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

TL;DR

This paper develops a gauge-invariant effective action for the Abelian-Higgs model in 1+1 dimensions, using integration and tensor methods, and proposes an optical lattice implementation with potential quantum simulation applications.

Contribution

It introduces a novel gauge-invariant effective action for the Abelian-Higgs model and extends it to optical lattice setups, combining analytical and numerical techniques.

Findings

Monte Carlo simulations validate the hopping parameter expansion.

Tensor renormalization group methods enable analysis at infinite self-coupling.

The model's spectrum matches a two-species Bose-Hubbard model at large onsite repulsion.

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.