Topological vacuum structure of the Schwinger model with matrix product states

Abstract

We numerically study the single-flavour Schwinger model in the Hamiltonian formulation with a topological θ-term corresponding to a constant electric background field. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial θ-dependence of several lattice and continuum quantities. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle θ, thus respecting CP invariance, while lattice artifacts still depend on θ. We also confirm that negative masses can be mapped to positive masses by shifting θ → θ + π due to the axial anomaly in the continuum, while lattice artifacts non-trivially distort this mapping.

Simulating lattice gauge theories within quantum technologies

“…In particular, in recent years, there has been a boost in the development of tensor network methods to simulate lattice gauge theories. There are different approaches, that range from the exploitation of mappings of some theories to spin models [103,104], to the development of gauge invariant tensor networks in the quantum link formulation [22,23,101,[105][106][107]. This section reviews some of the studies that appeared in the last years, covering most of the available approaches for Abelian and non-Abelian lattice gauge theories [103][104][105][108][109][110][111].…”

Real-time dynamics in 2+1D compact QED using complex periodic Gaussian states

“…The implementation of quantum simulators has been demonstrated using trapped ions [17] and ultracold atoms [18][19][20][21]. On the numerical side, there has been a lot of success in applying matrix product state methods to (1 + 1)-dimensional Abelian and non-Abelian lattice gauge theories [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], enabling the study of finite chemical potential scenarios and out-of-equilibrium dynamics which would not have been accessible in Monte Carlo simulations of Euclidean lattice gauge theory. Also, some generalizations of Gaussian states have proven to be suitable for these theories [37].…”

Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks

“…As tailored many-body quantum state ansätze, TNs are an efficient approximate entanglement-based representation of physical states, capable of efficiently describe equilibrium properties and real-time dynamics of systems described by complex actions, where Monte Carlo simulations fail to efficiently converge 22 . TN methods have proven remarkable success in simulating LGTs in (1+1) dimensions [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] , and very recently they have shown potential in (2+1) dimensions [42][43][44][45][46][47][48][49][50] . To date, due to the lack of efficient numerical algorithms to describe high-dimensional systems via TNs, no results are available regarding the realistic scenario of LGTs in three spatial dimensions.…”