Stripping the planar Quantum Compass Model to its basics

Abstract

We introduce a novel mean-field theory (MFT) around the exactly soluble two-leg ladder limit for the planar quantum compass model (QCM). In contrast to usual MFT, our construction respects the stringent constraints imposed by emergent, lower (here $d=1$) dimensional symmetries of the QCM. Specializing our construction to the QCM on a periodic four-leg ladder, we find that a first-order transition separates two mutually dual Ising nematic phases, in good accord with state-of-the-art numerics for the planar QCM. One pseudo-spin-flip excitation in the ordered phase turns out to be two (Jordan-Wigner) fermion bound states, reminiscent of spin waves in spin-$1/2$ Heisenberg chains. We discuss the novel implications of our work on (1) the emergence of coupled orbital and magnetic ordered and liquidlike disordered phases, and (2) a rare instance of orbital-spin separation in $d>1$, in the context of a Kugel-Khomskii view of multi-orbital Mott insulators.

arXiv comment18 pages, 7 figures

References in corpus (26)

• Anyons in an exactly solved model and beyond
• An RVB phase in the triangular lattice quantum dimer model
• Spin-Orbital Separation in the quasi 1D Mott-insulator Sr2CuO3
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Protected Qubits and Chern Simons theories in Josephson Junction Arrays
• Symmetry and Topological Order
• The Quantum Compass Model on the Square Lattice
• Generalized Elitzur's Theorem and Dimensional Reduction
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Self-duality and bound states of the toric code model in a transverse field
• Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays
• First order phase transition in the anisotropic quantum orbital compass model
• The "Strange Metal" is a Projected Fermi Liquid with Edge Singularities
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Finite temperature spin-dynamics and phase transitions in spin-orbital models
• Nature of the Quantum Phase Transition in Quantum Compass Model
• Dimensional reduction in superconducting arrays and frustrated magnets
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Orbital ordering in e_g orbital systems: Ground states and thermodynamics of the 120 degree model
• Magnetic properties of nanoscale compass-Heisenberg planar clusters
• Spin-waves in the $J_{1a}-J_{1b}-J_2$ orthorombic square-lattice Heisenberg models: Application to the iron pnictide materials
• Hidden dimer order in the quantum compass model
• Exact solution for a quantum compass ladder
• The Quantum Compass Model on the Square and Simple Cubic Lattices
• Orbital Compass Model as an Itinerant Electron System