A Path to Quantum Simulations of Topological Phases: (2+1)D Wilson Fermions Coupled To U(1) Background Gauge Fields

• URL: http://arxiv.org/abs/2504.21828v1
• Date: Wed, 30 Apr 2025 17:33:01 GMT
• Title: A Path to Quantum Simulations of Topological Phases: (2+1)D Wilson Fermions Coupled To U(1) Background Gauge Fields
• Authors: Sriram Bharadwaj, Emil Rosanowski, Simran Singh, Alice di Tucci, Changnan Peng, Karl Jansen, Lena Funcke, Di Luo,
• Abstract summary: A key challenge in lattice formulations is the proper realization of topological phases and the Chern-Simons terms.<n>We analyze staggered and Wilson fermions coupled to $textU(1)$ background gauge fields in the Hamiltonian formulation.<n>Our findings resolve existing ambiguities in Hamiltonian formulations and provide a theoretical foundation for future quantum simulations of gauge theories with topological phases.
• Score: 0.7070208147484192
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum simulation offers a powerful approach to studying quantum field theories, particularly (2+1)D quantum electrodynamics (QED$_3$), which hosts a rich landscape of physical phenomena. A key challenge in lattice formulations is the proper realization of topological phases and the Chern-Simons terms, where fermion discretization plays a crucial role. In this work, we analyze staggered and Wilson fermions coupled to $\text{U}(1)$ background gauge fields in the Hamiltonian formulation and demonstrate that staggered fermions fail to induce (2+1)D topological phases, while Wilson fermions admit a variety of topological phases including Chern insulator and quantum spin Hall phases. We additionally uncover a rich phase diagram for the two-flavor Wilson fermion model in the presence of a chemical potential. Our findings resolve existing ambiguities in Hamiltonian formulations and provide a theoretical foundation for future quantum simulations of gauge theories with topological phases. We further outline connections to experimental platforms, offering guidance for implementations on near-term quantum computing architectures.

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