{"title":"Operator dynamics and entanglement in space-time dual Hadamard lattices","authors":"Pieter W Claeys and Austen Lamacraft","doi":"10.1088/1751-8121/ad776a","DOIUrl":null,"url":null,"abstract":"Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys.49 112104) and in the limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A: Mathematical and Theoretical","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1751-8121/ad776a","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys.49 112104) and in the limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here.
在空间晶格和离散时间中定义的多体量子动力学--无论是频闪弗洛凯系统还是量子电路--几年来一直是一个活跃的研究领域。由于空间和时间都是离散的,自然会产生一个问题:什么时候可以把这样的模型看作是在空间和时间上都在单元地演化?具有这种特性(有时也称为时空二重性)的模型已被证明具有许多与纠缠增长和相关性有关的有趣特征。在(砖砌)量子电路的背景下,该特性产生的一种自然方式是选择双重单元门:在空间和时间方向上都是单元的两个站点算子。我们介绍了一类每个位点有 q 个状态的模型,这些状态在方格上由复数分割函数定义,并以 q × q 哈达玛矩阵来表示,具有时空对偶性。它们可以被解释为特殊的对偶单元电路或频闪演化系统,并概括了研究得很透彻的自偶踢伊辛模型。我们探讨了克利福德电路中的算子动力学,与克利福德蜂窝自动机(Schlingemann et al 2008 J. Math. Phys.49 112104)和多体混沌的经典时空猫模型(Gutkin et al 2021 Nonlinearity34 2800)建立了联系。我们为一个大的亚家族建立了可积分性和相应的守恒电荷,并展示了最近的论文(Lotkov et al 2022 Phys.
期刊介绍:
Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.