Quantum Simulation of the Universal Features of the Polyakov Loop

Abstract

Lattice gauge theories are fundamental to our understanding of high-energy physics. Nevertheless, the search for suitable platforms for their quantum simulation has proven difficult. We show that the Abelian Higgs model in 1+1 dimensions is a prime candidate for an experimental quantum simulation of a lattice gauge theory. To this end, we use a discrete tensor reformulation to smoothly connect the space-time isotropic version used in most numerical lattice simulations to the continuous-time limit corresponding to the Hamiltonian formulation. The eigenstates of the Hamiltonian are neutral for periodic boundary conditions, but we probe the nonzero charge sectors by either introducing a Polyakov loop or an external electric field. In both cases we obtain universal functions relating the mass gap, the gauge coupling, and the spatial size which are invariant under the deformation of the temporal lattice spacing. We propose to use a physical multi-leg ladder of atoms trapped in optical lattices and interacting with Rydberg-dressed interactions to quantum simulate the model and check the universal features. Our results provide a path to the analog quantum simulation of lattice gauge theories with atoms in optical lattices.

Examples of symmetry-preserving truncations in tensor field theory

“…For theories with compact fields like the nonlinear sigma models and Wilson lattice gauge theories, the tensor reformulation relies on character expansions and is always discretized [7]. This is suitable for quantum computations or quantum simulations [23][24][25]. In practical situations such as Tensor Renormalization Group (TRG) calculations, truncations of infinite sums appearing in the TFT formulation of models with continuous symmetries are necessary.…”

Review on novel methods for lattice gauge theories

“…Zhang et al [447] proposed the use of Rydberg interactions in an optical lattice with a multiladder geometry to implement an analog simulation of the (1+1)dimensional Abelian Higgs model. In this proposal, related to Ref.…”

Quantum simulation of scattering in the quantum Ising model

“…(21), is the noise rate for the system which is dependent upon the probability of gate errors occurring as in Eq. (19) and r is a scale factor such that r > 1. Due to the computational overhead of carrying out this methodology of error mitigation we only demonstrate a modification of it in our results for free propagation on a four site lattice.…”

“…This strategy is explained in Ref. [19]. The main goal is to provide reliable benchmark calculations in situations that will allow comparison among different platforms.…”