Exact solution for a quantum compass ladder

Abstract

We introduce a spin ladder with antiferromagnetic Ising ZZ interactions along the legs, and interactions on the rungs which interpolate between the Ising ladder and the quantum compass ladder. We show that the entire energy spectrum of the ladder may be determined exactly for finite number of spins 2N by mapping to the quantum Ising chain and using Jordan-Wigner transformation in invariant subspaces. We also demonstrate that subspaces with spin defects lead to excited states using finite size scaling, and the ground state corresponds to the quantum Ising model without defects. At the quantum phase transition to maximally frustrated interactions of the compass ladder, the ZZ spin correlation function on the rungs collapses to zero and the ground state degeneracy increases by 2. We formulate a systematic method to calculate the partition function for a mesoscopic system, and employ it to demonstrate that fragmentation of the compass ladder by kink defects increases with increasing temperature. The obtained heat capacity of a large compass ladder consisting of 2N=104 spins reveals two relevant energy scales and has a broad maximum due to dense energy spectrum. The present exact results elucidate the nature of the quantum phase transition from ordered to disordered ground state found in the compass model in two dimensions.

15 pages, 11 figures, to appear in Phys. Rev. B

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Cited by in corpus (24)

• Fingerprints of spin-orbital entanglement in transition metal oxides
• Logarithmic entanglement growth from disorder-free localization in the two-leg compass ladder
• Spin-orbital resonating valence bond liquid on a triangular lattice: Evidence from finite-cluster diagonalization
• Fidelity susceptibility in the two-dimensional spin-orbit models
• Magnetic properties of nanoscale compass-Heisenberg planar clusters
• Hidden dimer order in the quantum compass model
• Quantum phase transitions in exactly solvable one-dimensional compass models
• Symmetry properties and spectra of the two-dimensional quantum compass model
• Exact solution of a spin-1/2 $XX$ chain with three-site interactions in a random transverse field: Influence of randomness on quantum phase transition
• Quantum phase transitions in the exactly solved spin-1/2 Heisenberg-Ising ladder
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• The Quantum Compass Model on the Square and Simple Cubic Lattices
• Spin dynamics of the generalized quantum spin compass chain
• Frustration and Entanglement in Compass and Spin-Orbital Models
• Charge and orbital order in transition metal oxides
• Spin, orbital and topological order in models of strongly correlated electrons
• Topological Phase Transition in the Extended Cluster Compass Ladder
• Compass model on a ladder and square clusters
• Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model
• Ground state of a spin-1/2 Heisenberg-Ising two-leg ladder with XYZ intra-rung coupling
• One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization
• Stripping the planar Quantum Compass Model to its basics
• Families of $d=2$ 2D subsystem stabilizer codes for universal Hamiltonian quantum computation with two-body interactions
• Protecting Hilbert space fragmentation through quantum Zeno dynamics