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 $$\mu$$ on a 1+1 dimensional lattice. This formulation provides an expansion in the hopping parameter $$\kappa$$ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling $$\beta_{pl}=1/g^2$$ and small values of the scalar self-coupling $$\lambda$$. In the opposite limit of infinitely large $$\lambda$$, the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Gauss's law is automatically satisfied and the introduction of $$\mu$$ has consequences only if we have an external electric field, $g^2=0$ or an explicit gauge symmetry breaking. The time continuum limit of the blocked transfer matrix can be obtained numerically and, for $g^2=0$ and 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 on-site repulsion. We extend this procedure for finite $$\beta_{pl}$$ 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. Finally, we propose an optical lattice implementations involving a ladder structure.
- Authors:
-
- Univ. of Iowa, Iowa City, IA (United States); Univ. of California, Riverside, CA (United States)
- Univ. of Iowa, Iowa City, IA (United States)
- Univ. of California, Riverside, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of Iowa, Iowa City, IA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); USDOD
- OSTI Identifier:
- 1660402
- Alternate Identifier(s):
- OSTI ID: 1223562
- Grant/Contract Number:
- SC0010114; FG02-05ER41368; FG02-91ER40664; DMR-1411345; PHY11-25915
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology
- Additional Journal Information:
- Journal Volume: 92; Journal Issue: 7; Journal ID: ISSN 1550-7998
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice gauge theory; Quantum simulations with cold atoms
Citation Formats
Bazavov, A., Meurice, Y., Tsai, S. -W., Unmuth-Yockey, J., and Zhang, Jin. Gauge-invariant implementation of the Abelian-Higgs model on optical lattices. United States: N. p., 2015.
Web. doi:10.1103/physrevd.92.076003.
Bazavov, A., Meurice, Y., Tsai, S. -W., Unmuth-Yockey, J., & Zhang, Jin. Gauge-invariant implementation of the Abelian-Higgs model on optical lattices. United States. https://doi.org/10.1103/physrevd.92.076003
Bazavov, A., Meurice, Y., Tsai, S. -W., Unmuth-Yockey, J., and Zhang, Jin. Wed .
"Gauge-invariant implementation of the Abelian-Higgs model on optical lattices". United States. https://doi.org/10.1103/physrevd.92.076003. https://www.osti.gov/servlets/purl/1660402.
@article{osti_1660402,
title = {Gauge-invariant implementation of the Abelian-Higgs model on optical lattices},
author = {Bazavov, A. and Meurice, Y. and Tsai, S. -W. and Unmuth-Yockey, J. and Zhang, Jin},
abstractNote = {We present a gauge-invariant effective action for the Abelian Higgs model (scalar electrodynamics) with a chemical potential $\mu$ on a 1+1 dimensional lattice. This formulation provides an expansion in the hopping parameter $\kappa$ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling $\beta_{pl}=1/g^2$ and small values of the scalar self-coupling $\lambda$. In the opposite limit of infinitely large $\lambda$, the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Gauss's law is automatically satisfied and the introduction of $\mu$ has consequences only if we have an external electric field, $g^2=0$ or an explicit gauge symmetry breaking. The time continuum limit of the blocked transfer matrix can be obtained numerically and, for $g^2=0$ and 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 on-site repulsion. We extend this procedure for finite $\beta_{pl}$ 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. Finally, we propose an optical lattice implementations involving a ladder structure.},
doi = {10.1103/physrevd.92.076003},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 7,
volume = 92,
place = {United States},
year = {Wed Oct 14 00:00:00 EDT 2015},
month = {Wed Oct 14 00:00:00 EDT 2015}
}
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