Abstract
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 $\mathbb{Z}_N$ gauge symmetries. We study its phase diagram based on both an effective low-energy field theory and density matrix renormalization group simulations. For $N\ge 5$, 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.
Highlights
Gauge theories are both the backbone of the standard model of particle physics and the key to understand a wide variety of condensed matter systems [1]
Ladder setups offer the simplest realization of a lattice gauge theory whose dynamics crucially relies on the plaquette interactions
The first steps in this direction have already been accomplished in ultracold atom systems trapped in optical lattices: a recent experiment [11] has proved that a tunneling term mediated by an effective Z2 gauge degrees of freedom can be realized based on density-dependent laser-assisted tunneling techniques
Summary
Gauge theories are both the backbone of the standard model of particle physics and the key to understand a wide variety of condensed matter systems [1]. We address ZN LGTs in the geometry of ladder systems This geometry offers an interesting compromise between one and two dimensions: on one side, it is the simplest geometry featuring plaquette interactions, enabling a full investigation of the Kogut and Susskind Hamiltonian; on the other, its quasi-1D nature allows us to develop an effective quantum field theory based on bosonization [36], which guides us in the exploration of the phase diagram of the model. The last generation of experimental platforms for quantum simulators based on Rydberg atoms displayed the emergence of phases with discrete ZN symmetries [42] These Abelian LGTs constitute simplified models in which the gauge bosons mediating the interactions among the matter particles behave like photons and do not directly interact with themselves. The Appendixes are devoted to several details of the analysis of the model and its renormalization group study
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