Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. QLMs not only reproduce standard features of Wilson lattice gauge theories in equilibrium, but can also host new phenomena such as crystalline confined phases. The local constraints due to gauge invariance also provide kinetic restrictions that can influence substantially the real-time dynamics in these systems. We aim to characterize the nonequilibrium evolution in lattice gauge theories through the lens of dynamical quantum phase transitions, which provide general principles for real-time dynamics in quantum many-body systems. Specifically, we study quantum quenches for two representative cases, U(1) QLMs in (1+1)D and (2+1)D, for initial conditions exhibiting long-range order. Finally, we discuss the connection to the high-energy perspective and the experimental feasibility to observe the discussed phenomena in recent quantum simulator settings such as trapped ions, ultracold atoms, and Rydberg atoms.
Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. QLMs not only reproduce standard features of Wilson lattice gauge theories in equilibrium, but can also host new phenomena such as crystalline confined phases. The local constraints due to gauge invariance also provide kinetic restrictions that can influence substantially the real-time dynamics in these systems. We aim to characterize the nonequilibrium evolution in lattice gauge theories through the lens of dynamical quantum phase transitions, which provide general principles for real-time dynamics in quantum many-body systems. Specifically, we study quantum quenches for two representative cases, U(1) QLMs in (1+1)D and (2+1)D, for initial conditions exhibiting long-range order. Finally, we discuss the connection to the high-energy perspective and the experimental feasibility to observe the discussed phenomena in recent quantum simulator settings such as trapped ions, ultracold atoms, and Rydberg atoms.
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.
<!--HTML-->Quantum link models provide an extension of Wilson's lattice gauge theory in which the link variables have operator-valued entries. For example, in a U(1) quantum link model the link variables are raising and lowering operators of quantum spins that belong to a link-based SU(2) embedding algebra. For non-Abelian SU(N), Spin(N), or Sp(N) quantum link models, the embedding algebras are SU(2N), Spin(2N), and Sp(2N), respectively. In contrast to Wilson's framework, quantum link models can be realized in a finite-dimensional link Hilbert space corresponding to a representation of the embedding algebra. This is well suited for a resource efficient implementation of quantum link models in quantum simulation experiments. The quantum link dynamics can be embodied with a finite number of well-controlled states of ultra-cold matter, including atoms in an optical lattice, ions in a trap, or quantum circuits. For example, using dual variables, a densely encoded quantum circuit has recently been constructed for a (2+1)-d U(1) quantum link model on a triangular lattice that shows qualitatively new nematic phases with rich confining dynamics. Quantum spins and quantum links are discrete quantum variables which give rise to collective low-energy excitations. In (2+1)-d, SU(N) quantum spins give rise to massless Goldstone bosons which undergo dimensional reduction to (1+1)-d asymptotically free CP(N-1) models. This can be realized in quantum simulation experiments with alkaline-earth atoms in an optical lattice. In (3+1)-d, Abelian quantum links give rise to massless photons which undergo dimensional reduction to (2+1)-d confining U(1) gauge theory, which can be embodied with spin-ice. In (4+1)-d, non-Abelian quantum links give rise to massless gluons which undergo dimensional reduction to (3+1)-d Yang-Mills theory. Quarks are naturally included as domain wall fermions. The dimensional reduction of discrete quantum variables defines D-theory, in which quantum field theories emerge from a minimal set of degrees of freedom, thus enabling resource efficient implementations in quantum simulation experiments. D-theory provides a concrete vision how to realize the ultimate long-term goal of quantum simulating QCD.
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.
Confinement is an intriguing phenomenon prevalent in condensed matter and high-energy physics. Exploring its effect on the far-from-equilibrium criticality of quantum many-body systems is of great interest from both a fundamental and a technological point of view. Here, we employ large-scale uniform matrix product state calculations to show that a qualitative change in the type of dynamical quantum phase transitions (DQPTs) accompanies the confinement-deconfinement transition in three paradigmatic models: the power-law interacting quantum Ising chain, the two-dimensional quantum Ising model, and the spin- S U ( 1 ) quantum link model. By tuning a confining parameter in these models, it is found that () DQPTs arise as a signature of (de)confinement. Whereas manifold DQPTs are associated with a sign change of the order parameter, their branch counterparts are not, but rather occur even when the order parameter exhibits considerably constrained dynamics. Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.
Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories, and show rich physics beyond the phenomena of conventional Wilson gauge theories. Here we explore the physics of U(1) symmetric QLMs, both using a more conventional quantum spin-1/2 representation, as well as a fermionic representation. In 2D, we show that both bosonic and fermionic QLMs display the same physics. We then explore the models in 3D and find different behavior for the two QLMs. For the bosons, we see evidence for a quantum phase transition from a symmetry broken phase to a potential quantum spin liquid phase. For the fermions, we identify not one but two distinct phases in addition to a symmetry broken phase. We explore the symmetries of the ground state in the strong coupling limit, which breaks lattice symmetries and examine the spectrum for both models.