Confinement of spinons in the XXZ spin-1/2 chain in presence of the transverse magnetic field

Abstract

We study the tuning effect of a transverse magnetic field on the confinement of spinons in the infinite XXZ spin-1/2 chain. The spinon confinement in this model takes place in the gapped antiferromagnetic phase upon application of a staggered longitudinal magnetic field. The tuning transverse magnetic field has mutually orthogonal uniform and staggered components. The energy spectra of the two-spinon bound states (the `mesons') in the confinement regime are analytically calculated in this model using two different perturbative schemes. The first one applies in the extreme anisotropic (Ising) limit and employs the inverse anisotropy constant as a small parameter. The second perturbative scheme, which applies at any anisotropy in the gapped antiferromagnetic domain, exploits the integrability of the XXZ spin chain at zero magnetic field. The small parameters in the second technique are the components of the transverse, and staggered longitudinal magnetic fields. It is shown, that the weak transverse magnetic field mixes the transverse and longitudinal meson modes, and leads to an avoided crossing of their energies upon increase of its strength. The explicit formulas for the two-spinon contribution to the dynamical structure factors of local spin operators are obtained as well in this model in the weak confinement regime for wave-vectors close to the points k = 0 and k = π.

v3: 38 pages, 14 figures. One section added, misprints corrected

References in corpus (10)

• Novel ordering of an S = 1/2 quasi one-dimensional Ising-like anitiferromagnet in magnetic field
• Energy spectrum of bound-spinons in the quantum Ising spin-chain ferromagnet
• Spinon Confinement in the One-Dimensional Ising-Like Antiferromagnet SrCo2V2O8
• $E_8$ Spectra of Quasi-one-dimensional Antiferromagnet BaCo${}_2$V${}_2$O${}_8$ under Transverse Field
• Excited state TBA and renormalized TCSA in the scaling Potts model
• Confinement and bound states of bound states in a transverse-field two-leg Ising ladder
• Confinement in the spectrum of a Heisenberg-Ising spin ladder
• Phase transitions and spin dynamics of the quasi-one dimensional Ising-like antiferromagnet BaCo${}_2$V${}_2$O${}_8$ in a longitudinal magnetic field
• Spinon confinement in the gapped antiferromagnetic XXZ spin-1/2 chain
• Repulsively bound magnon excitations of a spin-1/2 XXZ chain in a staggered transverse field

Cited by in corpus (1)

• Chiral eigenbases of the XX and XY quantum spin chains