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Register a new userDistribution of exchange energy in a bond-alternating S=1 quantum spin chain
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The quasi-one-dimensional bond-alternating S=1 quantum antiferromagnet NTENP is studied by single crystal inelastic neutron scattering. Parameters of the measured dispersion relation for magnetic excitations are compared to existing numerical results and used to determine the magnitude of bond-strength alternation. The measured neutron scattering intensities are also analyzed using the 1st-moment sum rules for the magnetic dynamic structure factor, to directly determine the modulation of ground state exchange energies. These independently determined modulation parameters characterize the level of spin dimerization in NTENP. First-principle DMRG calculations are used to study the relation between these two quantities.
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Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].
One-dimensional gapped phases that avoid any symmetry breaking have drawn enduring attention. In this paper, we study such phases in a bond-alternating spin-1 $K$-$Gamma$ chain built of a Kitaev ($K$) interaction and an off-diagonal $Gamma$ term. In the case of isotropic bond strength, a Haldane phase, which resembles the ground state of a spin-$1$ Heisenberg chain, is identified in a wide region. A gapped Kitaev phase situated at dominant ferromagnetic and antiferromagnetic Kitaev limits is also found. The Kitaev phase has extremely short-range spin correlations and is characterized by finite $mathbb{Z}_2$-valued quantities on bonds. Its lowest entanglement spectrum is unique, in contrast to the Haldane phase whose entanglement spectrum is doubly degenerate. In addition, the Kitaev phase shows a double-peak structure in the specific heat at two different temperatures. In the pure Kitaev limit, the two peaks are representative of the development of short-range spin correlation at $T_h simeq 0.5680$ and the freezing of $mathbb{Z}_2$ quantities at $T_l simeq 0.0562$, respectively. By considering bond anisotropy, regions of Haldane phase and Kitaev phase are enlarged, accompanied by the emergence of dimerized phases and three distinct magnetically ordered states.
The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev ($K$) interaction and a symmetric off-diagonal $Gamma$ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-$1/2$ $g_x$-$g_y$ $K$-$Gamma$ chain by density-matrix renormalization group method where $g_x$ and $g_y$ are the bond strengths of the odd and even bonds, respectively. The phase diagram is dominated by even-Haldane ($g_x > g_y$) and odd-Haldane ($g_x < g_y$) phases where the former is topologically trivial while the latter is a symmetry-protected topological phase. Near the antiferromagnetic Kitaev limit, there are two gapped $A_x$ and $A_y$ phases characterized by distinct nonlocal string correlators. In contrast, the isotropic ferromagnetic (FM) Kitaev point serves as a multicritical point where two topological phase transitions meet. The remaining part of the phase diagram contains three symmetry-breaking magnetic phases. One is a six-fold degenerate FM$_{U_6}$ phase where all the spins are parallel to one of the $pm hat{x}$, $pm hat{y}$, and $pm hat{z}$ axes in a six-site spin rotated basis, while the other two have more complex spin structures with all the three spin components being finite. Existence of a rank-2 spin-nematic ordering in the latter is also discussed.
We successfully synthesized the zinc-verdazyl complex [Zn(hfac)$_2$]$cdot$($o$-Py-V) [hfac = 1,1,1,5,5,5-hexafluoroacetylacetonate; $o$-Py-V = 3-(2-pyridyl)-1,5-diphenylverdazyl], which is an ideal model compound with an $S$ = 1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain (F-AF AHC). $Ab$ $initio$ molecular orbital (MO) calculations indicate that two dominant interactions $J_{rm{F}}$ and $J_{rm{AF}}$ form the $S=1/2$ F-AF AHC in this compound. The magnetic susceptibility and magnetic specific heat of the compound exhibit thermally activated behavior below approximately 1 K. Furthermore, its magnetization curve is observed up to the saturation field and directly indicates a zero-field excitation gap of 0.5 T. These experimental results provide evidence for the existence of a Haldane gap. We successfully explain the results in terms of the $S=1/2$ F-AF AHC through quantum Monte Carlo calculations with $|J_{rm{AF}}/J_{rm{F}}|$ = 0.22. The $ab$ $initio$ MO calculations also indicate a weak AF interchain interaction $J$ and that the coupled F-AF AHCs form a honeycomb lattice. The $J$ dependence of the Haldane gap is calculated, and the actual value of $J$ is determined to be less than 0.01$|J_{rm{F}}|$.
Dynamics of S=1 antiferromagnetic bond-alternating chains in the dimer phase, in the vicinity of the critical point with the Haldane phase, is studied by a field theoretical method. This model is considered to represent the compound Ni(C$_9$H$_{24}$N$_4$)(NO$_2$)ClO$_4$ (abbreviated as NTENP). We construct the sine-Gordon (SG) field theory as a low-energy effective model of this system, starting from a Tomonaga-Luttinger liquid at the critical point. Using the exact solution of the SG theory, we give a field theoretical picture of the low-energy excitation spectrum of NTENP. Results derived from our picture are in a good agreement with results of inelastic neutron scattering experiments on NTENP and numerical calculation of the dynamical structure factor. Furthermore, on the basis of the obtained theoretical picture, we predict that the sharp peaks correspond to a single elementary excitation are absent in the Raman scattering spectrum of NTENP in contrast to the inelastic neutron scattering spectrum.
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