Topological blocking in quantum quench dynamics

Kells, Graham; Sen, Diptiman; Slingerland, Joost; Vishveshwara, Smitha

doi:10.1103/physrevb.89.235130

Cited by 40 publications

(47 citation statements)

References 96 publications

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“…By contrast, for nonbipartite lattices, the winding numbers can be defined only modulo 2, and there are four sectors defined by a pair of Z 2 invariants [24,25]. Noting the effect of topological blocking on quench dynamics [26] and recalling the case of integrable models, where the extensive number of conserved quantities invalidates ETH, it is natural to ask whether the existence of these topological invariants will influence ETH in the QDM [18].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Eigenstate thermalization hypothesis in quantum dimer models

Lan

Powell

2017

Phys. Rev. B

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“…In order to gain a better insight for the case in which the condition (5) is violated, we write explicitly the time evolution propagator (14) up to second order in :…”

Section: B Quench With the Xxz Hamiltonian In A Transverse Fieldmentioning

confidence: 99%

“…A number of theoretical works dealt with the problem of studying the dynamics in topological systems after a quantum quench [11][12][13][14][15][16][17][18][19]. A general analysis of the behavior of all the indicators of a symmetry-protected topological phase in the presence of a quantum quench is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Destruction of string order after a quantum quench

et al. 2016

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We investigate the evolution of string order in a spin-1 chain following a quantum quench. After initializing the chain in the Affleck-Kennedy-Lieb-Tasaki state, we analyze in detail how string order evolves as a function of time at different length scales. The Hamiltonian after the quench is chosen either to preserve or to suddenly break the symmetry which ensures the presence of string order. Depending on which of these two situations arises, string order is either preserved or lost even at infinitesimal times in the thermodynamic limit. The fact that nonlocal order may be abruptly destroyed, what we call string-order melting, makes it qualitatively different from typical order parameters in the manner of Landau. This situation is thoroughly characterized by means of numerical simulations based on matrix product states algorithms and analytical studies based on a short-time expansion for several simplified models.

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“…Isolated Majorana modes at the wire ends are no longer localized low-energy excitations of the array. Had they been used for quantum computation, a transition to this phase would imply that some, but not necessarily all, encoded information would be lost [60]. This phase still supports localized Majorana modes, but they appear now as collective modes centered at those dodecagonal plaquettes with W (12) = −1.…”

Section: B the 3-junction Network And The Y-k Modelmentioning

confidence: 99%

Kitaev spin models from topological nanowire networks

2014

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We show that networks of superconducting topological nanowires can realize the physics of exactly solvable Kitaev spin models on trivalent lattices. This connection arises from the low-energy theory of both systems being described by a tight-binding model of Majorana modes. In Kitaev spin models the Majorana description provides a convenient representation to solve the model, whereas in an array of Josephson junctions of topological nanowires it arises from localized physical Majorana modes tunneling between the wire ends. We explicitly show that an array of junctions of three wires-a setup relevant to topological quantum computing with nanowires-can realize the Yao-Kivelson model, a variant of Kitaev spin models on a decorated honeycomb lattice. Employing properties of the latter, we show that the network can be constructed to give rise to two-dimensional collective topological states characterized by Chern numbers ν = 0, ±1, and ±2, and that defects in the array can be associated with vortex-like quasiparticle excitations. In addition we show that the collective states are stable in the presence of disorder and superconducting phase fluctuations. When the network is operated as a quantum information processor, the connection to Kitaev spin models implies that decoherence mechanisms can in general be understood in terms of proliferation of the vortex-like quasiparticles.

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Topological blocking in quantum quench dynamics

Cited by 40 publications

References 96 publications

Eigenstate thermalization hypothesis in quantum dimer models

Eigenstate thermalization hypothesis in quantum dimer models

Destruction of string order after a quantum quench

Kitaev spin models from topological nanowire networks

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