Quantum Slow Relaxation and Metastability due to Dynamical Constraints

Lan, Zhihao; Horssen, Merlijn van; Powell, Stephen; Garrahan, Juan P.

doi:10.1103/physrevlett.121.040603

Cited by 121 publications

(84 citation statements)

References 76 publications

(69 reference statements)

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“…(1), but an alternative perspective on this question involves the time dependence of observables after a quantum quench [2]. Our results here suggest that interesting behavior should occur at large V (around V /t 5), where ETH begins to break down, and we indeed observe signatures of slow relaxation and metastability at such parameters [36]. Another interesting extension is the disordered QDM and its possible connections to many-body localization [37].…”

Section: Discussionmentioning

confidence: 68%

Eigenstate thermalization hypothesis in quantum dimer models

Lan

Powell

2017

Phys. Rev. B

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We use exact diagonalization to study the eigenstate thermalization hypothesis (ETH) in the quantum dimer model on the square and triangular lattices. Due to the nonergodicity of the local plaquette-flip dynamics, the Hilbert space, which consists of highly constrained close-packed dimer configurations, splits into sectors characterized by topological invariants. We show that this has important consequences for ETH: We find that ETH is clearly satisfied only when each topological sector is treated separately, and only for moderate ratios of the potential and kinetic terms in the Hamiltonian. By contrast, when the spectrum is treated as a whole, ETH breaks down on the square lattice and, apparently, also on the triangular lattice. These results demonstrate that quantum dimer models have interesting thermalization dynamics.

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Section: Discussionmentioning

confidence: 68%

Eigenstate thermalization hypothesis in quantum dimer models

Lan

Powell

2017

Phys. Rev. B

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“…We finish by noting that recent works suggest that other kinetic constraints, beyond those provided by con-finement, can also lead to nonthermal behavior. [29][30][31][32][33][34][35][36][37][38] This may have important implications for experiments on Rydberg gases. 28 of expectation values in the diagonal and microcanonical ensembles.…”

Section: Discussionmentioning

confidence: 99%

“…28 These models have been seen to have a polynomial-in-the-systemsize number of nonthermal states which are distributed throughout the many-body spectrum of the model. [29][30][31][32][33][34] There are also examples of nonthermal behavior in nonintegrable models with constrained dynamics, which includes the aforementioned models of Rydberg atoms and quantum dimer models, [35][36][37][38] and models with long-range interactions. 39,40 One significant issue in studying ETH is the lack of available techniques.…”

Section: Introductionmentioning

confidence: 99%

Signatures of rare states and thermalization in a theory with confinement

2019

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There is a dichotomy in the nonequilibrium dynamics of quantum many body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new 'meson' excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. We highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously. arXiv:1808.10782v2 [cond-mat.str-el]

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“…21,22 Similar type of physics has recently been explored in quantum systems where a "quasi many-body localized" behavior was proposed to occur in the absence of disorder. [23][24][25][26][27][28][29][30][31][32][33][34][35] Recently, a striking phenomenon suggestive of a different mechanism of weak ergodicity breaking was discovered experimentally. 36 A Rydberg atoms platform [36][37][38] was used to realize a quantum model with kinetic constraints induced by strong nearest-neighbour repulsion between atoms in excited states.…”

Section: Introductionmentioning

confidence: 99%

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

et al. 2018

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Recent realization of a kinetically-constrained chain of Rydberg atoms by Bernien et al. [Nature 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work, Turner et al. [arXiv:1711.03528], such dynamics was attributed to the existence of "quantum scarred" eigenstates in the many-body spectrum of the experimentally realized model. Here we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify non-ergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit sub-thermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum-scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of "canonical" thermalization. arXiv:1806.10933v2 [cond-mat.quant-gas]

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Quantum Slow Relaxation and Metastability due to Dynamical Constraints

Cited by 121 publications

References 76 publications

Eigenstate thermalization hypothesis in quantum dimer models

Eigenstate thermalization hypothesis in quantum dimer models

Signatures of rare states and thermalization in a theory with confinement

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

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