Phase Structure Analysis of a 2D Lattice CP(1) Model with a <i>θ</i> Term using the Tensor Renormalization Group Method

Abstract We investigate the phase structure of a 2D lattice CP(1) model with a $\theta$ term. In particular, we aim to identify a critical region expected to exist along a $\theta =\pi$ 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, $\beta _{\rm c}=0.5952(8)$, and its universality class as the SU(2)${}_{k=1}$ Wess–Zumino–Witten model.