Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice

Abstract

The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in J_xy, deconfined spinon excitations. We explore the role of cyclic exchange arising at order J^2_xy/J_z on the ice states and their associated spinon excitations. By mapping the original problem onto an equivalent quantum six--vertex model, we identify three different phases as a function of the chemical potential for flippable plaquettes - a phase with long range Neel order and confined spinon excitations, a non-magnetic state of resonating square plaquettes, and a quasi-collinear phase with gapped but deconfined spinon excitations. The relevance of the results to the square--lattice quantum dimer model is also discussed.

4 pages, 5 figures

References in corpus (1)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet

Cited by in corpus (35)

• Tensor Networks for Lattice Gauge Theories with continuous groups
• Quantum scars from zero modes in an Abelian lattice gauge theory on ladders
• Disorder-free localization in an interacting two-dimensional lattice gauge theory
• Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models
• From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories
• Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model
• Correlated Fermions on a Checkerboard Lattice
• Resonating plaquette phase of a quantum six-vertex model
• Spectral functions and optical conductivity of spinless fermions on a checkerboard lattice
• Doped Singlet-Pair Crystal in the Hubbard model on the checkerboard lattice
• Doping quantum dimer models on the square lattice
• Fully packed quantum loop model on the square lattice: phase diagram and application for Rydberg atoms
• Towards the real-time evolution of gauge-invariant ${\mathbb{Z}}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation
• Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Plaquette bond order wave in the quarter-filled extended Hubbard model on the checkerboard lattice
• Prethermal time-crystalline spin ice and monopole confinement in a driven magnet
• Exotic Mott phases of the extended t--J model on the checkerboard lattice at commensurate densities
• Quantum phase diagram of two-dimensional transverse field Ising model: unconstrained tree tensor network and mapping analysis
• Recent progress on cluster and meron algorithms for strongly correlated systems
• Fermionic quantum dimer and fully-packed loop models on the square lattice
• Solving the quantum dimer and six vertex models one electric field line at a time
• Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice
• Magnetic Order and Mott Transition on the Checkerboard Lattice
• Spectral response of disorder-free localized lattice gauge theories
• Hardcore bosons on checkerboard lattices near half filling: geometric frustration, vanishing charge order and fractional phase
• Projectification of point group symmetries with a background flux and Lieb-Schultz-Mattis theorem
• Classical fully-packed loop model with attractive interactions on the square lattice
• Crystalline phases at finite winding densities in a quantum link ladder
• Crystalline phases and devil's staircase in qubit spin ice
• Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model
• Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
• Fractionally charged excitations on frustrated lattices
• Disorder-free localization transition in a two-dimensional lattice gauge theory