (see also [32][33][34][35][36][37][38]). The result was again based on a time-channel approach and lead to an exact characterisation of the growth of entanglement when the system is initialised in a particular class of initial states.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

Klobas

Bertini

2021

SciPost Phys.

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We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule 54. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all Rényi entropies in the thermodynamic limit and their eventual saturation for finite subsystems. While in the case of von Neumann entropy we recover exactly the predictions of the quasiparticle picture, we find no physically meaningful quasiparticle description for other Rényi entropies. Our results apply to both homogeneous and inhomogeneous quenches.

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Section: Von Neumann Entropy: Exact Confirmation Of the Quasiparticle Picturementioning

confidence: 99%

Section: Now We Note Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

Klobas

Bertini

2021

SciPost Phys.

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“…The fixed-points given by the diagrams (54) generically exhibit bond dimension that grows exponentially with time t. However, as we argue below (and part of it was shown in [50]), in Rule 54 we can identify initial states and stationary states for which (54) reduce to an MPS with constant bond dimension χ = 3.…”

Section: A Solvable Case: Quantum Cellular Automaton Rule 54mentioning

confidence: 90%

“…An interesting route to achieve this goal has recently been pointed out in Refs. [50][51][52][53][54][55][56], which showed that in some special integrable models one can indeed access the full time evolution of local observables. In particular Ref.…”

Section: Introductionmentioning

confidence: 99%

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

Klobas

Bertini

2021

SciPost Phys.

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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.

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Many-body quantum chaos and dual-unitarity round-a-face

Prosen

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We propose a new type of locally interacting quantum circuits—quantum cellular automata—that are generated by unitary interactions round-a-face (IRF). Specifically, we discuss a set (or manifold) of dual-unitary IRFs with local Hilbert space dimension d [DUIRF(d)], which generate unitary evolutions both in space and time directions of an extended 1+1 dimensional lattice. We show how arbitrary dynamical correlation functions of local observables can be evaluated in terms of finite-dimensional completely positive trace preserving unital maps in complete analogy to recently studied circuits made of dual-unitary brick gates (DUBGs). The simplest non-vanishing local correlation functions in dual-unitary IRF circuits are shown to involve observables non-trivially supported on two neighboring sites. We completely characterize the ten-dimensional manifold of DUIRF(2) for qubits (d=2) and provide, for d=3,4,…,7, empirical estimates of its dimensionality based on numerically determined dimensions of tangent spaces at an ensemble of random instances of dual-unitary IRF gates. In parallel, we apply the same algorithm to determine dimDUBG(d) and show that they are of similar order though systematically larger than dimDUIRF(d) for d=2,3,…,7. It is remarkable that both sets have a rather complex topology for d≥3 in the sense that the dimension of the tangent space varies among different randomly generated points of the set. Finally, we provide additional data on dimensionality of the chiral extension of DUBG circuits with distinct local Hilbert spaces of dimensions d≠d′ residing at even/odd lattice sites.

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The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with a minimal set of charges

Cited by 54 publications

References 49 publications

Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

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

Many-body quantum chaos and dual-unitarity round-a-face

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