The spin-1 ladder : A bosonization study

Abstract

We construct a field-theoretic description of two coupled spin-1 Heisenberg chains, starting with the known representation of a single spin-1 chain in terms of Majorana fermions (or Ising models). After reexamining the bosonization rules for two Ising models, taking particular care of order and disorder operators, we obtain a bosonic description of the spin-1 ladder. From renormalization-group and mean-field arguments, we conclude that, for a small interchain coupling, the spin-1 ladder is approximately described by three decoupled, two-frequency sine-Gordon models. We then predict that, starting with decoupled chains, the spin gap decreases linearly with interchain coupling, both in the ferromagnetic and antiferromagnetic directions. Finally, we discuss the possibility of an incommensurate phase in the spin-1 zigzag chain.

12 pages, 4 figures

References in corpus (13)

• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
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• Exact expectation values of local fields in quantum sine-Gordon model
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• Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders
• Non-integrable aspects of the multi-frequency Sine-Gordon model
• Form-factors of exponential fields in the sine-Gordon model
• An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain
• Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain
• Semiclassical description of spin ladders
• Semi-classical description of the frustrated antiferromagnetic chain
• Non-Abelian Bosonization and Haldane's Conjecture
• The One-Dimensional ANNNI model in a Transverse Field: Analytic and numerical study of Effective Hamiltonians

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• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain
• Theory of non-Abelian Fabry-Perot interferometry in topological insulators
• Quantum phase transitions in three-leg spin tubes
• Antiferromagnetic Dimers of Ni(II) in the S=1 Spin-Ladder Na_2Ni_2(C_2O_4)_3(H_2O)_2
• The N-Leg spin-S Heisenberg ladders: A DMRG study
• N-leg integer-spin ladders and tubes in commensurate external fields -Nonlinear sigma model approach-
• Probing Majorana edge states with a flux qubit
• Model for frustrated spin-orbital chains: application to CaV2O4
• Physics of integer spin antiferromagnetic chains : Haldane gaps and edge states
• Magnon bands of N-leg integer-spin antiferromagnetic systems in the weak interchain-coupling regime
• Exact degenerate ground states for the F-AF spin chain with bond alternation
• Network construction of non-Abelian chiral spin liquids
• Electronic structure and magnetic properties of the strong-rung spin-1 ladder compound Rb${}_3$Ni${}_2$(NO${}_3$)${}_7$
• Chiral fixed point in a junction of critical spin-1 chains
• Symmetry protected topological phases in spin-1 ladders and their phase transitions
• Scaling Property of the F-AF Spin Chain Near the Exactly Solvable Point
• High field level crossing studies on spin dimers in the low dimensional quantum spin system Na${}_2$T${}_2$(C${}_2$O${}_4$)${}_3$(H${}_2$O)${}_2$ with T=Ni,Co,Fe,Mn
• Majorana Fermi surface state in a network of quantum spin chains
• Bosonic representation of spin operators in the field-induced critical phase of spin-1 Haldane chains
• Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas