We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.
We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.
Quantum phases of two-dimensional Z2 gauge theory coupled to spinless fermion matter
We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with U(1) symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure Z2 even and odd gauge theories, (ii) free fermions in a static background of deconfined Z2 gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of Z2 gauge-invariant spin 1/2 degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization.
A study of spinless matter fermions coupled to a constrained Z2 lattice gauge theory on a triangular ladder is presented. The triangular unit cell and the ladder geometry strongly modify the physics, as compared with a previous analysis on the square lattice. In the static case, the even and odd gauge theories for the empty and filled ladder are identical. The gauge field dynamics due to the electric coupling is drastically influenced by the absence of periodic boundary conditions, rendering the deconfinement-confinement process a crossover in general and a quantum phase transition (QPT) only for decorated couplings. At finite doping and in the static case, a staggered flux insulator at half-filling and vanishing magnetic energy competes with a uniform flux metal at elevated magnetic energy. As for the square lattice, a single QPT into a confined fermionic dimer gas is found vs electric coupling. Dimer resonances in the confined phase are, however, a second-order process only, likely reducing the tendency to phase separate for large magnetic energy. The results obtained employ a mapping to a pure spin model of Z2 gauge-invariant moments, adapted from the square lattice, and density matrix renormalization group calculations thereof for numerical purposes. Global scans of the quantum phases in the intermediate coupling regime are provided.
Abstract Coupling dynamical charges to gauge fields can result in highly non-local interactions with a linear confining potential. As a consequence, individual particles bind into mesons which, in one dimension, become the new constituents of emergent Luttinger liquids (LLs). Furthermore, at commensurate fillings, different Mott-insulating states can be stabilized by including nearest-neighbour (NN) interactions among charges. However, rich phase diagrams expected in such models have not been fully explored and still lack comprehensive theoretical explanation. Here, by combining numerical and analytical tools, we study a simple one-dimensional Z 2 lattice gauge theory at half-filling, where U(1) matter is coupled to gauge fields and interacts through NN repulsion. We uncover a rich phase diagram where the local NN interaction stabilizes a Mott state of individual charges (or partons) on the one hand, and an LL of confined mesons on the other. Furthermore, at the interface between these two phases, we uncover a highly frustrated regime arising due to the competition between the local NN repulsion and the non-local confining interactions, realizing a pre-formed parton plasma. Our work is motivated by the recent progress in ultracold atom experiments, where such simple model could be readily implemented. For this reason we calculate the static structure factor which we propose as a simple probe to explore the phase diagram in an experimental setup.
Matter-induced plaquette terms in a Z2 lattice gauge theory
Lattice gauge theories (LGTs) provide a powerful framework for studying confinement, topological order, and exotic quantum matter. In particular, the paradigmatic phenomenon of confinement, where dynamical matter is coupled to gauge fields and forms bound states, remains an open problem. In addition, LGTs can provide low-energy descriptions of quantum spin liquids, which is the focus of ongoing experimental research. However, the study of LGTs is often limited theoretically by their numerical complexity and experimentally in implementing challenging multi-body interactions, such as the plaquette terms crucial for the realization of many exotic phases of matter. Here we investigate a (2+1)D Z2 LGT coupled to hard-core bosonic matter featuring a global U(1) symmetry, and show that dynamical matter naturally induces sizable plaquette interactions even in the absence of explicit plaquette terms in the Hamiltonian. Using a combination of density matrix renormalization group simulations and neural quantum state calculations up to a system size of 20×20, we analyze the model across different fillings and electric field strengths. At small coupling strength, we find a large plaquette expectation value, independent of system size, for a wide range of fillings, which decreases in the presence of stronger electric fields. Furthermore, we observe signatures of a confinement-deconfinement transition at weak coupling strengths. Our results demonstrate that dynamical U(1) matter can induce complex multi-body interactions, suggesting a natural route to the realization of strong plaquette terms and paving the way for realizing a topological quantum spin liquid protected by a large gap.
Confinement is an ubiquitous phenomenon when matter couples to gauge fields, which manifests itself in a linear string potential between two static charges. Although gauge fields can be integrated out in one dimension, they can mediate nonlocal interactions which in turn influence the paradigmatic Luttinger liquid properties. However, when the charges become dynamical and their densities finite, understanding confinement becomes challenging. Here we show that confinement in 1D Z_{2} lattice gauge theories, with dynamical matter fields and arbitrary densities, is related to translational symmetry breaking in a nonlocal basis. The exact transformation to this string-length basis leads us to an exact mapping of Luttinger parameters reminiscent of a Luther-Emery rescaling. We include the effects of local, but beyond contact, interactions between the matter particles, and show that confined mesons can form a Mott-insulating state when the deconfined charges cannot. While the transition to the Mott state cannot be detected in the Green's function of the charges, we show that the metallic state is characterized by hidden off-diagonal quasi-long-range order. Our predictions provide new insights to the physics of confinement of dynamical charges, and can be experimentally addressed in Rydberg-dressed quantum gases in optical lattices.
Emergent superconformal symmetry in the phase diagram of a 1D Z2 lattice gauge theory
We investigate the phase diagram and critical properties of a one-dimensional Z2 lattice gauge theory describing an orthogonal metal, where spinless fermions and Ising spins are minimally coupled to a deconfined Z2 gauge field. Working at half-filling of fermions, we derive an exact gauge-invariant formulation that maps the model onto decoupled XXZ and transverse-field Ising chains. This mapping enables a controlled low-energy field-theory description in terms of a perturbed Luttinger liquid and Ising conformal field theories. Combining analytical arguments with numerical simulations, we determine the full phase diagram and identify various critical and multi-critical regimes. Along a specific multi-critical line, where the fermionic and bosonic velocities coincide, we find strong evidence for an emergent superconformal symmetry. Our results establish a minimal lattice realization of emergent superconformal criticalities in a gauge-matter system and provide a route toward its exploration in quantum simulators.