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.
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.
Lattice gauge theories (LGTs)1–4 can be used to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials5–7. Studying dynamical properties of emergent phases can be challenging, as it requires solving many-body problems that are generally beyond perturbative limits8–10. Here we investigate the dynamics of local excitations in a
Z2 LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit that prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics by means of a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT, from which we uncover two distinct regimes inside the confining phase: for weak confinement, the string fluctuates strongly in the transverse direction, whereas for strong confinement, transverse fluctuations are effectively frozen11,12. We also demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a new set of techniques for investigating emergent excitations and string dynamics. In a quantum simulation of a (2+1)D lattice gauge theory using a superconducting quantum processor, the dynamics of strings reveal the transition from deconfined to confined excitations as the effective electric field is increased.
Topological phases of matter can support fractionalized quasiparticles localized at topological defects. The current understanding of these exotic excitations, based on the celebrated bulk-defect correspondence, typically relies on crude approximations where such defects are replaced by a static classical background coupled to the matter sector. In this work, we explore the strongly correlated nature of symmetry-protected topological defects by focusing on situations where such defects arise spontaneously as dynamical solitons in intertwined topological phases, where symmetry breaking coexists with topological symmetry protection. In particular, we focus on the
Z2 Bose-Hubbard model, a one-dimensional chain of interacting bosons coupled to
Z2 fields, and show how solitons with
Zn topological charges appear for particle/hole dopings about certain commensurate fillings, extending the results in D. Gonz\'alez-Cuadra et al. [Phys. Rev. Lett. 125, 265301 (2020)] beyond half filling. We show that these defects host fractionalized bosonic quasiparticles, forming bound states that travel through the system unless externally pinned, and repel each other giving rise to a fractional soliton lattice for sufficiently high densities. Moreover, we uncover the topological origin of these fractional bound excitations through a pumping mechanism, where the quantization of the intersoliton transport allows us to establish a generalized bulk-defect correspondence. This in-depth analysis of dynamical topological defects bound to fractionalized quasiparticles, together with the possibility of implementing our model in cold-atomic experiments, paves the way for further exploration of exotic topological phenomena in strongly correlated systems.
Using Quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with
N flavors of fermions per site for
N=1,2 and
3. The models have an extensive number of conserved quantities but are not integrable, and have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond Landau-Ginzburg paradigm. In particular, one of the prominent phase for
N>1 corresponds to
2N gapless Dirac fermions coupled to an emergent
Z2 gauge field in its deconfined phase. However, unlike a conventional
Z2 gauge theory, we do not impose the `Gauss's Law' by hand and instead, it emerges due to spontaneous symmetry breaking. Correspondingly, unlike a conventional
Z2 gauge theory in two spatial dimensions, our models have a finite temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss's law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short range entangled phase, which corresponds to N\'eel/Superconductor for
N=2 and a Valence Bond Solid for
N=3. Furthermore, for
N=3, the Valence Bond Solid further undergoes a transition to a N\'eel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.
Gauge theories are ubiquitous in contemporary physics. Here, the authors investigate the many-body phase diagram of a model where dynamical discrete Ising gauge fields mediate interactions between single-component fermionic matter. Such a system remained intractable for years, due to the lack of sign-problem-free Monte-Carlo simulations. With the help of a combination of analytical and state-of-the-art numerical tensor-network-based methods, the authors uncover the salient features of an intricate quantum phase diagram and reveal surprising aspects of quantum constrained dynamics. The recent advances in cold-atoms-based setups might soon allow experimental explorations of this model.