Dynamics and correlations in Motzkin and Fredkin spin chains

Dell’Anna, Luca; Barbiero, Luca; Trombettoni, Andrea

doi:10.1088/1742-5468/ab5703

Cited by 4 publications

(6 citation statements)

References 31 publications

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“…In this paper we have shown that the ground states of the novel quantum spin models under study exhibit a robust non-local behavior, the long-distance entanglement, in addition to the violation of cluster decomposition property. Since the mutual information gives a upper bound for the squared connected correlation functions, our results are in agreement with analytical [9,21] and numerical [16] results on the long-distance behavior of some spin correlators. The strong entanglement shared by any segments of the spin chains survives at infinite distances either if the subsystems are located close to the edges or inside the bulk.…”

Section: Discussionsupporting

confidence: 87%

“…the mutual information, I AB for the system A∪B made by two disjoint subsystems A and B, the quantity I AB does not vanish when the distance between A and B goes to infinity. This result is consistent with the fact that also some connected correlation functions do not vanish in the thermodynamic limit [9,16,21], being the mutual information an upper bound for normalized connected correlators [22,24].…”

supporting

confidence: 88%

“…11 (right panel) is due to the fact that the numbers D ( ) hh are zero for ( + h + h ) odd integers. This feature is also present in other ground-state quantities like the magnetization and the correlation functions [9,21].…”

Section: Fredkin Modelmentioning

confidence: 79%

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Long-distance entanglement in Motzkin and Fredkin spin chains

Dell’Anna

2019

SciPost Phys.

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We derive some entanglement properties of the ground states of two classes of quantum spin chains described by the Fredkin model, for half-integer spins, and the Motzkin model, for integer ones. Since the ground states of the two models are known analytically, we can calculate the entanglement entropy, the negativity and the quantum mutual information exactly. We show, in particular, that these systems exhibit long-distance entanglement, namely two disjoint regions of the chains remain entangled even when the separation is sent to infinity, i.e. these systems are not affected by decoherence. This strongly entangled behavior, occurring both for colorful versions of the models (with spin larger than 1/2 or 1, respectively) and for colorless cases (spin 1/2 and 1), is consistent with the violation of the cluster decomposition property. Moreover we show that this behavior involves disjoint segments located both at the edges and in the bulk of the chains. Contents arXiv:1904.05205v3 [cond-mat.stat-mech]The study of nonlocal properties and their consequences on the dynamics in addition to the violation of the area law for the entanglement entropy are certainly, at the present date, a very challenging field of research. The concept of locality plays a crucial role in physical theories, with far reaching consequences, a fundamental one being the cluster decomposition property [1,2]. This property implies that two-point connected correlation functions go to zero when the separation of the points goes to infinity. This is the reason why two systems very far apart, separated by a large distance, behave independently.Another aspect related to correlations is the quantum entanglement. In bipartite systems the von Neumann or entanglement entropy quantifies how the two parts of the whole system in a quantum state are entangled. This quantity measures non-local quantum correlations and has universal properties, like the fact that, for gapped systems in the ground states, it scales with the area of the boundary of the two subsystems [3]. This property is called area law and is valid for systems with shortrange interactions. In other words, if the interactions are short-ranged the information among the constituents of the system propagates with a finite speed involving a surface surrounding the source of the signal, like an electromagnetic impulse propagating with the speed of light. For critical onedimensional short-range systems the area law is violated logarithmically [4]. Quantum spin chains are promising tools for universal quantum computation [5] and the efficiency may be related to the amount of quantum entanglement. Spin systems with entanglement entropy larger than that dictated by the area law can be used for quantum computing even more efficiently, and breaking down the speed of the propagation of the excitations can represent a breakthrough for quantum information processing.Recently, novel quantum spin models have been introduced, with integer [6-8] (Motzkin model) and half-integer [9, 10] spins (Fredkin model), which...

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Section: Discussionsupporting

confidence: 87%

supporting

confidence: 88%

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Long-distance entanglement in Motzkin and Fredkin spin chains

Dell’Anna

2019

SciPost Phys.

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“…Eq. (7). In terms of the RW representation of configurations this corresponds to the set of RW excursions.…”

Section: B Equilibrium Phase Diagram From Numerical Mpsmentioning

confidence: 99%

“…random walk (RW) excursions, with appropriate endpoints, with an entanglement entropy which scales logarithmically in system size, thus violating the area law [1][2][3][4]. Furthermore, the model has slow unitary evolution [5][6][7][8] due to dynamical "jamming". With the addition of particular potential energy terms the model features a ground state phase transition between states of bounded and extensive entanglement entropy [9,10].…”

Section: Introductionmentioning

confidence: 99%

Slow dynamics and large deviations in classical stochastic Fredkin chains

2022

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The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical stochastic version of the Fredkin model, which can be thought of as a simple exclusion process subject to additional kinetic constraints, and study its classical stochastic dynamics. The ground state phase transition of the quantum chain implies an equilibrium phase transition in the stochastic problem, whose properties we quantify in terms of numerical matrix product states (MPS). The stochastic model displays slow dynamics, including power law decaying autocorrelation functions and hierarchical relaxation processes due to exponential localization. Like in other kinetically constrained models, the Fredkin chain has a rich structure in its dynamical large deviations -which we compute accurately via numerical MPS -including an active-inactive phase transition, and a hierarchy of trajectory phases connected to particular equilibrium states of the model. We also propose, via its height field representation, a generalization of the Fredkin model to two dimensions in terms of constrained dimer coverings of the honeycomb lattice.

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New trends in nonequilibrium statistical mechanics: classical and quantum systems

Spagnolo¹,

Dubkov²,

Valenti³

2020

J. Stat. Mech.

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The main aim of this special issue is to report recent advances and new trends in nonequilibrium statistical mechanics of classical and quantum systems, from both theoretical and experimental points of view, within an interdisciplinary context. In particular, the nonlinear relaxation processes in the dynamics of out-of-equilibrium systems and the role of the metastability and environmental noise will be overviewed. Three main areas of nonequilibrium statistical mechanics will be covered: slow relaxation phenomena and dissipative dynamics; long-range interactions and classical systems; quantum systems. New trends such as quantum thermodynamics and novel types of quantum phase transitions occurring in nonequilibrium steady states and topological phase transitions will be also highlighted.

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Dynamics and correlations in Motzkin and Fredkin spin chains

Cited by 4 publications

References 31 publications

Long-distance entanglement in Motzkin and Fredkin spin chains

Long-distance entanglement in Motzkin and Fredkin spin chains

Slow dynamics and large deviations in classical stochastic Fredkin chains

New trends in nonequilibrium statistical mechanics: classical and quantum systems

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