Violation of cluster decomposition and absence of light cones in local integer and half-integer spin chains

Dell’Anna, Luca; Salberger, Olof; Barbiero, Luca; Trombettoni, Andrea; Korepin, V. E.

doi:10.1103/physrevb.94.155140

Cited by 55 publications

(133 citation statements)

References 42 publications

(51 reference statements)

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“…Interestingly, we also found a singly-degenerate excited state with higher energy in the S z tot = 0 sector; it has dynamical exponent z 0 = 2.71 < z. The proximity of z 0 to the previous DMRG result [20] suggests that these authors worked in the S z tot = 0 sector, thus missing the lowest excitations. We have also analyzed the excitations in the S As we tune c away from 1, the groundstate is still annihilated by all the local interaction terms, as is the case in (2) [9].…”

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confidence: 71%

Quantum spin chains with multiple dynamics

2017

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Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultra-cold atoms. We investigate such non-trivial quantum dynamics in a new setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled groundstate, but a gapless excitation spectrum that is poorly understood. By using large-scale DMRG simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2 ≤ z < 2.7, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wavefunction for the groundstate, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the non-equilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in 2d.It is common for many-body quantum systems to possess multiple time-scales that determine the low-energy dynamics. In a gapless system, the dynamics will be characterized by the dispersion relation of the excited states (quasiparticles need not exist), E = Ak z , where k is the wavevector of the mode and z the dynamical exponent. Different modes can have different z exponents. For instance, a metal near a quantum critical point can have different dispersions for the electrons and the various order parameter fluctuations [1][2][3][4][5][6]. However, this phenomenon has been far less studied in other types of systems. Many studies have examined simpler systems, such as models described by relativistic conformal field theories having z = 1, which enjoy additional symmetries that constrain the dynamics [3,7,8].In this work, we reveal multiple dynamical exponents in a new setting: a strongly correlated 1d spin system. Further, these exponents will be shown to vary continuously as a function of a coupling in the Hamiltonian. The spin 1 quantum spin chain in question is a generalization of the so-called Motzkin Hamiltonian introduced by Bravyi et al [9]. Its groundstate can be determined exactly but not its excitation spectrum. With the help of large-scale Density Matrix Renormalization Group (DMRG) simulations, we discover low lying excitations with different dynamical exponents. In order to gain insight in the low-lying spectrum we determine a continuum version of the groundstate, and find a parent Hamiltonian. The latter possesses an excitation spectrum that is distinct from the spin chain but can provide useful insight into the construction of the full low energy field theory. This illustrates how a given groundstate can have starkly different excitations, and offers some g...

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confidence: 71%

Quantum spin chains with multiple dynamics

2017

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“…The deformation induced by t = 1 keeps the model frustration-free [14], and, while for t = 1 we recover the undeformed model [10][11][12], for t > 1 (t < 1) the paths having larger (smaller) h are favored in the ground state. Notice that for t = 1 one can have analytical expressions for the magnetizatazion and the z − z correlation functions, which were tested against DMRG results in [12]. However, for t = 1 the corresponding results are not available and therefore we will rely on DMRG results to have a physical description of the properties of the model.…”

Section: Pacs Numbersmentioning

confidence: 63%

“…and, as exactly shown in [12], an exponential decay of S [25] thus resembling the XY phase of XXZ models but, with the key feature that both AL decay and CDP are violated for s = 2.…”

Section: Pacs Numbersmentioning

confidence: 76%

“…Among others interesting aspects, their importance is given by the fact that they own a level of entanglement entropy which strongly exceeds the one exhibited by other previously known local models. Relevantly, also for half-integer spins, a similar class of Hamiltonians, the Fredkin spin chains, exhibiting the same features [12,13] has been introduced. In addition to their entanglement properties Motzkin chains own further very peculiar properties.…”

Section: Pacs Numbersmentioning

confidence: 99%

“…of the entanglement entropy [12]. Very recently, a deformed version of Motzkin [14] and of Fredkin [15] [19,20].…”

Section: Pacs Numbersmentioning

confidence: 99%

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Haldane topological orders in Motzkin spin chains

et al. 2017

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Motzkin spin chains are frustration-free models whose ground-state is a combination of Motzkin paths. The weight of such path contributions can be controlled by a deformation parameter t. As a function of the latter these models, beside the formation of domain wall structures, exhibit gapped Haldane topological orders with constant decay of the string order parameters for t < 1. A behavior compatible with a Berezinskii-KosterlitzThouless phase transition at t = 1 is also presented. By means of numerical calculations we show that the topological properties of the Haldane phases depend on the spin value. This allows to classify different kinds of hidden antiferromagnetic Haldane gapped regimes associated to nontrivial features like symmetry-protected topological order. Our results from one side allow to clarify the physical properties of Motzkin frustration-free chains and from the other suggest them as a new interesting and paradigmatic class of local spin Hamiltonians. [6] has been discovered for spin-1 XXZ Heisenberg chains. This has driven significant efforts to look for new kinds of models whose topological order can be described in terms of a SOP [7] motivating the discovery of the celebrated AffleckKennedy-Lieb-Tasaki (AKLT) model [8]. Although the argument of Haldane is given for integer spin chains, only integer spin XXZ-like and AKLT-like chains own topological HP and is therefore non-trivial to find and study new classes of Hamiltonians where HP emerges. Thanks to the strongest quantum "resource", namely the entanglement, spin models have also a fundamental role in the simulation of quantum logical gates for quantum computation [4]. For this reason finding and studying Hamiltonians with highly entangled spins is currently one of the most challenging and intriguing fields in quantum physics. In this direction local integer frustration-free spin Hamiltonians whose ground-state can be expressed as a combination of Motzkin paths [9] have been recently introduced [10,11]. Among others interesting aspects, their importance is given by the fact that they own a level of entanglement entropy which strongly exceeds the one exhibited by other previously known local models. Relevantly, also for half-integer spins, a similar class of Hamiltonians, the Fredkin spin chains, exhibiting the same features [12,13] has been introduced. In addition to their entanglement properties Motzkin chains own further very peculiar properties. Indeed, even if they are purely local models, for high spin values s (i.e., s ≥ 2) they behave as de facto long range Hamiltonians being able to violate cluster decomposition properties (CDP) and area law (AL) scaling DMRG local magnetization for a system of length 2n = 60 at different t deformation values S z i for c) s = 1 and d) s = 2. Lower panels: Thermodynamic limit of the gap ∆ = E1 − E0 as a function of t for e) s = 1 (red circles) and f) s = 2 (blue squares). The continuos lines are fitted with the form ∼ exp(−b/ √ tc − t) with tc = 1 and b a fitting parameter. The thermodynamic limit ...

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Generalized Entanglement Entropy in New Spin Chains

Sugino

Korepin

2020

Springer Proceedings in Physics

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Violation of cluster decomposition and absence of light cones in local integer and half-integer spin chains

Cited by 55 publications

References 42 publications

Quantum spin chains with multiple dynamics

Quantum spin chains with multiple dynamics

Haldane topological orders in Motzkin spin chains

Generalized Entanglement Entropy in New Spin Chains

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