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Effective action for the Abelian-Higgs model for a gauge-invariant implementation on optical lattices
Conference proceeding   Open access

Effective action for the Abelian-Higgs model for a gauge-invariant implementation on optical lattices

Alexei Bazavov, Yannick Meurice, Shan-Wen Tsai, Judah Unmuth-Yockey and Jin Zhang
The 33rd International Symposium on Lattice Field Theory (LATTICE 2015) - Applications Beyond QCD (talks)
Proceedings of Science, v. 251
07/15/2016
DOI: 10.22323/1.251.0047
url
https://doi.org/10.22323/1.251.0047View
Published (Version of record) Open Access

Abstract

We present a gauge-invariant effective action for the Abelian-Higgs model in 1+1 dimensions. It is constructed by integrating out the gauge field and then using the hopping parameter expansion. The latter is tested with Monte Carlo simulations for small values of the scalar self-coupling. In the opposite limit, at infinitely large self-coupling, the Higgs mode is frozen and the partition function can be written in terms of local tensors and the tensor renormalization group blocking can be applied. The numerical implementation requires truncations and the time continuum limit of the blocked transfer matrix can be obtained numerically. At zero gauge coupling and with a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large onsite repulsion. The procedure is extended to finite gauge coupling and we derive a spin-1 approximation of the Hamiltonian which involves terms corresponding to transitions among the two species in the Bose-Hubbard model. An optical lattice implementation involving a ladder structure is proposed.
 Mathematical Models Approximation Computer simulation Coupling Energy spectra Invariants Optical lattices Partitions (mathematics) Tensors

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