We discuss the U(1)-Higgs model in two dimensions in the strongly coupled regime.If we neglect the plaquette interactions, we generate an effective theory where link variables are integrated out, producing 4-field operators.Plaquette interactions can be restored order by order as in recent calculations with staggered fermions.In the case of a SU(2) gauge theory with fermions, this strong coupling expansion can be related to the strong coupling expansion of Fermi-Hubbard models possibly implementable on optical lattice.We would like to provide a similar construction relating the U(1)-Higgs model to some Bose-Hubbard model.As a first step in this direction, we discuss a recent proposal to implement the O(2) model on optical lattices using a 87 Rb and 41 K Bose-Bose mixture of cold atoms.We discuss the U(1)-Higgs model in two dimensions in the strongly coupled regime.If we neglect the plaquette interactions, we generate an effective theory where link variables are integrated out, producing 4-field operators.Plaquette interactions can be restored order by order as in recent calculations with staggered fermions.In the case of a SU(2) gauge theory with fermions, this strong coupling expansion can be related to the strong coupling expansion of Fermi-Hubbard models possibly implementable on optical lattice.We would like to provide a similar construction relating the U(1)-Higgs model to some Bose-Hubbard model.As a first step in this direction, we discuss a recent proposal to implement the O(2) model on optical lattices using a 87 Rb and 41 K Bose-Bose mixture of cold atoms.

International Symposium on Lattice Field Theory (LATTICE)May 21, 20151 citation

Local gauge symmetry on optical lattices?

Yuzhi Liu A, Yannick Meurice, Shan-Wen Tsai

The versatile technology of cold atoms confined in optical lattices allows the creation of a vast number of lattice geometries and interactions, providing a promising platform for emulating various lattice models.This opens the possibility of letting nature take care of sign problems and real time evolution in carefully prepared situations.Up to now, experimentalists have succeeded to implement several types of Hubbard models considered by condensed matter theorists.In this proceeding, we discuss the possibility of extending this effort to lattice gauge theory.We report recent efforts to establish the strong coupling equivalence between the Fermi Hubbard model and SU(2) pure gauge theory in 2+1 dimensions by standard determinantal methods developed by Robert Sugar and collaborators.We discuss the possibility of using dipolar molecules and external fields to build models where the equivalence holds beyond the leading order in the strong coupling expansion.The versatile technology of cold atoms confined in optical lattices allows the creation of a vast number of lattice geometries and interactions, providing a promising platform for emulating various lattice models.This opens the possibility of letting nature take care of sign problems and real time evolution in carefully prepared situations.Up to now, experimentalists have succeeded to implement several types of Hubbard models considered by condensed matter theorists.In this proceeding, we discuss the possibility of extending this effort to lattice gauge theory.We report recent efforts to establish the strong coupling equivalence between the Fermi Hubbard model and SU(2) pure gauge theory in 2+1 dimensions by standard determinantal methods developed by Robert Sugar and collaborators.We discuss the possibility of using dipolar molecules and external fields to build models where the equivalence holds beyond the leading order in the strong coupling expansion.

arXiv:1211.4126International Symposium on Lattice Field Theory (LATTICE)Dec 20, 20123 citations

Atomic Quantum Simulation of the Lattice Gauge-Higgs Model: Higgs Couplings and Emergence of Exact Local Gauge Symmetry

Kenichi Kasamatsu, Ikuo Ichinose, Tetsuo Matsui

Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.

arXiv:1212.4952Physical Review LettersSep 9, 201350 citations

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

Yoshihito Kuno, Shinya Sakane, Kenichi Kasamatsu +2 more

In this paper, we study theoretically atomic quantum simulations of a U(1) gauge-Higgs model on a three-dimensional (3D) spatial lattice by using an extended Bose-Hubbard model with intersite repulsions on a 3D optical lattice. Here, the phase and density fluctuations of the boson variable on each site of the optical lattice describe the vector potential and the electric field on each link of the gauge-model lattice, respectively. The target gauge model is different from the standard Wilson-type U(1) gauge-Higgs model because it has plaquette and Higgs interactions with asymmetric couplings in the space-time directions. Nevertheless, the corresponding quantum simulation is still important as it provides us with a platform to study unexplored time-dependent phenomena characteristic of each phase in the general gauge-Higgs models. To determine the phase diagram of the gauge-Higgs model at zero temperature, we perform Monte Carlo simulations of the corresponding 3+1-dimensional U(1) gauge-Higgs model, and obtain the confinement and Higgs phases. To investigate the dynamical properties of the gauge-Higgs model, we apply the Gross-Pitaevskii equations to the extended Bose-Hubbard model. We simulate the time evolution of an electric flux that initially is put on a straight line connecting two external point charges. We also calculate the potential energy between this pair of charges and obtain the string tension in the confinement phase. Finally, we propose a feasible experimental setup for the atomic simulations of this quantum gauge-Higgs model on the 3D optical lattice. These results may serve as theoretical guides for future experiments.In this paper, we study theoretically atomic quantum simulations of a U(1) gauge-Higgs model on a three-dimensional (3D) spatial lattice by using an extended Bose-Hubbard model with intersite repulsions on a 3D optical lattice. Here, the phase and density fluctuations of the boson variable on each site of the optical lattice describe the vector potential and the electric field on each link of the gauge-model lattice, respectively. The target gauge model is different from the standard Wilson-type U(1) gauge-Higgs model because it has plaquette and Higgs interactions with asymmetric couplings in the space-time directions. Nevertheless, the corresponding quantum simulation is still important as it provides us with a platform to study unexplored time-dependent phenomena characteristic of each phase in the general gauge-Higgs models. To determine the phase diagram of the gauge-Higgs model at zero temperature, we perform Monte Carlo simulations of the corresponding 3+1-dimensional U(1) gauge-Higgs model, and obtain the confinement and Higgs phases. To investigate the dynamical properties of the gauge-Higgs model, we apply the Gross-Pitaevskii equations to the extended Bose-Hubbard model. We simulate the time evolution of an electric flux that initially is put on a straight line connecting two external point charges. We also calculate the potential energy between this pair of charges and obtain the string tension in the confinement phase. Finally, we propose a feasible experimental setup for the atomic simulations of this quantum gauge-Higgs model on the 3D optical lattice. These results may serve as theoretical guides for future experiments.

arXiv:1605.02502Physical Review ADec 27, 201618 citations

Progress towards quantum simulating the classical O(2) model

Haiyuan Zou, Yuzhi Liu A, Chen-Yen Lai +8 more

We connect explicitly the classical $\text{O}(2)$ model in $1+1$ dimensions, a model sharing important features with $\text{U}(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}\mathrm{Rb}$ and $^{41}\mathrm{K}$ Bose-Bose mixture.We connect explicitly the classical $\text{O}(2)$ model in $1+1$ dimensions, a model sharing important features with $\text{U}(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}\mathrm{Rb}$ and $^{41}\mathrm{K}$ Bose-Bose mixture.

arXiv:1403.5238Physical Review ADec 1, 201441 citations

Quantum simulation of ( 1 + 1 )-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases

Yoshihito Kuno, Shinya Sakane, Kenichi Kasamatsu +2 more

We present a theoretical study of quantum simulations of ( $1+1$ )-dimensional U(1) lattice gauge-Higgs models, which contain a compact U(1) gauge field and a Higgs matter field, by using ultracold bosonic gases on a one-dimensional optical lattice. Starting from the extended Bose-Hubbard model with on-site and nearest-neighbor interactions, we derive the U(1) lattice gauge-Higgs model as a low-energy effective theory. The derived gauge-Higgs model exhibits nontrivial phase transitions between the confinement and Higgs phases, and we discuss the relation with the phase transition in the extended Bose-Hubbard model. Finally, we study the real-time dynamics of an electric flux by the Gross-Pitaevskii equations and the truncated Wigner approximation. The dynamics is governed by a bosonic analog of the Schwinger mechanism---i.e., the shielding of an electric flux by a condensation of Higgs fields, which occurs differently in the Higgs and the confinement phases. These results, together with the obtained phase diagrams, shall guide experimentalists in designing quantum simulations of the gauge-Higgs models by using cold gases.We present a theoretical study of quantum simulations of ($1+1$)-dimensional U(1) lattice gauge-Higgs models, which contain a compact U(1) gauge field and a Higgs matter field, by using ultracold bosonic gases on a one-dimensional optical lattice. Starting from the extended Bose-Hubbard model with on-site and nearest-neighbor interactions, we derive the U(1) lattice gauge-Higgs model as a low-energy effective theory. The derived gauge-Higgs model exhibits nontrivial phase transitions between the confinement and Higgs phases, and we discuss the relation with the phase transition in the extended Bose-Hubbard model. Finally, we study the real-time dynamics of an electric flux by the Gross-Pitaevskii equations and the truncated Wigner approximation. The dynamics is governed by a bosonic analog of the Schwinger mechanism---i.e., the shielding of an electric flux by a condensation of Higgs fields, which occurs differently in the Higgs and the confinement phases. These results, together with the obtained phase diagrams, shall guide experimentalists in designing quantum simulations of the gauge-Higgs models by using cold gases.

arXiv:1605.00333Physical review. D/Physical review. D.May 16, 201763 citations

We connect explicitly the classical

\text{O}(2)

model in

1+1

dimensions, a model sharing important features with

\text{U}(1)

lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a

^{87}\mathrm{Rb}

and

^{41}\mathrm{K}

Bose-Bose mixture.

We present a theoretical study of quantum simulations of (

1+1

)-dimensional U(1) lattice gauge-Higgs models, which contain a compact U(1) gauge field and a Higgs matter field, by using ultracold bosonic gases on a one-dimensional optical lattice. Starting from the extended Bose-Hubbard model with on-site and nearest-neighbor interactions, we derive the U(1) lattice gauge-Higgs model as a low-energy effective theory. The derived gauge-Higgs model exhibits nontrivial phase transitions between the confinement and Higgs phases, and we discuss the relation with the phase transition in the extended Bose-Hubbard model. Finally, we study the real-time dynamics of an electric flux by the Gross-Pitaevskii equations and the truncated Wigner approximation. The dynamics is governed by a bosonic analog of the Schwinger mechanism---i.e., the shielding of an electric flux by a condensation of Higgs fields, which occurs differently in the Higgs and the confinement phases. These results, together with the obtained phase diagrams, shall guide experimentalists in designing quantum simulations of the gauge-Higgs models by using cold gases.