Gauge-invariant implementation of the Abelian-Higgs model on optical lattices

Abstract

We present a gauge-invariant effective action for the Abelian Higgs model (scalar electrodynamics) with a chemical potential µ on a 1+1 dimensional lattice. This formulation provides an expansion in the hopping parameter κ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling β pl and small values of the scalar self-coupling λ. In the opposite limit of infinitely large λ, the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Their numerical implementation requires truncations but there is no sign problem for arbitrary values of µ. We show that the time continuum limit of the blocked transfer matrix can be obtained numerically and, in the limit of infinite β pl 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. We extend this procedure for finite β pl and derive a spin-1 approximation of the Hamiltonian. It involves new terms corresponding to transitions among the two species in the Bose-Hubbard model. We propose an optical lattice implementation involving a ladder structure.

Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model

“…(16). This brings no difficulties such as the negative-sign problem because the system involves only bosonic variables and has a positive definite probability.…”

“…(16). By replacing Φ x as Φ x → γ/ √ 2∆τ × φ x and choosing as ρ ′ 0 γ 2 /(2∆τ ) = ρ 0 , we obtainZ GH of Eq.…”

“…Stimulated by the enormous progress made in experimental ultra-cold atomic systems, theoretical proposals have been made for quantum simulations of various physical systems and associated phenomena [2,3]. One such proposal is atomic quantum simulation of lattice gauge theories (LGTs) [4][5][6][7][8][9][10][11][12][13][14][15][16].…”

“…(6), whose partition function is given by Eq. (16). Readers who are not interested in the details of the statistical analysis of the Monte-Carlo simulations in Sec.…”

Probing the conformal Calabrese-Cardy scaling with cold atoms

“…In the following, we use the spin-1 and spin-2 approximations for numerical calculations. Quantum simulators involving two species of bosonic atoms have been proposed for the spin-1 approximation [28,35]. This effort is directly related to recent attempts (for recent reviews see Refs.…”