Quantum link models: A discrete approach to gauge theories

Chandrasekharan, Shailesh; Wiese, U.‐J.

doi:10.1016/s0550-3213(97)80041-7

Cited by 321 publications

(325 citation statements)

References 41 publications

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“…The Hamiltonian of the quantum dimer model coincides with the Hamiltonian of the (2 + 1)-d U(1) quantum link model [20][21][22]. However, the corresponding Gauss law is realized differently.…”

Section: A Modelmentioning

confidence: 88%

Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

et al. 2016

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We present detailed analytic calculations of finite-volume energy spectra, mean-field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. An emergent approximate spontaneously broken SO(2) symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phononlike excitation, which is massless at the Rokhsar-Kivelson (RK) point, exists far beyond this point. The Goldstone physics is captured by a systematic low-energy effective field theory. We determine its low-energy parameters by matching the analytic effective field theory with exact diagonalization results. This confirms that the model exists in the columnar (and not in a plaquette or mixed) phase all the way to the RK point.

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Section: A Modelmentioning

confidence: 88%

Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

et al. 2016

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“…A different mechanism of dimensional reduction was proposed in the context of the Dtheory regularization of non-Abelian gauge theories [28,29,30]. Here a non-Abelian gauge theory in five dimensions arises as a low-energy effective description of a five-dimensional quantum link model.…”

Section: Dimensional Reductionmentioning

confidence: 99%

Lattice gauge theory approach to spontaneous symmetry breaking from an extra dimension

Irges

Knechtli

2007

Nuclear Physics B

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We present lattice simulation results corresponding to an SU(2) pure gauge theory defined on the orbifold space E 4 × I 1 , where E 4 is the four-dimensional Euclidean space and I 1 is an interval, with the gauge symmetry broken to a U(1) subgroup at the two ends of the interval by appropriate boundary conditions. We demonstrate that the U(1) gauge boson acquires a mass from a Higgs mechanism. The mechanism is driven by two of the extra-dimensional components of the five-dimensional gauge field which play respectively the role of the longitudinal component of the gauge boson and a massive real physical scalar, the Higgs particle. Despite the non-renormalizable nature of the theory, we observe only a mild cut-off dependence of the physical observables. We also show evidence that there is a region in the parameter space where the system behaves in a way consistent with dimensional reduction.

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“…the lines discussed here can be made in the quantum link D-theory formulation of the problem [12,13].…”

mentioning

confidence: 99%

Meron-Cluster Solution of Fermion Sign Problems

1999

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We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for non-relativistic lattice fermions. A configuration of fermion world-lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron-clusters contribute 0 to the path integral, while all other configurations contribute 1. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.Comment: 4 pages, ReVTe

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Quantum link models: A discrete approach to gauge theories

Cited by 321 publications

References 41 publications

Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

Lattice gauge theory approach to spontaneous symmetry breaking from an extra dimension

Meron-Cluster Solution of Fermion Sign Problems

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