Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics

TL;DR

This paper introduces the Renormalized Dual Basis (RDB), a new truncation scheme for simulating 2+1D compact quantum electrodynamics, demonstrating improved accuracy and scalability using tensor networks.

Contribution

The paper applies the RDB truncation scheme to 2+1D cQED, showing enhanced precision and scalability for lattice gauge theory simulations across different coupling regimes.

Findings

Achieved improved ground state energy estimates for small lattices.

Extended the method to larger lattices using tensor networks.

Demonstrated the RDB's efficiency across all coupling regimes.

Abstract

The classical and quantum simulation of lattice gauge theories (LGTs) with Lie groups is hindered by the infinite-dimensional Hilbert space of gauge degrees of freedom. In a recent work [Phys. Rev. X 15, 031065 (2025)], we introduced a new truncation scheme -- here renamed as Renormalized Dual Basis (RDB) -- based on the resolution of the single-plaquette problem, and demonstrated its performance for SU(2) LGTs. In this paper, we apply the RDB to compact quantum electrodynamics (cQED) in three spacetime dimensions (2+1D). We variationally determine the ground state of the theory for small lattices with periodic (for pure gauge) and open (in presence of fermionic matter) boundary conditions, achieving improved precision for the plaquette operator compared to previous approaches. By leveraging tensor networks, we extend the study to larger lattices and demonstrate the scalability of the method. Overall, we show that the RDB provides an efficient description across all coupling regimes.