Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and high-energy physics, along with potential applications in quantum information and science technologies. In light of the impressive ongoing efforts to achieve such realizations, a fundamental question regarding quantum link model regularizations of lattice gauge theories is how faithfully they capture the quantum field theory limit of gauge theories. Recent work \cite{zache2021achieving} has shown through analytic derivations, exact diagonalization, and infinite matrix product state calculations that the low-energy physics of 1+1 D U(1) quantum link models approaches the quantum field theory limit already at small link spin length S . Here, we show that the approach to this limit also lends itself to the far-from-equilibrium quench dynamics of lattice gauge theories, as demonstrated by our numerical simulations of the Loschmidt return rate and the chiral condensate in infinite matrix product states, which work directly in the thermodynamic limit. Similar to our findings in equilibrium that show a distinct behavior between half-integer and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between half-integer and integer spin quantum link models in the regime of strong electric-field coupling. Our results further affirm that state-of-the-art finite-size ultracold-atom and NISQ-device implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the far-from-equilibrium regime.
Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and high-energy physics, along with potential applications in quantum information and science technologies. In light of the impressive ongoing efforts to achieve such realizations, a fundamental question regarding quantum link model regularizations of lattice gauge theories is how faithfully they capture the quantum field theory limit of gauge theories. Recent work \cite{zache2021achieving} has shown through analytic derivations, exact diagonalization, and infinite matrix product state calculations that the low-energy physics of 1+1 D U(1) quantum link models approaches the quantum field theory limit already at small link spin length S . Here, we show that the approach to this limit also lends itself to the far-from-equilibrium quench dynamics of lattice gauge theories, as demonstrated by our numerical simulations of the Loschmidt return rate and the chiral condensate in infinite matrix product states, which work directly in the thermodynamic limit. Similar to our findings in equilibrium that show a distinct behavior between half-integer and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between half-integer and integer spin quantum link models in the regime of strong electric-field coupling. Our results further affirm that state-of-the-art finite-size ultracold-atom and NISQ-device implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the far-from-equilibrium regime.
The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for U(1) gauge theories regularized via finite-dimensional Hilbert spaces of quantum spin-S operators, known as quantum link models. For quantum electrodynamics (QED) in one spatial dimension, we numerically demonstrate the continuum limit by extrapolating the ground state energy, the scalar, and the vector meson masses to large spin lengths S, large volume N, and vanishing lattice spacing a. By analytically solving Gauss' law for arbitrary S, we obtain a generalized PXP spin model and count the physical Hilbert space dimension analytically. This allows us to quantify the required resources for reliable extrapolations to the continuum limit on quantum devices. We use a functional integral approach to relate the model with large values of half-integer spins to the physics at topological angle Θ=π. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.
Abstract Quantum link models (QLMs) offer the realistic prospect for the practical implementation of lattice quantum electrodynamics (QED) on modern quantum simulators, and they provide a venue for exploring various nonergodic phenomena relevant to quantum many-body physics. In these models, gauge and electric fields are represented by spin- S operators. So far, large-scale realizations of QLMs have been restricted to S = 1/2 representations, whereas the lattice-QED limit is approached at S → ∞ . Here, we present a bosonic mapping for the representation of gauge and electric fields with effective spin- S operators for arbitrarily large values of S . Based on this mapping, we then propose an experimental scheme for the realization of a large-scale spin-1 U(1) QLM using spinless bosons in an optical superlattice. Using perturbation theory and infinite matrix product state calculations, which work directly in the thermodynamic limit, we demonstrate the faithfulness of the mapping and stability of gauge invariance throughout all accessible evolution times. We further demonstrate the potential of our proposed quantum simulator to address relevant high-energy physics by probing the (de)confinement of an electron–positron pair by tuning the gauge coupling. Our work provides an essential step towards gauge-theory quantum simulators in the quantum-field-theory limit.
Spin-SU(1) Quantum Link Models with Dynamical Matter on a Quantum Simulator
Quantum link models (QLMs) offer the realistic prospect for the practical implementation of lattice quantum electrodynamics (QED) on modern quantum simulators, and they provide a venue for exploring various nonergodic phenomena relevant to quantum many-body physics. In these models, gauge and electric fields are represented by spin-S operators. So far, large-scale realizations of QLMs have been restricted to S=1/2 representations, whereas the lattice-QED limit is approached at S→∞. Here, we present a bosonic mapping for the representation of gauge and electric fields with effective spin-S operators for arbitrarily large values of S. Based on this mapping, we then propose an experimental scheme for the realization of a large-scale spin-1U(1) QLM using spinless bosons in an optical superlattice. Using perturbation theory and infinite matrix product state calculations, which work directly in the thermodynamic limit, we demonstrate the faithfulness of the mapping and stability of gauge invariance throughout all accessible evolution times. We further demonstrate the potential of our proposed quantum simulator to address relevant high-energy physics by probing the (de)confinement of an electron--positron pair by tuning the gauge coupling. Our work provides an essential step towards gauge-theory quantum simulators in the quantum-field-theory limit.
Ground-state phase diagram of quantum link electrodynamics in (2+1)-d
The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a U(1) quantum link lattice gauge theory where the gauge fields, represented by spin-21 operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in (2+1)-d. This model allows us to smoothly tune between the U(1) quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.
Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body systems. With the strong ongoing experimental drive to quantum simulate lattice gauge theories, it becomes important to investigate DQPTs in these models in order to better understand their far-from-equilibrium properties. In this work, we use infinite matrix product state techniques to study DQPTs in spin-SU(1) quantum link models. Although we are able to reproduce literature results directly connecting DQPTs to a sign change in the dynamical order parameter in the case of S=1/2 for quenches starting in a vacuum initial state, we find that for different quench protocols or different values of the link spin length S>1/2 this direct connection is no longer present. In particular, we find that there is an abundance of different types of DQPTs not directly associated with any sign change of the order parameter. Our findings indicate that DQPTs are fundamentally different between the Wilson-Kogut-Susskind limit and its representation through the quantum link formalism.
In the last decade the non-equilibrium dynamics of isolated quantum systems has raised a huge interest for both its conceptual and practical implications. Simulation of quantum dynamics represents by now a very active research effort, with highly controllable quantum devices composed of hundreds of qubits already being realized in numerous setups. These offer the unprecedented possibility to access real-time quantum dynamics and strongly correlated quantum many-body states, opening numerous avenues not only for future quantum technologies, but also for long-standing theoretical problems. One of the most sought-after applications is the computation of real-time evolution in theories of fundamental interactions. Since Wilson's proposal in 1974, the equilibrium phase diagrams of lattice gauge theories have been successfully investigated with Monte Carlo simulations in a wide range of parameters. Nonequilibrium properties, on the other hand, cannot be accessed with conventional techniques. Thanks to the recent advances in numerics (e.g. tensor networks) and experiments (quantum simulation), new promising tools are now available for tackling these questions. Remarkable works have already demonstrated that applying these techniques to simple theories, such as one-dimensional quantum electrodynamics, can help to detect the signatures of confinement and pair creation. Despite these impressive achievements, investigating the non-equilibrium dynamics of gauge theories with quantum simulators turned out to be extremely challenging. This is mostly due to the complex constrained dynamics of these theories, which make their simulation with realistic atomic platforms particularly difficult. At the same time, the dynamical constraints can play a key role in determining novel interesting phenomena and peculiar non-equilibrium properties. These phenomena -- which include, for example, quantum scars, fractons, Hilbert space fragmentation -- can lead to anomalous dynamics, eventually evading the paradigm of thermalization, which predicts the relaxation of physical observable to their thermodynamic values. The aim of this thesis is twofold: first, we want to address through a combination of numerical and analytical tools some of the open questions regarding the non-equilibrium dynamics of quantum many-body systems with constrained Hilbert spaces, including lattice gauge theories. In addition, the work reported here is part of a large effort of the community towards the quantum simulation of complex phenomena of condensed matter and high-energy physics.