Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta =\pi$ term

Abstract

We perform a tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta =\pi$ term. Within the Hamiltonian formulation, this field theory emerges as the finite-temperature partition function of a modified quantum rotor model decorated with magnetic monopoles. Using the monopole harmonics basis, we derive the matrix representation for this modified quantum rotor model, which enables tensor network simulations. We employ our recently developed continuous matrix product operator method [Tang et al., Phys. Rev. Lett. 125, 170604 (2020)] to study the finite-temperature properties of this model and reveal its massless nature. The central charge as a function of the coupling constant is directly extracted in our calculations and compared with field theory predictions.

arXiv commentPublished version. 13 pages, 7 figures, code: https://github.com/TensorBFS/U1cMPO

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Cited by in corpus (5)

• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• Toward quantum computations of the $O(3)$ model using qumodes
• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations
• Kac-Moody symmetries in one-dimensional bosonic systems