Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term

Abstract

We determine the mass gap of a two-dimensional $O(3)$ nonlinear sigma model augmented with a topological $\theta$-term using tensor network and digital quantum algorithms. As proof of principle, we consider the example $\theta =\pi$ and study its critical behaviour on a quantum simulator by examining the entanglement entropy of the ground state. We confirm that the quantum theory is massless in the strong-coupling regime, in agreement with analytical results. However, we also highlight the limitations of current quantum algorithms, designed for noisy intermediate-scale quantum devices, in the theory simulation at weak coupling. Finally, we compare the performance of our quantum algorithms to classical tensor network methods.

12 pages, 6 figures, 2 tables. v2: minor modifications, references added

References in corpus (7)

• The density-matrix renormalization group in the age of matrix product states
• A class of quantum many-body states that can be efficiently simulated
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class
• Qubitization strategies for bosonic field theories
• Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models

Cited by in corpus (7)

• Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• Enhancing Quantum Field Theory Simulations on NISQ Devices with Hamiltonian Truncation
• Toward hybrid quantum simulations with qubits and qumodes on trapped-ion platforms
• State preparation of lattice field theories using quantum optimal control
• Exploring thermal equilibria of the Fermi-Hubbard model with variational quantum algorithms