Non-Linear Sigma Model for Inhomogeneous Spin Chains

Abstract

We derive a non-linear sigma model (NLSM) generally representing antiferromagnetic Heisenberg spin chains with inhomogeneous spin magnitudes and inhomogeneous nearest-neighbor exchange constants arrayed in finite periods. Only a restriction is that the average of spin magnitudes on one sublattice is the same as that on the other sublattice. The NLSM gives the gapless condition explicitly written by the spin magnitudes and the exchange constants. We apply this gapless condition to several cases including systems with impurities.

4 pages, no figure, RevTex

References in corpus (5)

• Experimental Verification of the Gapless Point in the $S$=1 Antiferromagnetic Bond Alternating Chain
• Spin Chains with Periodic Array of Impurities
• Alternating spin chains with singlet ground states
• Ground-State and Thermodynamic Properties of the Quantum Mixed Spin-1/2-1/2-1-1 Chain
• Ground State Properties of One Dimensional S=1/2 Heisenberg Model with Dimerization and Quadrumerization

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• Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry
• Frustration Induced Quantum Phases in Mixed Spin Chain with Frustrated Side Chains
• Magnetization plateaux, Haldane-like gap, string order and hidden symmetry in a spin-1/2 tetrameric Heisenberg antiferromagnetic chain
• Frustration-induced phase transitions in the spin-S orthogonal-dimer chain
• Phase Diagrams of Mixed Spin Chains with Period 4 by the Nonlinear $\sigma$ Model
• Entanglement and quantum phase transition in quantum mixed spin chains
• Fermionic versus bosonic descriptions of one-dimensional spin-gapped antiferromagnets
• Disordered ground states in a quantum frustrated spin chain with side chains
• The Partition Function Zeroes of Quantum Critical Points
• Nonlinear sigma model study of a frustrated spin ladder
• Phase Diagram of the 1/2-1/2-1-1 Spin Chain by the Nonlinear Sigma Model
• Spin-Gap States of a Periodic Mixed Spin Chain