Incommensurability in the magnetic excitations of the bilinear-biquadratic spin-1 chain

TL;DR

This paper investigates the magnetic excitation spectrum of a spin-1 chain in the Haldane phase, revealing a transition to incommensurate excitations at a critical parameter value, with implications for understanding magnetization behavior.

Contribution

It provides a detailed analysis of incommensurability in the excitation spectrum of the bilinear-biquadratic spin-1 chain using numerical techniques, identifying a critical point and the nature of excitations.

Findings

Magnon dispersion minimum shifts from q=pi to incommensurate values at theta_c

The mode remains isolated with no spinon deconfinement before theta=pi/4

The results explain the observed magnetization curve near the critical point

Abstract

We study the magnetic excitation spectrum of the S=1 quantum Heisenberg spin chain with Hamiltonian : H = sum_i cos(theta) S_i S_i+1 + sin(theta) (S_i S_i+1)^2. We focus on the range -pi/4 < theta < +pi/4 where the spin chain is in the gapped Haldane phase. The excitation spectrum and static structure factor is studied using direct Lanczos diagonalization of small systems and density-matrix renormalization group techniques combined with the single-mode approximation. The magnon dispersion has a minimum at q=pi until a critical value theta_c = 0.38 is reached at which the curvature (velocity) vanishes. Beyond this point, which is distinct from the VBS point and the Lifshitz point, the minimum lies at an incommensurate value that goes smoothly to 2pi/3 when theta approaches pi/4, the Lai-Sutherland point. The mode remains isolated from the other states: there is no evidence of spinon deconfinement before the point theta =+pi/4. These findings explain recent observation of the magnetization curve M approx (H -H_c)^1/4 for theta =theta_c.