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arXiv:1605.02502 · Physical Review A

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

Yoshihito Kuno, Shinya Sakane, Kenichi Kasamatsu, Ikuo Ichinose, Tetsuo Matsui

Published Dec 27, 2016• 18 citations
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Abstract

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.

DOI
10.1103/physreva.94.063641

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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 atomic quantum simulations of (1+1)(1+1)(1+1)-dimensional((1+1)(1+1)(1+1)D) U(1) gauge-Higgs models (GHMs) defined on a lattice. We explain how U(1) lattice GHMs appear from an extended Bose-Hubbard model (EBHM) describing ultra-cold atoms with a nearest neighbor repulsion in a 1D optical lattice. We first study a phase diagram of the 1D EBHM at low fillings by means of a quantum Monte-Carlo(MC) simulation. Next, we study the EBHM at large fillings and also GHMs by the MC simulations in the path-integral formalism and show that there are four phases, i.e., the Higgs phase(superfluid), the confinement phase (Mott insulator), and phases corresponding to the density wave and the supersolid. With the obtained phase diagrams, we investigate the relationship between the two models. Finally, we study real-time dynamic of an electric flux in the GHMs by the Gross-Pitaevskii equations and the truncated Wigner approximation.
We present a theoretical study of quantum simulations of (1+11+11+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.
In the previous works, we proposed atomic quantum simulations of the U(1) gauge-Higgs model by ultracold Bose gases. By studying extended Bose-Hubbard models (EBHMs) including long-range repulsions, we clarified the locations of the confinement, Coulomb, and Higgs phases. In this paper, we study the EBHM with nearest-neighbor repulsions in one and two dimensions at large fillings by the Gutzwiller variational method. We obtain phase diagrams and investigate dynamical behavior of electric flux from the gauge-theoretical point of view. We also study if the system exhibits glassy quantum dynamics in the absence and presence of quenched disorder. We explain that the obtained results have a natural interpretation in the gauge theory framework. Our results suggest important perspective on many-body localization in strongly correlated systems. They are also closely related to anomalously slow dynamics observed by recent experiments performed on the Rydberg atom chain, and our study indicates existence of similar phenomenon in two-dimensional space.
Lattice gauge theory has provided a crucial non-perturbative method in studying canonical models in high-energy physics such as quantum chromodynamics. Among other models of lattice gauge theory, the lattice gauge–Higgs model is a quite important one because it describes a wide variety of phenomena/models related to the Anderson–Higgs mechanism, such as superconductivity, the standard model of particle physics, and the inflation process of the early Universe. In this paper, we first show that atomic description of the lattice gauge model allows us to explore real-time dynamics of the gauge variables by using the Gross–Pitaevskii equations. Numerical simulations of the time development of an electric flux reveal some interesting characteristics of the dynamic aspect of the model and determine its phase diagram. Next, to realize a quantum simulator of the U(1) lattice gauge–Higgs model on an optical lattice filled by cold atoms, we propose two feasible methods: (i) Wannier states in the excited bands and (ii) dipolar atoms in a multilayer optical lattice. We pay attention to the constraint of Gauss's law and avoid nonlocal gauge interactions.
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.
This thesis presents our recent studies on quantum simulation of the Abelian Higgs lattice gauge theory with quantum systems engineered with ultracold atoms in optical lattices and quantum equilibration and thermalization dynamics in the context of Joule expansion in cold atom systems.In the first part, we give proposals for the analog quantum simulation of lattice gauge theories with cold atoms in optical lattices with current experimental techniques, aiming at maximal simplicity on both the theoretical and experimental side. We search for the suitable platform for quantum simulation of the (1+1)(1+1)(1+1)-dimensional Abelian Higgs model, which is the scalar quantum electrodynamics replacing the fermionic fields by complex scalar fields. We use a discrete tensor reformulation to smoothly connect the space-time isotropic version used in most numerical lattice simulations to the continuous-time limit corresponding to the Hamiltonian formulation. We propose to use the Bose Hubbard model as a quantum simulator to probe the conformal Calabrese-Cardy scaling of its O(2) limit with a chemical potential. We also propose to use a physical multileg ladder of atoms trapped in optical lattices and interacting with Rydberg-dressed interactions to quantum simulate the model and measure the Polyakov loop. Numeric results from the Monte Carlo, the tensor renormalization group and the density matrix renormalization group techniques are cross-checked to support our proposals.In the second part of this thesis, we investigate the Joule expansion of nonintegrable quantum systems that contain bosons or spinless fermions in one-dimensional lattices. Initially a barrier confines the particles to be in half of the system in a thermal state described by the canonical ensemble and is removed at time t=0t = 0t=0. We study the properties of the time-evolved density matrix, the diagonal ensemble density matrix and the corresponding canonical ensemble density matrix with an effective temperature determined by the total energy conservation. We discuss the equilibration and thermalization for the R\\'enyi entropy of subsystems, few-body observables and reduced density matrices in subsystems. We finally discuss the difference between bosons and fermions in finite size scaling of the effective temperature. We propose the Joule expansion as a way to dynamically create negative temperature states for fermion systems with repulsive interactions.