Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

Abstract

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 \mathrm{U}(1)U(1) quantum link lattice gauge theory where the gauge fields, represented by spin-\frac{1}{2}12 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)(2+1)-d. This model allows us to smoothly tune between the \mathrm{U}(1)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.

Entanglement Witnessing for Lattice Gauge Theories

“…As an illustrative example, we consider-in addition to gauge fields living on the links the lattice L-single-species fermions living on the lattice sites. Concretely, we consider staggered fermions [56] (see, e.g., references [55,57] for applications to quantum link models), where negatively (positively) charged (anti-)particles are associated in an alternating fashion to the sites of the lattice. The gauge generators of equation (3.1) are then modified to…”

Disorder-Free Localization in $2+1$D Lattice Gauge Theories with Dynamical Matter

“…Even though one can in principle employ Gauss's law to integrate out matter degrees of freedom in, e.g., U(N ) and SU(N ) LGTs, this usually comes at the cost of extending the range of interactions, introducing additional local constraints, and breaking the gauge symmetry [47], which gives rise to a model vastly different from the pure LGT. Indeed, it is known that retaining dynamical fermionic matter in 2 + 1D can lead to significantly richer physics, such as, e.g., possible exotic quantum spin liquid phases in regularized lattice QED [48]. Furthermore, recent concrete proposals for the realization of different kinds of 2 + 1D LGTs with dynamical matter on cold-atom platforms [49][50][51] provides further impetus to understand DFL behavior in such models.…”