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Register a new userSpin excitations under fields in an anisotropic bond-alternating quantum S=1 chain: contrast with Haldane spin chains
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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)].
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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.
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 Haldane phase represents one of the most important symmetry protected states in modern physics. This state can be realized using spin-1 and spin-${1over 2}$ Heisenberg models and bosonic particles. Here we explore the emergent Haldane phase in an alternating bond $mathbb{Z}_3$ parafermion chain, which is different from the previous proposals from fundamental statistics and symmetries. We show that this emergent phase can also be characterized by a modified long-range string order, as well as four-fold degeneracy in the ground state energies and entanglement spectra. This phase is protected by both the charge conjugate and parity symmetry, and the edge modes are shown to satisfy parafermionic statistics, in which braiding of the two edge modes yields a ${2pi over 3}$ phase. This model also supports rich phases, including topological ferromagnetic parafermion (FP) phase, trivial paramagnetic parafermion phase, classical dimer phase and gapless phase. The boundaries of the FP phase are shown to be gapless and critical with central charge $c = 4/5$. Even in the topological FP phase, it is also characterized by the long-range string order, thus we observe a drop of string order across the phase boundary between the FP phase and Haldane phase. These phenomena are quite general and this work opens a new way for finding exotic topological phases in $mathbb{Z}_k$ parafermion models.
Thermodynamic properties of a tetrameric bond-alternating Heisenberg spin chain with ferromagnetic-ferromagnetic-antiferromagnetic-antiferromagnetic exchange interactions are studied using the transfer-matrix renormalization group and compared to experimental measurements. The temperature dependence of the uniform susceptibility exhibits typical ferrimagnetic features. Both the uniform and staggered magnetic susceptibilities diverge in the limit $Tto 0$, indicating that the ground state has both ferromagnetic and antiferromagnetic long-range orders. A double-peak structure appears in the temperature dependence of the specific heat. Our numerical calculation gives a good account for the temperature and field dependence of the susceptibility, the magnetization, and the specific heat for Cu(3-Clpy)$_{2}$(N$_{3}$)$_{2}$ (3-Clpy=3-Chloroyridine).
Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 $XXZ$ chain with single-ion anisotropy $D$. We demonstrate that the Haldane phase between large-$D$ and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-$D$ and antiferromagnetic phases with central charge $c=1/2$, which terminates at a critical end-point where $c=7/10$. Calculating the critical exponents of the order parameter, neutral gap and spin-spin-correlation function, we find $beta=1/8$ (1/24), $ u=1$ (5/9), and $eta=1/4$ (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.
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