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arXiv:2108.01401 · Physical review. B./Physical review. B

Possibility to detect the bound state of the Heisenberg ferromagnetic chain at intermediate temperature

Mithilesh Nayak, Frédéric Mila

Published Mar 4, 2022• 5 citations
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Abstract

Motivated by the lack of direct evidence with inelastic neutron scattering of the well documented bound state of Heisenberg ferromagnets, we use the time-dependent thermal density matrix renormalization group algorithm to study the temperature dependence of the dynamical spin structure factor of Heisenberg ferromagnetic spin chains. For spin 1/2, we show that the bound state appears as a well defined excitation with significant spectral weight in the temperature range $J/12\ensuremath{\lesssim}T\ensuremath{\lesssim}J/3$, pointing to the possibility of detecting it with inelastic neutron scattering near $k=\ensuremath{\pi}$ provided the temperature is neither too low nor too high---at low temperature, the spectral weight only grows as ${T}^{3/2}$ and, at high temperature, the bound state peak merges with the two-magnon continuum. For spin 1, the situation is more subtle because the bound state with two neighboring spin flips competes with an antibound state with two spin flips on the same site. As a consequence, the relative spectral weight of the bound state is smaller than for spin 1/2 and a weak resonance due to the antibound state appears in the continuum. A clearer signature of the bound state (antibound state) can be obtained if a negative (positive) biquadratic interaction is present.

DOI
10.1103/physrevb.105.094407

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The antiferromagnetic spin-one chain is considerably one of the most fundamental quantum many-body systems, with symmetry-protected topological order in the ground state. Here, we present results for its dynamical spin structure factor at finite temperatures, based on a combination of exact numerical diagonalization, matrix-product-state calculations, and quantum Monte Carlo simulations. Open finite chains exhibit a subgap band in the thermal spectral functions, indicative of localized edge states. Moreover, we observe the thermal activation of a distinct low-energy continuum contribution to the spin spectral function with an enhanced spectral weight at low momenta and its upper threshold. This emerging thermal spectral feature of the Haldane spin-one chain is shown to result from intraband magnon scattering due to the thermal population of the single-magnon branch, which features a large bandwidth-to-gap ratio. These findings are discussed with respect to possible future studies on spin-one chain compounds based on inelastic neutron scattering.
We investigate the dynamical spin structure factor $S(q,\ensuremath{\omega})$ for the Heisenberg chain with ferromagnetic nearest-neighbor (J1<0{J}_{1}<0J1​<0) and antiferromagnetic next-nearest-neighbor (J2>0{J}_{2}>0J2​>0) exchange using bosonization and a time-dependent density-matrix renormalization group algorithm. For $|{J}_{1}|\ensuremath{\ll}{J}_{2}$ and low energies we analytically find and numerically confirm two spinon branches with different velocities and different spectral weights. Following the evolution of $S(q,\ensuremath{\omega})$ with decreasing J1/J2{J}_{1}/{J}_{2}J1​/J2​, we find that helimagnons develop at high energies just before entering the ferromagnetic phase. Furthermore, we show that a recent interpretation of neutron-scattering data for LiCuVO4{}_{4}4​ in terms of two weakly coupled antiferromagnetic chains ($|{J}_{1}|\ensuremath{\ll}{J}_{2}$) is not viable. We demonstrate that the data are instead fully consistent with a dominant ferromagnetic coupling, ${J}_{1}/{J}_{2}\ensuremath{\approx}\ensuremath{-}2$.
We present results for the dynamic structure factor of the S=1∕2S=1∕2S=1∕2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $\ensuremath{\lambda}\ensuremath{\approx}0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spin diffusion in its variation from low to high temperatures are discussed. The one-magnon peak acquires an asymmetric shape with increasing temperature. The two-magnon peak is dominated by the S=1S=1S=1 bound state which remains well defined up to temperatures of the order of JJJ. The variation with temperature and wave vector of the integrated intensity for one-magnon and two-magnon scattering and of the central peak are discussed.
Abstract We investigate the spin dynamics of a 1D spin-1/2 Heisenberg tetramer chain. Employing a combination of density matrix renormalization group, quantum renormalization group, and perturbation theory techniques, we compute the energy levels and the quantum phase diagram, analyze the phase transitions, and evaluate the dynamical structure factor (DSF), which is related to the inelastic neutron scattering (INS) spectrum and the resonant inelastic x-ray scattering (RIXS) spectrum of fractionalized and collective excitations. Our calculations suggest that the chain can transition between a hidden Z 2 × Z 2 discrete symmetry preserving tetramer phase and a Haldane phase with non-vanishing string order that breaks the hidden symmetry. These two gapped phases are intervened by an intermediate deconfined quantum critical state comprising of free spins and three-site doublets, which is a gapless critical phase with deconfined spinons that can be detected either by INS or L -edge RIXS. We find that the tetramer chain can support fractionalized (spinon) and collective (triplon and quinton) excitations. In the ferromagnetic intra-tetramer limit, the chain can support a quinton excitation which has a five-fold degenerate excited state. String order parameter calculations suggest CuInVO 5 should be in a Haldane-like phase whose INS or L -edge RIXS spectrum can support observable single-spin excitations including triplon and quinton excitations. We also identify possible two-particle excitations (two-singlon, two-triplon, triplon-quinton, and two-quinton excitations) resulting from the double spin-flip effect in the K -edge RIXS spectrum.
We consider the spin-1/2 Heisenberg XXZXXZXXZ chain in the regime of large Ising-type anisotropy $\ensuremath{\Delta}$. By a combination of duality and Jordan-Wigner transformations we derive a mapping to weakly interacting spinless fermions, which represent domain walls between the two degenerate ground states. We develop a perturbative expansion in $1/\ensuremath{\Delta}$ for the transverse dynamical spin structure factor at finite temperatures and in an applied transverse magnetic field. We present a unified description for both the low-energy temperature-activated response and the temperature evolution of the T=0T=0T=0 two-spinon continuum. We find that the two-spinon continuum narrows in energy with increasing temperature. At the same time spectral weight is transferred from the two-spinon continuum to the low-energy intraband scattering continuum, which is strongly peaked around the position of the (single) spinon dispersion (``Villain mode'').
We determine the spin-exchange dynamical structure factor of the Heisenberg spin chain, as is measured by indirect resonant inelastic x-ray scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into two-spinon states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type.