Integrable Trotterization: Local Conservation Laws and Boundary Driving

Vanicat, Matthieu; Zadnik, Lenart; Prosen, Tomaž

doi:10.1103/physrevlett.121.030606

Cited by 85 publications

(139 citation statements)

References 34 publications

(37 reference statements)

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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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Section: The Dual-unitary Dynamicsmentioning

confidence: 99%

Exact dynamics in dual-unitary quantum circuits

et al. 2020

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“…Since a direct computation of higher conserved charges is tedious, it would be of interest if the conserved charges of the model could be equipped with a boost 10Žiga Krajnik, Tomaž Prosen operation that would facilitate their automated computation, similarly as in the quantum case [21].…”

Section: Integrability Of the Modelmentioning

confidence: 99%

Kardar–Parisi–Zhang Physics in Integrable Rotationally Symmetric Dynamics on Discrete Space–Time Lattice

Krajnik

Prosen

2020

J Stat Phys

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We introduce a deterministic SO(3) invariant dynamics of classical spins on a discrete space-time lattice and prove its complete integrability by explicitly finding a related non-constant (baxterized) solution of the set-theoretic quantum Yang-Baxter equation over the 2-sphere. Equipping the algebraic structure with the corresponding Lax operator we derive an infinite sequence of conserved quantities with local densities. The dynamics depend on a single continuous spectral parameter and reduce to a (lattice) Landau-Lifshitz model in the limit of a small parameter which corresponds to the continuous time limit. Using quasiexact numerical simulations of deterministic dynamics and Monte Carlo sampling of initial conditions corresponding to a maximum entropy equilibrium state we determine spin-spin spatio-temporal (dynamical) correlation functions with relative accuracy of three orders of magnitude. We demonstrate that in the equilibrium state with a vanishing total magnetization the correlation function precisely follow Kardar-Parisi-Zhang scaling hence the spin transport belongs to the universality class with dynamical exponent z = 3/2, in accordance to recent related simulations in discrete and continuous time quantum Heisenberg spin 1/2 chains.

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“…Although MBL can protect [40][41][42] Floquet topological phases [20,[43][44][45][46][47][48][49][50][51][52], these phases are localized and do not host chiral modes. However, in addition to MBL systems, interacting integrable systems are another broad class of systems-including the canonical Hubbard, Heisenberg, and Lieb-Liniger models-that do not heat up to infinite temperature [53][54][55]; whether distinctively Floquet versions of these models exist has been less discussed [56][57][58][59].…”

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confidence: 99%

Integrable Many-Body Quantum Floquet-Thouless Pumps

2019

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We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model, and show that these take on a particularly simple form that allows for an exact solution: essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem to be possible in other interacting integrable systems. This model illustrates the existence a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.with gatesÛ j−1,j,j+1 ≡ CNOT(1 → 2) CNOT(3 → 2) Toff.(1, 3 → 2), in terms of controlled NOT (CNOT) arXiv:1905.03265v1 [cond-mat.stat-mech]

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Integrable Trotterization: Local Conservation Laws and Boundary Driving

Cited by 85 publications

References 34 publications

Exact dynamics in dual-unitary quantum circuits

Exact dynamics in dual-unitary quantum circuits

Kardar–Parisi–Zhang Physics in Integrable Rotationally Symmetric Dynamics on Discrete Space–Time Lattice

Integrable Many-Body Quantum Floquet-Thouless Pumps

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