String and conventional order parameters in the solvable modulated quantum chain

Abstract

The phase diagram and the order parameters of the exactly solvable quantum 1D model are analysed. The model in its spin representation is the dimerized XY spin chain in the presence of uniform and staggered transverse fields. In the fermionic representation this model is the dimerized non-interacting Kitaev chain with a modulated chemical potential. The model has a rich phase diagram which contains phases with local and non-local (string) orders. We have calculated within the same systematic framework the local order parameters (spontaneous magnetization) and the non-local string order parameters, along with the topological winding numbers for all domains of the phase diagram. The topologically nontrivial phase is shown to have a peculiar oscillating string order with the wavenumber $q=\pi /2$, awaiting for its experimental confirmation.

15 pages, 6 figures, 2 appendices

References in corpus (27)

• Topological characterization of quantum phase transitions in a S=1/2 spin model
• 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
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Quenching along a gapless line: A different exponent for defect density
• Majorana fermions in density modulated p-wave superconducting wires
• Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Local and nonlocal order parameters in the Kitaev chain
• Non-local String Order Parameter in the $S=1/2$ Kitaev-Heisenberg Ladder
• Non-local order parameters for the 1D Hubbard model
• Ground state and low-energy excitations of the Kitaev-Heisenberg ladder
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solutions and topological phase diagram in interacting dimerized Kitaev topological superconductors
• Quantum Criticality in Dimerized Spin Ladders
• DMRG study of the Bond Alternating \textbf{S}=1/2 Heisenberg ladder with Ferro-Antiferromagnetic couplings
• Majorana Zero-Energy Mode and Fractal Structure in Fibonacci-Kitaev Chain
• Spin-Peierls instability in the three-leg Heisenberg ladder
• Onsager algebra and cluster XY-models in a transverse magnetic field
• Critical Lines and Massive Phases in Quantum Spin Ladders with Dimerization
• The anisotropic XY model on the inhomogeneous periodic chain
• Twisted Order Parameter applied to Dimerized Ladders
• Topological phase transitions in random Kitaev $\alpha$-chains
• Detecting topological phases via survival probabilities of edge Majorana fermions
• Modified Szego-Widom Asymptotics for Block Toeplitz Matrices with Zero Modes

Cited by in corpus (10)

• Concurrence Percolation in Quantum Networks
• Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain
• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Disorder lines, modulation, and partition function zeros in free fermion models
• Driven one-dimensional noisy Kitaev chain
• Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields
• Disentanglement, disorder lines, and Majorana edge states in a solvable quantum chain
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Brane order and quantum magnetism in modulated anisotropic ladders
• Fermi surface as a quantum critical manifold: gaplessness, order parameter, and scaling in $d$-dimensions