${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry

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.

31 pages, 20 figures; published version with additional appendix

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• Bosonizing one-dimensional cold atomic gases
• Strong and weak thermalization of infinite non-integrable quantum systems
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Digital lattice gauge theories
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Quantum simulation of the Schwinger model: A study of feasibility
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Qudit surface codes and gauge theory with finite cyclic groups
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Phase transition of the q-state clock model: duality and tensor renormalization
• Commensurate and Incommensurate States of Topological Quantum Matter
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase

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• Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models
• Confinement-Induced Enhancement of Superconductivity in a Spin-$\frac{1}{2}$ Fermion Chain Coupled to a ${\mathbb{Z}}_2$ Lattice Gauge Field
• Engineering a Josephson junction chain for the simulation of the clock model
• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup