Ballistic Spin Transport in a Periodically Driven Integrable Quantum System

Ljubotina, Marko; Zadnik, Lenart; Prosen, Tomaž

doi:10.1103/physrevlett.122.150605

Cited by 76 publications

(87 citation statements)

References 38 publications

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“…In this view, the full map Φ full τ can be perceived as an 'integrable Trotterrization', closely resembling the integrable Trotterization of the quantum Heisenberg model obtained in [83,84]. Indeed, we will shortly demonstrate in Section 2.6 below that Eqs.…”

Section: Dynamical Mapmentioning

confidence: 69%

Integrable matrix models in discrete space-time

2020

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We introduce a class of integrable dynamical systems of interacting classical matrix-valued fields propagating on a discrete space-time lattice, realized as many-body circuits built from elementary symplectic two-body maps. The models provide an efficient integrable Trotterization of non-relativistic \sigmaσ-models with complex Grassmannian manifolds as target spaces, including, as special cases, the higher-rank analogues of the Landau–Lifshitz field theory on complex projective spaces. As an application, we study transport of Noether charges in canonical local equilibrium states. We find a clear signature of superdiffusive behavior in the Kardar–Parisi–Zhang universality class, irrespectively of the chosen underlying global unitary symmetry group and the quotient structure of the compact phase space, providing a strong indication of superuniversal physics.

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Section: Dynamical Mapmentioning

confidence: 69%

Integrable matrix models in discrete space-time

2020

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“…Furthermore, it was shown that this family includes both integrable [60][61][62] and non-integrable cases. In particular, it contains a full parameter line of the integrable trotterized XXZ chain 61,62…”

Section: The Dual-unitary Dynamicsmentioning

confidence: 99%

Exact dynamics in dual-unitary quantum circuits

et al. 2020

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We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of "solvable" matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size reaches infinite temperature after a time t ∝ , irrespective of the presence of conserved quantities, the light-cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of non-solvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs.

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“…To illustrate how persistent oscillations of extensive many-body observables occur, we consider a Floquet driven spin-1/2 chain of even size N ∈ 2N, introduced in Refs. [34,35] as an integrable Trotterization of the anisotropic Heisenberg (XXZ) model. For simplicity we assume that the thermal ensemble corresponds to the infinite-temperature state…”

Section: Driven Heisenberg Chain At Root-of-unity Anisotropiesmentioning

confidence: 99%

“…The lower bounds are derived for autonomous Hamiltonian dynamics as well as for periodically driven (Floquet) systems. We apply our results to a nontrivial example of a many-body Floquet system that breaks the discrete time-translation symmetry, specifically to the integrable Trotterization of the spin-1/2 XXZ model [34,35].…”

Section: Introductionmentioning

confidence: 99%

Rigorous bounds on dynamical response functions and time-translation symmetry breaking

Medenjak¹,

Prosen

Zadnik

2020

SciPost Phys.

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Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e., extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.

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Ballistic Spin Transport in a Periodically Driven Integrable Quantum System

Cited by 76 publications

References 38 publications

Integrable matrix models in discrete space-time

Integrable matrix models in discrete space-time

Exact dynamics in dual-unitary quantum circuits

Rigorous bounds on dynamical response functions and time-translation symmetry breaking

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