Phase structure analysis of 2d lattice CP(1) model with $\theta$ term using tensor renormalization group method

Abstract

We investigate the phase structure of a two-dimensional 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 non-perturbatively 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 of 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, ${\beta }_{\mathrm{c}}=0.5952(8)$ and its universality class as the SU(2)${}_{k=1}$ Wess-Zumino-Witten model.

arXiv comment32 pages, 19 figures, 2 Tables

References in corpus (25)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Tensor renormalization group approach to 2D classical lattice models
• Measurement of the permanent electric dipole moment of the neutron
• Coarse-graining renormalization by higher-order singular value decomposition
• Tensor Network Renormalization
• Renormalization of tensor networks using graph independent local truncations
• Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Anisotropic Tensor Renormalization Group
• Grassmann tensor renormalization group for one-flavor lattice Gross-Neveu model with finite chemical potential
• Tensor network formulation for two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a $\theta$ term
• Finite-size and finite bond dimension effects of tensor network renormalization
• Restoration of chiral symmetry in cold and dense Nambu--Jona-Lasinio model with tensor renormalization group
• Resolving the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model with tensor-network based level spectroscopy
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class
• From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model
• First-principle simulations of 1+1d quantum field theories at $\theta =\pi$ and spin-chains
• A Strong-Coupling Analysis of the Lattice $C{P}^{N-1}$ Models in the Presence of a $\theta$ Term
• Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations
• Phase structure of the CP(1) model in the presence of a topological $\theta$-term
• Loop-TNR analysis of CP(1) model with theta term
• Real Space Renormalization Group Analysis of U(1)-Gauge Theory with theta-term in 2 Dimensions

Cited by in corpus (3)

• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Tensor renormalization group study of cold and dense QCD in the strong coupling limit