We consider multileg ladders of Rydberg atoms which have been proposed as quantum simulators for the compact Abelian Higgs model (CAHM) in $1+1$ dimensions [Y. Meurice, Phys. Rev. D 104, 094513 (2021)] and modified versions of theses simulators such as triangular prisms. Starting with the physical Hamiltonian for the analog simulator, we construct translation-invariant effective Hamiltonians by integrating over the simulator high-energy states produced by the blockade mechanism when some of the atoms are sufficiently close to each other. Remarkably, for all the simulators considered, the effective Hamiltonians have the three types of terms present for the CAHM (electric field, matter charge, and current energy), but in addition, they have terms quartic in the electric field. For the two-leg ladder, these additional terms cannot be removed by fine-tuning the adjustable parameters of currently available devices. For positive detuning, the new terms create highly degenerate vacua, resulting in a very interesting phase diagram. Using numerical methods, we demonstrate the close correspondence between the physical simulator and the effective description for the ground-state energy and real-time evolution. We discuss the phase diagram at fixed geometry with variable Rabi frequency and detuning, and we show that a rich variety of phases can be reached with potential interest in the context of QCD at finite density. We illustrate how the effective description can be used to design simulators with desirable properties from the point of view of constructing hybrid event generators.
We consider multileg ladders of Rydberg atoms which have been proposed as quantum simulators for the compact Abelian Higgs model (CAHM) in 1+1 dimensions [Y. Meurice, Phys. Rev. D 104, 094513 (2021)] and modified versions of theses simulators such as triangular prisms. Starting with the physical Hamiltonian for the analog simulator, we construct translation-invariant effective Hamiltonians by integrating over the simulator high-energy states produced by the blockade mechanism when some of the atoms are sufficiently close to each other. Remarkably, for all the simulators considered, the effective Hamiltonians have the three types of terms present for the CAHM (electric field, matter charge, and current energy), but in addition, they have terms quartic in the electric field. For the two-leg ladder, these additional terms cannot be removed by fine-tuning the adjustable parameters of currently available devices. For positive detuning, the new terms create highly degenerate vacua, resulting in a very interesting phase diagram. Using numerical methods, we demonstrate the close correspondence between the physical simulator and the effective description for the ground-state energy and real-time evolution. We discuss the phase diagram at fixed geometry with variable Rabi frequency and detuning, and we show that a rich variety of phases can be reached with potential interest in the context of QCD at finite density. We illustrate how the effective description can be used to design simulators with desirable properties from the point of view of constructing hybrid event generators.
We review recent suggestions to quantum simulate scalar electrodynamics (the lattice Abelian Higgs model) in 1+1 dimensions with rectangular arrays of Rydberg atoms. We show that platforms made publicly available recently allow empirical explorations of the critical behavior of quantum simulators. We discuss recent progress regarding the phase diagram of two-leg ladders, effective Hamiltonian approaches and the construction of hybrid quantum algorithms targeting hadronization in collider physics event generators.
Lattice gauge theories are fundamental to our understanding of high-energy physics. Nevertheless, the search for suitable platforms for their quantum simulation has proven difficult. We show that the Abelian Higgs model in 1+1 dimensions is a prime candidate for an experimental quantum simulation of a lattice gauge theory. To this end, we use a discrete tensor reformulation to smoothly connect the space-time isotropic version used in most numerical lattice simulations to the continuous-time limit corresponding to the Hamiltonian formulation. The eigenstates of the Hamiltonian are neutral for periodic boundary conditions, but we probe the nonzero charge sectors by introducing either a Polyakov loop or an external electric field. In both cases we obtain universal functions relating the mass gap, the gauge coupling, and the spatial size, which are invariant under the deformation of the temporal lattice spacing. We propose to use a physical multileg ladder of atoms trapped in optical lattices and interacting with Rydberg-dressed interactions to quantum simulate the model and check the universal features. Our results provide a path to the analog quantum simulation of lattice gauge theories with atoms in optical lattices.
We study the ground-state phase diagram of Rydberg atoms in a triangular-prism optical tweezer array using the density matrix renormalization group. By tuning the detuning-to-Rabi-frequency ratio and the Rydberg blockade radius, the system realizes several density-wave phases with spontaneous breaking of translational and leg-exchange symmetries. Unlike two-leg Rydberg ladders with Z2 leg-exchange symmetry, the triangular prism has D3 symmetry, leading to a richer set of ordered phases and transitions. For blockade radius moderately larger than the lattice spacing, a phase with alternating double and single Rydberg occupancy appears at large detuning. It breaks Z2 translational and Z3 rotational symmetry while preserving a rung reflection symmetry. Upon decreasing detuning, it melts through two Berezinskii-Kosterlitz-Thouless transitions with an intermediate critical phase described by a Z6 clock model. At larger blockade radius, a phase with one Rydberg excitation per triangle and broken D3 symmetry appears through a first-order transition. When double occupation of neighboring triangles is suppressed, rung-trimerized density waves develop as detuning increases from the disordered phase. Their melting follows the same structure as in Rydberg chains and two-leg ladders: the Z2 case has Ising critical lines, while the Z3 and Z4 cases have chiral critical lines, with Potts and Ashkin-Teller points only on the corresponding commensurate lines. Inside the Z2 rung-trimerized phase, an entanglement-entropy peak signals a crossover regime with enhanced period-2 density modulation before a first-order transition into a Z2×D3 phase. Floating phases with incommensurate quasi-long-range order appear between trimerized states of different periods.
The lattice compact Abelian Higgs model is a nonperturbative regularized formulation of low-energy scalar quantum electrodynamics. In 1+1 dimensions, this model can be quantum simulated using a ladder-shaped optical lattice with Rydberg-dressed atoms [J. Zhang et al., Phys. Rev. Lett. 121, 223201 (2018)]. In this setup, one spatial dimension is used to carry the angular momentum of the quantum rotors. One can use truncations corresponding to spin-2 and spin-1 to build local Hilbert spaces associated with the links of the lattice. We argue that ladder-shaped configurable arrays of Rydberg atoms can be used for the same purpose. We make concrete proposals involving two and three Rydberg atoms to build one local spin-1 space (a qutrit). We show that the building blocks of the Hamiltonian calculations are models with one and two spins. We compare target and simulators using perturbative and numerical methods. The two-atom setup provides an easily controllable simulator of the one-spin model while the three-atom setup involves solving nonlinear equations. We discuss approximate methods to couple two spin-1 spaces. The article provides analytical and numerical tools necessary to design and build the proposed simulators with current technology.
Under the perspective of realizing analog quantum simulations of lattice gauge theories, ladder geometries offer an intriguing playground, relevant for ultracold atom experiments.Here, we investigate Hamiltonian lattice gauge theories defined in two-leg ladders.We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local Z N gauge symmetries.We study its phase diagram based on both an effective low-energy field theory and density matrix renormalization group simulations.For N 5, an extended gapless Coulomb phase emerges, which is separated by a Berezinskii-Kosterlitz-Thouless phase transition from the surrounding gapped phase.Besides the traditional confined and Higgs regimes, we also observe a novel quadrupolar region, originated by the ladder geometry.
Gauge theories and topological phases play a fundamental role in different areas of physics. The first ones are at the basis of the Standard Model in the field of particle physics, describing the electroweak and strong interactions through a non-Abelian gauge theory. In condensed matter and statistical physics, gauge theories arise as low-energy effective descriptions of strongly correlated phenomena, such as quantum spin liquids and quantum Hall effect. In this realm there is a strong connection with topological phases and order, as emergent gauge fermions and bosons often describe collective excitations of new exotic states of matter of spin models. The discretization on a lattice is a possible way of dealing with the strongly coupled nature of these theories, due to the fact that this formulation at finite volume provides natural regularizing cut-offs, i.e. the lattice size and spacing. This allows for the investigation of different non-perturbative properties both numerically and analytically. Despite the success of these methods, there are various aspects which remain intractable due to the sign or complex action problems, like the out of equilibrium real time evolution or the analysis of quantum chromodynamics with finite chemical potential. In this respect, quantum simulators of many-body systems to simulate high energy physics arise as promising alternatives to face these problems in the near future. They are quantum systems that can be controlled and used to simulate more complicated systems, whose properties could not be analysed with classical computational, experimental or theoretical tools. In the last decades, there has been a huge development in the fields of quantum optics and atomic physics, allowing for the realization highly precise and controllable platforms by means of trapped ions, superconducting circuits, Rydberg atoms and ultracold atoms in optical lattices. This work of Thesis is part of these fields and has different purposes, all of them connected with the study of gauge theories and topological phases. Firstly, we want to develop a reformulation of lattice gauge theories in terms of gauge invariant fields, in a way to deal solely with physical variables directly in the action. Among several possible advantages, a crucial point is that this can be particularly helpful for the construction of consistent approximation schemes, such as mean-field theories, in order to understand and capture some of the physical features of the theory and make the mean-field approximation consistent with the Elitzur theorem, stating that a local gauge symmetry can not be spontaneously broken. As a second point, we face the problem of simulating higher dimensional gauge theories with ultracold atoms. One of the challenges in more than one dimension is indeed the realization of plaquette interaction terms in the Hamiltonian of lattice gauge theories: these can be engineered through four correlated hoppings in perturbation theory, or by means of constrained hoppings in the dual formulation. In this respect, our main target is to set up an ultracold atomic platform generating the plaquette term in two dimensions using only two correlated hoppings, and protecting gauge invariance through angular momentum conservation. The last point we address in the Thesis is related to the analysis of particles moving in static background gauge potentials, i.e. when the considered gauge field has no dynamical term in the action of the system. Indeed, the dynamics of quantum particles in the presence of static gauge fields gives rise to intriguing physical phenomena. In particular, using ultracold atom setups, the realization of artificial gauge potentials can be used to investigate the physics of topological semimetals, such as Weyl or Dirac type. In the last ten years, a lot of attention has been paid to their characterization, due to the appearence of clear theoretical predictions and very well-controlled experimental techniques. We investigate here the relation between topological phase transitions and van Hove singularities, i.e. the discontinuities in the energy derivative of the density of states, in three-dimensional gapless systems. In such materials, topological phase transitions can be defined by changes of the topological invariants of the Fermi sheets, happening at specific singular points. Moreover, Fermi surface singularities result in the presence of the so-called van Hove points. We then present a general argument to relate topological phase transitions and van Hove singularities, and show observable consequences that are related to the transport properties of the system. We exemplify our argument in Weyl systems by analyzing the three-dimensional Hofstadter model for various commensurate fluxes, which offers the opportunity to consider different kinds of Weyl metals and to understand the features of their density of states.