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arXiv:2307.08328 · Physical review. B./Physical review. B

Confinement of spinons in the XXZ spin- 12 chain in presence of a transverse magnetic field

S. B. Rutkevich

Published Jan 12, 2024• 2 citations
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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 $\ensuremath{\pi}$.

DOI
10.1103/physrevb.109.014411

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The infinite Heisenberg XXZ spin-12\frac{1}{2}21​ chain in the gapped antiferromagnetic regime has two degenerate vacua and kink topological excitations (which are also called spinons) interpolating between these vacua as elementary excitations. Application of an arbitrary weak staggered longitudinal magnetic field hhh induces a long-range attractive potential between two adjacent spinons leading to their confinement into ``meson'' bound states. Exploiting the integrability of the XXZ model in the deconfined phase h=0h=0h=0, we perform perturbative calculations of the energy spectra of the two-spinon bound states in the weak confinement regime at $h\ensuremath{\rightarrow}+0$, using the strength of the staggered magnetic field hhh as a small parameter. Both transverse and longitudinal dynamical structure factors of the local spin operators are calculated as well in the two-spinon approximation in the weak confinement regime to the leading order in hhh.
The Heisenberg XXZ spin-(1/2) chain is considered in the massive antiferromagnetic regime in the presence of a staggered longitudinal magnetic field. The Hamiltonian of the model is characterised by the anisotropy parameter and by the magnetic-field strength h . At zero magnetic field, the model is exactly solvable. In the thermodynamic limit, it has two degenerate vacua and the kinks (which are also called spinons) interpolating between these vacua, as elementary excitations. Application of the staggered magnetic field breaks integrability of the model and induces the long-range attractive potential between two adjacent kinks leading to their confinement into the bound states. The energy spectra of the resulting two-kink bound states are perturbatively calculated in the extreme anisotropic (Ising) limit to the first order in the inverse anisotropy constant , and also for any to the first order in the weak magnetic field h .
We study the excitation spectrum of the one-dimensional spin-12\frac{1}{2}21​ XXZ chain with antiferromagnetic Ising anisotropy across a magnetic quantum phase transition induced by the application of a site-dependent transverse magnetic field. Motivated by the chain antiferromagnet BaCo2V2O8{\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}BaCo2​V2​O8​, we consider a situation where the transverse magnetic field has a strong uniform component and a weaker staggered part. To determine the nature of the excitations giving rise to the spin dynamical structure factor, we use a combination of analytical approaches and the numerically exact time-dependent matrix product state method. We identify below the quantum phase transition high-energy many-body two-magnon and three-magnon repulsively bound states which are clearly visible due to the staggered component of the magnetic field. At high magnetic fields and low temperature, single magnons dominate the dynamics. Our theory results are in very good agreement with terahertz spectroscopy experimental results.
We consider the transverse dynamical structure factor of the anisotropic Heisenberg spin-1/2 chain ( XXZ model) in the gapped antiferromagnetic regime (Δ>1). Specializing to the case of zero field, we use two independent approaches based on integrability (one valid for finite size, the other for the infinite lattice) to obtain the exact two-spinon part of this correlator. We discuss in particular its asymmetry with respect to the π/2-momentum line, its overall anisotropy dependence, and its contribution to sum rules.
We consider the easy-plane anisotropic spin-12\frac{1}{2}21​ Heisenberg chain in combined uniform longitudinal and transverse staggered magnetic fields. The low-energy limit of his model is described by the sine-Gordon quantum field theory. Using methods of integrable quantum field theory we determine the various components of the dynamical structure factor. To do so, we derive explicit expressions for all matrix elements of the low-energy projections of the spin operators involving at most two particles. We discuss applications of our results to experiments on one-dimensional quantum magnets.
We study the transverse dynamical susceptibility of an antiferromagnetic spin-1/2 chain in the presence of a longitudinal Zeeman field. In the low magnetization regime in the gapless phase, we show that the marginally irrelevant backscattering interaction between the spinons creates a nonzero gap between two branches of excitations at small momentum. We further demonstrate how this gap varies upon introducing a second neighbor antiferromagnetic interaction, vanishing in the limit of a noninteracting "spinon gas." In the high magnetization regime, as the Zeeman field approaches the saturation value, we uncover the appearance of two-magnon bound states in the transverse susceptibility. This bound state feature generalizes the one arising from string states in the Bethe ansatz solution of the integrable case. Our results are based on numerically accurate, unbiased matrix-product-state techniques as well as analytic approximations.