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 and 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 $(1+1)\mathrm{D}$ 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 nonzero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.
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 and 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 nonzero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.
We study the ground-state properties of a class of Zn lattice gauge theories in 1+1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the U(1) group, preserve the unitary character of the minimal coupling and have, therefore, the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-n limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main features and phenomenology of the target theory, in view of implementations of cold-atom quantum simulators of QED. In this paper, we study the cases $n=2\textdiv{}8$ by means of a DMRG code that exactly implements Gauss's law. We perform a careful scaling analysis and show that, in absence of a background field, all Zn models exhibit a phase transition which falls in the Ising universality class, with spontaneous symmetry breaking of the CP symmetry. We then perform the large-n limit and find that the asymptotic values of the critical parameters approach the ones obtained for the known phase transition of the zero-charge sector of the massive Schwinger model, which occurs at negative mass.
Abstract : In this project, we have developed a scheme for using cold atom systems on optical lattices as quantum simulators for lattice gauge theories. We designed cold atom experimental setups that could be used to learn about the phase diagrams of Lattice Gauge Theory models and real time evolution, which cannot be studied using conventional methods. We first constructed a sequence of theoretical steps connecting the classical O(2) model in 1+1 dimensions to a boson model that can be implemented on optical lattices, showing a proof-of-principle that quantum computing via optical lattices is possible for classical lattice models. We then extended this protocol to limits of the Abelian Higgs model, a model that exhibits important features of QCD such as confinement. Our results include construction of effective actions, testing with Monte Carlo simulations, tensor renormalization group technique development and application, mappings to quantum spin and boson Hamiltonians, and analysis of candidate systems for experimental realization. We verified that in the superfluid phase the central charge can be extracted from the entanglement entropy as predicted by conformal symmetry. We calculated and compared the Polyakov loop, an order parameter for confinement, in the two formulations, and propose that it can be a useful quantity to probe experimentally. The results from our project opens the door for exciting new research directions, such as quantum simulation of the Schwinger model and of non-Abelian models.
Abstract Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract
Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach -applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.
Abstract: Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract:
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high local symmetry content native to these systems by describing only the gauge invariant subspace. Compared to a standard tensor network description, the gauge invariant model allows one to increase real and imaginary time evolution up to a factor that is square of the dimension of the link variable. The gauge invariant tensor network description is based on the quantum link formulation, a compact and intuitive formulation for gauge theories on the lattice, which is alternative to and can be combined with the global symmetric tensor network description. We present some paradigmatic examples that show how this architecture might be used to describe the physics of condensed matter and high-energy physics systems. Finally, we present a cellular automata analysis which estimates the gauge invariant Hilbert space dimension as a function of the number of lattice sites that might guide the search for effective simplified models of complex theories.