Non-trivial θ-Vacuum Effects in the 2-d O(3) Model

Abstract

We study θ-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do not spoil the non-trivial continuum limit at θ non-zero, and there are different continuum theories for each value of θ. A very precise Monte Carlo study of the step scaling function indirectly confirms the exact S-matrix of the 2-d O(3) model at θ= π.

4 pages, 3 figures

References in corpus (4)

• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Topological Lattice Actions
• Logarithmic corrections to O(a^2) lattice artifacts
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class

Cited by in corpus (21)

• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
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• Tensor renormalization group analysis of CP(N-1) model
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case
• An ideal toy model for confining, walking and conformal gauge theories: the O(3) sigma model with theta-term
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model
• Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Instantons, renormalons and the theta angle in integrable sigma models
• Topological Lattice Actions for the 2d XY Model
• Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta =\pi$ term
• Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models
• Topological Susceptibility of the 2d O(3) Model under Gradient Flow
• Loop-TNR analysis of CP(1) model with theta term
• An Improved Single-Plaquette Gauge Action
• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations
• Renormalization of the Nonlinear O(3) Model with Theta-Term
• Study of theta-Vacua in the 2-d O(3) Model