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Register a new userDensity of states approach for lattice gauge theory with a $theta$-term
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We discuss a new strategy for treating the complex action problem of lattice field theories with a $theta$-term based on density of states (DoS) methods. The key ingredient is to use open boundary conditions where the topological charge is not quantized to integers and the density of states is sufficiently well behaved such that it can be computed precisely with recently developed DoS techniques. After a general discussion of the approach and the role of the boundary conditions, we analyze the method for 2-d U(1) lattice gauge theory with a $theta$-term, a model that can be solved in closed form. We show that in the continuum limit periodic and open boundary conditions describe the same physics and derive the DoS, demonstrating that only for open boundary conditions the density is sufficiently well behaved for a numerical evaluation. We conclude our proof of principle analysis with a small test simulation where we numerically compute the density and compare it with the analytical result.
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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.
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.
The simulation of dense fermionic matters is a long-standing problem in lattice gauge theory. One hopeful solution would be the use of quantum computers. In this paper, digital quantum simulation is designed for lattice gauge theory at nonzero density. The quantum variational algorithm is adopted to obtain the ground state at nonzero density. A benchmark test is performed in the lattice Schwinger model.
Lattice field theory with the $theta$ term suffers from the sign problem. The sign problem appears as flattening of the free energy. As an alternative to the conventional method, the Fourier transform method (FTM), we apply the maximum entropy method (MEM) to Monte Carlo data obtained using the CP$^3$ model with the $theta$ term. For data without flattening, we obtain the most probable images of the partition function ${hat{cal Z}}(theta)$ with rather small errors. The results are quantitatively close to the result obtained with the FTM. Motivated by this fact, we systematically investigate flattening in terms of the MEM. Obtained images ${hat{cal Z}}(theta)$ are consistent with the FTM for small values of $theta$, while the behavior of ${hat{cal Z}}(theta)$ depends strongly on the default model for large values of $theta$. This behavior of ${hat{cal Z}}(theta)$ reflects the flattening phenomenon.
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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