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Register a new userCritical exponents in U(1) lattice gauge theory with a monopole term
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We investigate critical properties of the phase transition in the four-dimensional compact U(1) lattice gauge theory supplemented by a monopole term for values of the monopole coupling $lambda$ such that the transition is of second order. It has been previously shown that at $lambda= 0.9$ the critical exponent is already characteristic of a second-order transition and that it is different from the one of the Gaussian case. In the present study we perform a finite size analysis at $lambda=1.1$ to get information wether the value of this exponent is universal.
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In 4D compact U(1) lattice gauge theory with a monopole term added to the Wilson action we first reveal some properties of a third phase region at negative $beta$. Then at some larger values of the monopole coupling $lambda$ by a finite-size analysis we find values of the critical exponent $ u$ close to, however, different from the Gaussian value.
We investigate four-dimensional compact U(1) lattice gauge theory with a monopole term added to the Wilson action. First we consider the phase structure at negative $beta$, revealing some properties of a third phase region there, in particular the existence of a number of different states. Then our present studies concentrate on larger values of the monopole coupling $lambda$ where the confinement-Coulomb phase transition turns out to become of second order. Performing a finite-size analysis we find that the critical exponent $ u$ is close to, however, different from the gaussian value and that in the range considered $ u$ increases somewhat with $lambda$.
A conceptually simple model for strongly interacting compact U(1) lattice gauge theory is expressed as operators acting on qubits. The number of independent gauge links is reduced to its minimum through the use of Gausss law. The model can be implemented with any number of qubits per gauge link, and a choice as small as two is shown to be useful. Real-time propagation and real-time collisions are observed on lattices in two spatial dimensions. The extension to three spatial dimensions is also developed, and a first look at 3-dimensional real-time dynamics is presented.
We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with $N$-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N=1 model. For N=2, we found that the system has a second-order phase transition line $tilde{c}_1(c_2)$ in the $c_2$(gauge coupling)$-c_1$(Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N=3, we found that there exists a critical line similar to that in the N=2 model, but the critical line is separated into two parts; one for $c_2 < c_{2{rm tc}}=2.4pm 0.1$ with first-order transitions, and the other for $ c_{2{rm tc}} < c_2$ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N=4 and N=5 systems. We also studied the case of anistropic Higgs coupling in the N=3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an enhancement of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.
Monte Carlo simulation of gauge theories with a $theta$ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which is a promising approach for its low computational cost. The drawback of this method, however, is the existence of a condition that has to be met in order for the results to be correct. As a first step, we apply the method to 2D U(1) gauge theory on a torus with a $theta$ term, which can be solved analytically. We find that a naive implementation of the method fails because of the topological nature of the $theta$ term. In order to circumvent this problem, we simulate the same theory on a punctured torus, which is equivalent to the original model in the infinite volume limit for $ |theta| < pi$. Rather surprisingly, we find that the CLM works and reproduces the exact results for a punctured torus even at large $theta$, where the link variables near the puncture become very far from being unitary.
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