Superintegrable cellular automata and dual unitary gates from  Yang-Baxter maps

Gombor, Tamás; Pozsgay, Balázs

doi:10.21468/scipostphys.12.3.102

Cited by 26 publications

(18 citation statements)

References 70 publications

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“…One of the most interesting questions is, whether these ideas and methods are applicable to other superintegrable models, for example those studied in the recent works [23,24]. Is particle number conservation crucial for our methods to work?…”

Section: Discussionmentioning

confidence: 99%

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Integrable deformations of superintegrable quantum circuits

Gombor¹,

Pozsgay²

2022

Preprint

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Superintegrable models are very special dynamical systems: they possess more conservation laws than what is necessary for complete integrability. This severely constrains their dynamical processes, and it often leads to their exact solvability, even in non-equilibrium situations. In this paper we consider special Hamiltonian deformations of superintegrable quantum circuits. The deformations break superintegrability, but they preserve integrability. We focus on a selection of concrete models and show that for each model there is an (at least) one parameter family of integrable deformations. Our most interesting example is the so-called Rule54 model. We show that the model is compatible with a one parameter family of Yang-Baxter integrable spin chains with six-site interaction. Therefore, the Rule54 model does not have a unique integrability structure, instead it lies at the intersection of a family of quantum integrable models.

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Section: Discussionmentioning

confidence: 99%

“…Gliders can be constructed in special cases, when the two-site unitary operator U satisfies the braid relation (spectral parameter independent Yang-Baxter equation) [23]. Other examples can be found in the so-called dual unitary circuits [18], where it is known that all conserved charges come from gliders [22].…”

Section: Superintegrable Quantum Circuitsmentioning

confidence: 99%

Integrable deformations of superintegrable quantum circuits

Gombor¹,

Pozsgay²

2022

Preprint

Self Cite

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“…An example of time evolution for a random initial configuration with 4 particle species is shown in Figure 1. For further discussion of integrability of related cellular automata we refer the reader to the recent work [18].…”

Section: Integrability Structure Of Qhcgmentioning

confidence: 99%

“…Cellular automata are manybody systems where both time and space are discrete and the evolution deterministic. Recently they attracted a significant amount of attention in the study of strongly interacting out-of-equilibrium systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], as they admit analytical solutions of dynamics and exhibit wast range of dynamical phenomena, which also occur in more complicated systems. Thus, they provide an optimal setup to test different conjectures rigorously.…”

Section: Introductionmentioning

confidence: 99%

Operator spreading in quantum hardcore gases

Medenjak¹

2022

Preprint

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In this article we study integrable quantum cellular automata (QHCG) with an arbitrary local Hilbert space dimension, and discuss the matrix product ansatz based approach for solving the dynamics of local operators analytically. Subsequently, we focus on the dynamics of operator spreading, in particular on the out-of-time ordered correlation functions (OTOCs) and on the operator weight spreading. Both of the quantities are believed to provide signifying features of integrable systems and quantum chaos. We show that in QHCG OTOCs spread diffusively and that in the limit of the large local Hilbert space dimension they increase linearly with time, despite their integrability. On the other hand, it was recently conjectured that operator weight front, which is associated with the extent of operators, spreads diffusively in both, integrable and generic systems, but its decay seems to differ in these two cases [1]. We observe that the spreading of operator weight front in QHCG is markedly different from chaotic, generic integrable and free systems, as the front freezes in the long time limit.

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“…This correspondence has been noted in multiple cases, see e.g. [22][23][24][25][26][27][28][29]; how general it is, and how the properties of the stochastic and integrable versions of the model are related, remain open questions.…”

mentioning

confidence: 98%

The Fredkin staircase: An integrable system with a finite-frequency Drude peak

Singh¹,

Vasseur²,

Gopalakrishnan³

2022

Preprint

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We introduce and explore an interacting integrable cellular automaton, the Fredkin staircase, that lies outside the existing classification of such automata, and has a structure that seems to lie beyond that of any existing Bethe-solvable model. The Fredkin staircase has two families of ballistically propagating quasiparticles, each with infinitely many species. Despite the presence of ballistic quasiparticles, charge transport is diffusive in the d.c. limit, albeit with a highly nongaussian dynamic structure factor. Remarkably, this model exhibits persistent temporal oscillations of the current, leading to a delta-function singularity (Drude peak) in the a.c. conductivity at nonzero frequency. We analytically construct an extensive set of operators that anticommute with the time-evolution operator; the existence of these operators both demonstrates the integrability of the model and allows us to lower-bound the weight of this finite-frequency singularity.

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Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps

Cited by 26 publications

References 70 publications

Integrable deformations of superintegrable quantum circuits

Integrable deformations of superintegrable quantum circuits

Operator spreading in quantum hardcore gases

The Fredkin staircase: An integrable system with a finite-frequency Drude peak

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