Cold atoms meet lattice gauge theory

Abstract

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more ‘accessible’ and easier to manipulate for experimentalists, but this ‘substitution’ also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or Z 2 Bose–Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz–Hubbard ladder, or Gross–Neveu–Wilson and Wilson–Hubbard models. This article is not a general review of the rapidly growing field—it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Large-$S$ and tensor-network methods for strongly-interacting topological insulators

“…In the limit r → 1, we recover the quantum compass model with the directional spin-spin couplings of Eq. ( 19), which supports Lorentz-breaking fermion condensates (20) as discussed in [60,61]. In the isotropic a 1 = a 2 and naive-fermion r → 0 limits, we recover a model that is unitarily equivalent to the Heisenberg model on a square lattice with antiferromagnetic couplings J j,a → J = 1/g 2 and staggered field h z → h z (−1) n 1 +n 2 .…”

“…In the context of low-dimensional QFTs, QSs can be tailored such that one has full control of the microscopic parameters and, moreover, can access the continuum limit in a controlled fashion. In order to do so, QSs of QFTs [16][17][18][19][20][21] typically follow the approach of lattice field theories [22] in their Hamiltonian formulation [23]. Rather than reducing the lattice spacing to recover the continuum limit, one may tune the microscopic couplings of these QSs to approach a critical point where the correlation length is much larger than that spacing, and the continuum description sets in.…”

Weak Ergodicity Breaking in the Schwinger Model

“…Recently, a concerted experimental effort has emerged for the implementation of gauge theories in synthetic quantum matter (SQM) devices [36][37][38][39][40][41][42][43][44][45][46]. This has been facilitated in large part due to the great progress achieved in the precision and control of SQM setups [47,48], making the quantum simulation of gauge theories a realistic endeavor [49][50][51][52][53][54][55]. Due to the complexity involved in these experiments, the implementations often focus on quantum link formulations of gauge theories, where spin-S operators model the gauge fields, which in QED span an infinite-dimensional Hilbert space [56].…”

Robust quantum many-body scars in lattice gauge theories

“…Moreover, scars have recently also been shown to exist in a Z 2 lattice gauge theory (LGT) [44,45] and in higher-dimensional gauge theories as well [46]. Given that quantum many-body scarring is known not to be stable against perturbations [47], and in light of an impressive experimental effort towards realizing gauge theories in synthetic quantum matter devices [42,43,[48][49][50][51][52][53][54][55][56][57], it is important to investigate methods that may protect scarred dynamics in the presence of errors.…”