Cold atoms meet lattice gauge theory

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’.

Dynamics of string-like states of a hole in a quantum antiferromagnet: A diagrammatic Monte Carlo simulation

The dynamics of a hole motion in a quantum antiferromagnet has been studied in the past three decade because of its relationship to models related to superconductivity in cuprates. The same problem has received significant attention because of its connection to very recent experiments of the dynamics of ultra-cold atoms in optical lattices where models of strongly correlated electrons can be simulated. In this paper we apply the diagrammatic Monte Carlo method to calculate the single-hole Green's function in the t-J model, where the $J$ term is linearized, in a wide range of imaginary-time with the aim to examine the polaron formation and in particular the details of the contribution of the so-called {\it string excitations} found in such recent experiments. We calculate the single-hole spectral function by analytic continuation from imaginary to real time and study the various aspects that constitute the string picture, such as, the energy-momentum dependence of the main quasiparticle peak and its residue, the {\it internal excitations} of the string which appear as multiple peaks in the spectral function as well as their momentum dependence. We find that the earlier analysis of the spectral function based on a mobile-hole connected with a string of overturn spins and the contribution of the internal string excitations as obtained from the non-crossing approximation is accurate.

Restricted Boltzmann Machine based on a Fermi sea

In recent years, there has been an intensive research on how to exploit the quantum laws of nature in the machine learning. Models have been put forward which employ spins, photons, and cold atoms. In this work we study the possibility of using the lattice fermions to learn the classical data. We propose an alternative to the quantum Boltzmann Machine, the so-called Spin-Fermion Machine (SFM), in which the spins represent the degrees of freedom of the observable data (to be learned), and the fermions represent the correlations between the data. The coupling is linear in spins and quadratic in fermions. The fermions are allowed to tunnel between the lattice sites. The training of SFM can be eciently implemented since there are closed expressions for the log- likelihood gradient. We nd that SFM is more powerful than the classical Restricted Boltzmann Machine (RBM) with the same number of physical degrees of freedom. The reason is that SFM has additional freedom due to the rotation of the Fermi sea. We show examples for several data sets.

Tensor-network Study of Correlation-spreading Dynamics in the Two-dimensional Bose-Hubbard Model

Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly challenging for dynamics of systems with more than one spatial dimension. Here we demonstrate that a tensor-network method running on classical computers is useful for this purpose. We specifically analyze real-time dynamics of the two-dimensional Bose-Hubbard model after a sudden quench starting from the Mott insulator by means of the infinite projected entangled pair state algorithm. Calculated single-particle correlation functions are found to be in good agreement with a recent experiment [Y. Takasu et al., Sci. Adv. 6, eaba9255 (2020)]. By estimating the phase and group velocities from the single-particle and density-density correlation functions, we predict how these velocities vary in the moderate interaction region, which serves as a quantitative benchmark for future experiments.