Phase structure of the CP(1) model in the presence of a topological $\theta$-term

Abstract

We numerically study the phase structure of the CP(1) model in the presence of a topological $\theta$-term, a regime afflicted by the sign problem for conventional lattice Monte Carlo simulations. Using a bond-weighted tensor renormalization group method, we compute the free energy for inverse couplings ranging from $0\le \beta \le 1.1$ and find a CP-violating, first-order phase transition at $\theta =\pi$. In contrast to previous findings, our numerical results provide no evidence for a critical coupling ${\beta }_c<1.1$ above which a second-order phase transition emerges at $\theta =\pi$ and/or the first-order transition line bifurcates at $\theta \ne \pi$. If such a critical coupling exists, as suggested by Haldane's conjecture, our study indicates that is larger than ${\beta }_c>1.1$.

10 pages, 9 figures, v2: updated to match journal version

References in corpus (13)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Tensor renormalization group approach to 2D classical lattice models
• Measurement of the permanent electric dipole moment of the neutron
• Optical Abelian Lattice Gauge Theories
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Quantum simulation of the Schwinger model: A study of feasibility
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Variational Monte Carlo simulation with tensor networks of a pure ${\mathbb{Z}}_3$ gauge theory in (2+1)d
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class

Cited by in corpus (13)

• Quantum Simulation for High Energy Physics
• Critical endpoint of (3+1)-dimensional finite density $Z_3$ gauge-Higgs model with tensor renormalization group
• Exploring the CP-violating Dashen phase in the Schwinger model with tensor networks
• Bond-weighting method for the Grassmann tensor renormalization group
• Tensor renormalization group study of (1+1)-dimensional U(1) gauge-Higgs model at $\theta =\pi$ with Lüscher's admissibility condition
• Initial tensor construction and dependence of the tensor renormalization group on initial tensors
• Phase structure analysis of 2d lattice CP(1) model with $\theta$ term using tensor renormalization group method
• Spectroscopy with the tensor renormalization group method
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory
• Tensor renormalization group study of cold and dense QCD in the strong coupling limit
• Grassmann tensor renormalization group for the massive Schwinger model with a $\theta$ term using staggered fermions