Confinement and Mott Transitions of Dynamical Charges in One-Dimensional Lattice Gauge Theories

Abstract

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 non-local 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 Z2 lattice gauge theories, with dynamical matter fields and arbitrary densities, is related to translational symmetry breaking in a non-local basis. The exact transformation to this string-length basis leads us to an exact mapping of Luttinger parameters reminiscent of a Luther-Emery re-scaling. 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.

Fractionalized holes in one-dimensional $\mathbb{Z}_2$ gauge theory coupled to fermion matter -- deconfined dynamics and emergent integrability

“…We uncover emergent integrability of the slow hole dynamics in that regime and demonstrate its equivalence to the constrained XXZ model of Alcaraz and Bariev [42]. Moreover, following [33], we investigate the salient consequences of additional short-range fermion interactions in this lattice gauge theory. While for the repulsive case these interactions can stabilize the Mott state at the hole filling ν h = 1/3, in the case of attraction we predict the phenomenon of clustering of holes into large conglomerates, whose hopping scales exponentially with their length.…”

“…Here we consider one-component U (1)-symmetric quantum fermion matter hopping on a one-dimensional lattice coupled to dynamical Z 2 gauge fields [27][28][29][30][31][32][33][34][35]. Despite the confining nature of the attractive interaction between lattice fermions mediated by the gauge field, the model is known to form a Luttinger liquid that exhibits gapless deconfined low-energy excitations.…”

“…Despite the confining nature of the attractive interaction between lattice fermions mediated by the gauge field, the model is known to form a Luttinger liquid that exhibits gapless deconfined low-energy excitations. [27,31,33]. In this paper we draw attention to and investigate the peculiar physics of the fractionalized holes which are domain walls between vacuua fully filled with fermions.…”

Probing confinement in a $\mathbb{Z}_2$ lattice gauge theory on a quantum computer

“…The Z 2 LGT in 1+1D considered in the main text is equivalent to the more common formulation with fermionic matter, described by the Hamiltonian [19,30]…”

Enhancing disorder-free localization through dynamically emergent local symmetries

“…Drawing inspiration from recent experimental [13] and theoretical [77,78] work, we consider the (1 + 1)−dimensional Z 2 lattice gauge theory given by the Hamiltonian [79][80][81][82]…”