Lattice gauge theories simulations in the quantum information era

The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analyzing the symmetry properties of Hamiltonian and states: the most striking example are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realization of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.Comment: Pedagogical review article. Originally submitted to Contemporary Physics, the final version will appear soon on the on-line version of the journal. 34 page

Homogeneous and inhomogeneous magnetic phases of constrained dipolar bosons

We study the emergence of several magnetic phases in dipolar bosonic gases subject to three-body loss mechanism employing numerical simulations based on the density matrix renormalization group(DMRG) algorithm. After mapping the original Hamiltonian in spin language, we find a strong parallelism between the bosonic theory and the spin-1 Heisenberg model with single ion anisotropy and long-range interactions. A rich phase diagram, including ferromagnetic, antiferromagnetic and non-local ordered phases, emerges in the half-filled one-dimensional case, and is preserved even in presence of a trapping potential.Comment: v2: 9 pages, 15 figures, extended version, new numerical calculations on the BKT transition, accepted for pubblication in PR

Measuring von Neumann entanglement entropies without wave functions

We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories

Entanglement guided search for parent Hamiltonians

We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several non-trivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave-functions considerably simplifies the search for parent Hamiltonians.Comment: 5 pages, 5 figures, supplementary materia

Magnetic properties of commensurate Bose-Bose mixtures in one-dimensional optical lattices

We investigate magnetic properties of strongly interacting bosonic mixtures confined in one dimensional geometries, focusing on recently realized Rb-K gases with tunable interspecies interactions. By combining analytical perturbation theory results with density-matrix-renormalization group calculations, we provide quantitative estimates of the ground state phase diagram as a function of the relevant microscopic quantities, identifying the more favorable experimental regimes in order to access the various magnetic phases. Finally, we qualitatively discuss the observability of such phases in realistic setups when finite temperature effects have to be considered.Comment: 9 pages, 7 figures, to be published in EPJ ST special issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases

Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation

We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.Comment: 9 pages, 9 figures. Published versio

Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks

Tensor network algorithms provide a suitable route for tackling real-time dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1+1) dimensions in the presence of dynamical matter for different mass and electric field couplings, a theory akin to quantum-electrodynamics in one-dimension, which displays string-breaking: the confining string between charges can spontaneously break during quench experiments, giving rise to charge-anticharge pairs according to the Schwinger mechanism. We study the real-time spreading of excitations in the system by means of electric field and particle fluctuations: we determine a dynamical state diagram for string breaking and quantitatively evaluate the time-scales for mass production. We also show that the time evolution of the quantum correlations can be detected via bipartite von Neumann entropies, thus demonstrating that the Schwinger mechanism is tightly linked to entanglement spreading. To present the variety of possible applications of this simulation platform, we show how one could follow the real-time scattering processes between mesons and the creation of entanglement during scattering processes. Finally, we test the quality of quantum simulations of these dynamics, quantifying the role of possible imperfections in cold atoms, trapped ions, and superconducting circuit systems. Our results demonstrate how entanglement properties can be used to deepen our understanding of basic phenomena in the real-time dynamics of gauge theories such as string breaking and collisions.Comment: 15 pages, 25 figures. Published versio

Unitary nn-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of R\'enyi entropies

We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary $n$-designs, and their application to the measurement of R\'enyi entropies. We generalize our protocol presented in [Elben2017: arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and spin lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.Comment: This is a new and extended version of the Supplementary material presented in arXiv:1709.05060v1, rewritten as a companion paper. Version accepted to Phys. Rev. A. Minus sign corrected in Eq (5

Trimer liquids and crystals of polar molecules in coupled wires

We investigate the pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. By means of analytical and quasi-exact numerical techniques, we show that gases of composite molecular dimers as well as trimers can be stabilized as a function of the density difference between the wires. A shallow optical lattice can pin both liquids, realizing crystals of composite bosons or fermions. We show that these exotic quantum phases should be realizable under current experimental conditions in finite-size confining potentials.Comment: 5 pages, 3 figures plus additional material; Accepted for publication in Phys. Rev. Let