The phase diagram of the three-dimensionalZ2 gauge Higgs system at zero and finite temperature

Genovese, Luigi; Gliozzi, F.; Rago, Antonio; Torrero, C.

doi:10.1016/s0920-5632(03)01713-4

Cited by 17 publications

(23 citation statements)

References 16 publications

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“…9 the authors used an approximate mapping of TCM onto the anisotropic Z 2 gauge Higgs model, and computed the phase diagram of the corresponding 3D classical model in the isotropic limit, extending previous studies of the Z 2 gauge Higgs model, see Ref. 13, to larger system sizes. The behavior of TCM in a parallel field and/or a transverse field was also studied using several perturbative (high order) treatments [10][11][12] .…”

Section: Introductionmentioning

confidence: 76%

Phase diagram of the toric code model in a parallel magnetic field

Deng²,

Prokof’ev³

2012

Phys. Rev. B

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Ground-state phase diagram of the toric code model in a parallel magnetic field has three distinct phases: topological, charge-condensed, and vortex-condensed states. To study it we consider an implicit local order parameter characterizing the transition between the topological and chargecondensed phases, and sample it using continuous-time Monte Carlo simulations. The corresponding second-order transition line is obtained by finite-size scaling analysis of this order parameter. Symmetry breaking between charges and vortices along the first-order transition line is also observed, and our numerical result shows that the end point of the first-order transition line is located at h

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Section: Introductionmentioning

confidence: 76%

Phase diagram of the toric code model in a parallel magnetic field

Deng²,

Prokof’ev³

2012

Phys. Rev. B

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“…The conjecture was that the second-order lines might become first-order before merging. Subsequent simulations on lattices with up to 30 3 sites by Genovese et al 11 revealed strong finite-size effects in this region of the phase diagram and rejected the conjecture. The actual topology of connections between the lines remained unanswered, leaving three possible scenarios: ͑1͒ a single point where all three lines end, ͑2͒ disconnected first-order line, and ͑3͒ termination of second-order transitions at the first-order line, see inset in Fig.…”

Section: Introductionmentioning

confidence: 95%

Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model

et al. 2010

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We construct a mapping between the two-dimensional toric code model in external magnetic fields, h z and h x , and the three-dimensional classical Ising system with plaquette interactions, which is equivalent to the three-dimensional Z 2 gauge Higgs model with anisotropy between the imaginary time and spatial directions. The isotropic limit of the latter model was studied using Monte Carlo simulations on large ͑up to 60 3 ͒ lattices in order to determine the stability of the topological phase against generic magnetic field perturbations and to resolve fine details of the phase diagram. We find that the topological phase is bounded by second-order transition lines, which merge into a first-order line at what appears to be a multicritical point arising from the competition between the Higgs and confinement transitions in the Z 2 gauge system. An effective field theory for this type of multicritical point ͑if one actually exists͒ is not known. Our results have potential applications to frustrated magnets, quantum computation, lattice gauge models in particle physics, and critical phenomena.

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“…The two topological trivial phases are dual to each other with a self-dual line λ b = −0.5 ln tanh λ p as their phase boundary. Numerical pursuits of the phase diagram with increased system sizes and computational efforts [15][16][17][18] established the phase boundary between a disordered (magnetically ordered) phase and topological phase at around λ p 0.76 (λ b 0.223) with the critical λ p value from the topological phase toward the disordered phase displaying a very slight negative dependence upon increasing λ b . The goal of our QLT-based machine learning approach is to reproduce these known results in a way that can be extended to other models whose phase diagrams remain a open question in the future.…”

Section: Machine Learning Topological Phase Diagrammentioning

confidence: 99%

Machine learning Z2 quantum spin liquids with quasiparticle statistics

2017

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After decades of progress and effort, obtaining a phase diagram for a strongly-correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these non-local observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasi-particle statistics. We then use mutual statistics between the spinons and visons to detect a Z 2 quantum spin liquid in a multi-parameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed forward neural network. Furthermore we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

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The phase diagram of the three-dimensionalZ2 gauge Higgs system at zero and finite temperature

Cited by 17 publications

References 16 publications

Phase diagram of the toric code model in a parallel magnetic field

Phase diagram of the toric code model in a parallel magnetic field

Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model

Machine learning Z2 quantum spin liquids with quasiparticle statistics

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