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arXiv:1911.06480 · Journal of High Energy Physics

Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a θ term

Yoshinobu Kuramashi, Yusuke Yoshimura

Published Apr 1, 2020• 37 citations
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Abstract

Abstract We make an analysis of the two-dimensional U(1) lattice gauge theory with a θ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at θ = π toward the thermodynamic limit. In addition finite size scaling analysis of the topological susceptibility up to V = L × L = 1024 × 1024 allows us to determine the phase transition at θ = π is the first order.

DOI
10.1007/jhep04(2020)089

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Abstract We make an analysis of the two-dimensional U(1) lattice gauge theory with a θ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at θ = π toward the thermodynamic limit. In addition finite size scaling analysis of the topological susceptibility up to V = L × L = 1024 × 1024 allows us to determine the phase transition at θ = π is the first order.
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A bstract We use the Grassmann tensor renormalization group method to investigate the N f = 2 Schwinger model with the staggered fermions in the presence of a 2 π periodic θ term in a broad range of mass. The method allows us to deal with the massive staggered fermions straightforwardly and to study the θ dependence of the free energy and topological charge in the thermodynamic limit. Our calculation provides consistent results with not only the analytical solution in the large mass limit but also the previous Monte Carlo studies in the small mass regime. Our numerical results also suggest that the N f = 2 Schwinger model on a lattice has a different phase structure, than the model in the continuum limit.
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Abstract We investigate the phase structure of a 2D lattice CP(1) model with a θ\thetaθ term. In particular, we aim to identify a critical region expected to exist along a θ=π\theta =\piθ=π line. To explore the phase structure nonperturbatively and avoid the sign problem, we employ the tensor renormalization group method. We make two improvements compared to previous tensor network studies. The first improvement involves refining the initial tensor. Specifically, we construct it using a quadrature method, which achieves higher accuracy compared to the conventional approach. The second improvement consists of analyzing the phase structure using the information on the conformal field theory, namely the central charge and the scaling dimensions, which can be accessed relatively easily via the tensor renormalization group method. Thanks to these improvements, we identify both the onset of the critical region, βc=0.5952(8)\beta _{\rm c}=0.5952(8)βc​=0.5952(8), and its universality class as the SU(2)k=1{}_{k=1}k=1​ Wess–Zumino–Witten model.