Brane order and quantum magnetism in modulated anisotropic ladders

Abstract

Two-leg spin-$\frac{1}{2}$ ladders with anisotropy and two different dimerization patterns are analyzed at zero temperature. This model is equivalent to a modulated interacting (Kitaev) ladder. The Hartree-Fock mean-field approximation reduces the model to a sum of two quadratic effective Majorana Hamiltonians, which are dual to a sum of two (even/odd) XY quantum chains in the alternating transverse fields. The mapping between the effective Hamiltonian of the ladder and the pair of the dual XY chains considerably simplifies calculations the order parameters and analysis of the hidden symmetry breaking. The ground-state phase diagram of the staggered ladder contains nine phases, four of them are conventional antiferromagnets, while the other five possess non-local brane orders. Using the dualities and the newly found exact results for the local and string order parameters of the transverse XY chains, we were able to find analytically all the magnetizations and the brane order parameters for the staggered case, as functions of the renormalized couplings of the effective Hamiltonian. The columnar ladder has three ground-state phases and does not possess magnetic long-ranged order. The brane order parameters for these three phases are calculated numerically from the Toeplitz determinants. We expect this study to motivate the search for the real spin-Peierls anisotropic ladder compounds which can undergo the predicted quantum phase transitions with gap closures and distinct brane orders.

16 pages, 8 figures, 1 table. V-2 bbl problems fixed. V-3: final version to be published, 18.5 pages; results on Majorana modes, disorder lines, and disentanglement are added

References in corpus (19)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• String order and symmetries in quantum spin lattices
• Rise and fall of hidden string order of lattice bosons
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Divergence of the entanglement range in low dimensional quantum systems
• Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders
• Non-local order parameters for the 1D Hubbard model
• Ground state and low-energy excitations of the Kitaev-Heisenberg ladder
• Quantum Criticality in Dimerized Spin Ladders
• DMRG study of the Bond Alternating \textbf{S}=1/2 Heisenberg ladder with Ferro-Antiferromagnetic couplings
• Phase diagram of an interacting staggered Su-Schrieffer-Heeger two-chain ladder close to a quantum critical point
• Spin-Peierls instability in the three-leg Heisenberg ladder
• Critical Lines and Massive Phases in Quantum Spin Ladders with Dimerization
• Flat bands and entanglement in the Kitaev ladder
• Twisted Order Parameter applied to Dimerized Ladders
• Disorder lines, modulation, and partition function zeros in free fermion models
• Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields

Cited by in corpus (3)

• Disentanglement, disorder lines, and Majorana edge states in a solvable quantum chain
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Fermi surface as a quantum critical manifold: gaplessness, order parameter, and scaling in $d$-dimensions