By using mainly numerical methods, we investigate the ground-state phase diagram (GSPD) of an $S=1$ ferromagnetic-antiferromagnetic bond-alternating chain with the $XXZ$ and the on-site anisotropies. This system can be mapped onto an anisotropic spin-2 chain when the ferromagnetic interaction is much stronger than the antiferromagnetic interaction. Since there are many quantum parameters in this system, we numerically obtained the GSPD on the plane of the magnitude of the antiferromagnetic coupling versus its $XXZ$ anisotropy, by use of the exact diagonalization, the level spectroscopy as well as the phenomenological renormalization group. The obtained GSPD consists of six phases. They are the $XY$1, the large-$D$ (LD), the intermediate-$D$ (ID), the Haldane (H), the spin-1 singlet dimer (SD), and the Néel phases. Among them, the LD, the H, and the SD phases are the trivial phases, while the ID phase is the symmetry-protected topological phase. The former three are smoothly connected without any quantum phase transitions. It is also emphasized that the ID phase appears in a wider region compared with the case of the GSPD of the anisotropic spin-2 chain with the $XXZ$ and the on-site anisotropies. We also compare the obtained GSPD with the result of the perturbation theory.
The magnetic behaviors of a spin-1/2 alternating Heisenberg antiferromagnetic chain in a staggered transverse magnetic field is studied by means of the density-matrix renormalization group method and Jordan-Wigner transformation. Quantum phase transitions of different types are observed in the S=1 Neel and XY-like gapless phases, which result from the competitions between the staggered transverse field and magnetic orders induced by anisotropy and alternating interactions. The results are compared with the mean-field and some exactly resolved results.
A spin-singlet ground state with a spin gap has been discovered in antiferromagnetic spin chain substances when the spin value is 1/2, 1 or 2. To find spin gap (singlet-triplet) excitations in spin-3/2 chain substances, we performed inelastic neutron scattering and magnetization measurements on {\it R}CrGeO$_5$ ({\it R} = Y or Sm) powders. As expected, we observed spin gap excitations and the dispersion relation of the lowest magnetic excitations. We proved that the spin system of Cr$^{3+}$ was an antiferromagnetic alternating spin-3/2 chain.
We present the first experimental realization of an $S=2$ ferromagnetic-antiferromagnetic (F-AF) alternating chain in a new Mn-verdazyl complex [Mn(hfac)$_2$]$\cdot$($o$-Py-V) [hfac=1,1,1,5,5,5-hexafluoroacetylacetonate; $o$-Py-V=3-(2-pyridyl)-1,5-diphenylverdazyl]. Through the $ab$ $initio$ molecular orbital calculation, magnetization, and ESR measurements, this compound is confirmed to form an $S=2$ F-AF alternating chain with Ising anisotropy below about 100 K. Furthermore, we find an anomalous change in magnetization at 1/4 of the saturation value, which is probably a manifestation of the …
We calculate dynamical structure factors of the S=1 bond-alternating Heisenberg chain with a single-ion anisotropy in transverse magnetic fields, using a continued fraction method based on the Lanczos algorithm. In the Haldane-gap phase and the dimer phase, dynamical structure factors show characteristic field dependence. Possible interpretations are discussed. The numerical results are in qualitative agreement with recent results for inelastic neutron-scattering experiments on the S=1 bond-alternating Heisenberg-chain compound $\rm{Ni(C_{9}D_{24}N_{4})(NO_{2})ClO_{4}}$ and the S=1 Haldane-gap…
Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and s…
Local-susceptibility measurements via the NMR shifts of $^{31}$P and $^{51}$V nuclei in the high-pressure phase of (VO)$_{2}$P$_{2}$O$_{7}$ confirmed the existence of a unique alternating antiferromagnetic chain with a zero-field spin gap of 34 K. The $^{31}$P nuclear spin-lattice relaxation rate scales with the uniform spin susceptibility below about 15 K which shows that the temperature dependence of both the static and dynamical spin susceptibilities becomes identical at temperatures not far below the spin-gap energy.
Dynamical structure factors of the S=1 bond-alternating spin chains in the dimer phase are calculated at finite temperature, using the pair dynamical correlated-effective-field approximation. At T=0, the delta-function-type peak of the one-magnon mode appears. When temperature is increased, such a sharp peak is broadened and the additional weak peak caused by the excitation from the triplet state to the quintet state emerges in the higher energy region. The results are discussed in comparison with those obtained by the exact diagonalization method.
In this work, we analyze the nonsymmorphic symmetry group structures for a variety of generalized Kitaev spin chains and ladders with bond alternations, including Kitaev-Gamma chain, Kitaev-Heisenberg-Gamma chain, beyond nearest neighbor interactions, and two-leg spin ladders. The symmetry analysis is applied to determine the symmetry breaking patterns of several magnetically ordered phases in the bond-alternating Kitaev-Gamma spin chains, as well as the dimerization order parameters for spontaneous dimerizations. Our work is useful in understanding the magnetic phases in related models and ma…
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…
We present a study of the spin-1/2 Heisenberg chain with alternating ferro- and antiferromagnetic exchange, focusing on the role of the exchange couplings to cover both, dimer and Haldane limit. Employing a complementary combination of perturbation theory and quantum Monte Carlo simulation, we report results for the magnetic susceptibility as well as the dynamic structure factor over a wide range of coupling constants and for different temperatures to extract the spin gap. For a small ferromagnetic coupling, we find good agreement between perturbation theory and quantum Monte Carlo. For arbitr…
We study different phases of the one-dimensional bond-alternating spin-$1/2$ Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on …
With extensive variational Monte Carlo simulation, we show that the uniform resonating valence bond state(U-RVB) on square lattice is actually antiferromagnetic long range ordered. The ordered moment is estimated to be $m\approx 0.17$. Finite size scaling analysis on lattice up to lattice size of $50\times 50$ shows that the spin structure factor at the antiferromagnetic ordering wave vector follows perfectly the $\mathrm{S}_{\mathrm{q}=(π,π)} \simeq S_{0}+α(1/L)^{5/4}$ behavior, where $L$ is linear scale of the lattice. Such a behavior is quite unexpected from the slave Boson mean field treat…
In conventional quasi-one-dimensional antiferromagnets with quantum spins, magnetic excitations are carried by either magnons or spinons in different energy regimes: they do not coexist independently, nor could they interact with each other. In this Letter, by combining inelastic neutron scattering, quantum Monte Carlo simulations and Random Phase Approximation calculations, we report the discovery and discuss the physics of the coexistence of magnons and spinons and their interactions in Botallackite-Cu2(OH)3Br. This is a unique quantum antiferromagnet consisting of alternating ferromagnetic …
We report large-scale quantum Monte Carlo calculations at the T=0 antiferromagnetic to valence-bond-solid (VBS) transition of a two-dimensional S=1/2 XY model with four-spin interactions. Finite-size scaling suggests a discontinuous spin stiffness, but a continuous VBS order-parameter. We propose that this is a continuous VBS transition without critical spin fluctuations. We also argue that the system is close to a point, in an extended parameter space, where both the magnetic and VBS fluctuations are critical--possibly a deconfined quantum-critical point.
We present the zero temperature phase diagram of the bond alternating Ising chain in the presence of Dzyaloshinskii-Moriya interaction. An abrupt change in ground state fidelity is a signature of quantum phase transition. We obtain the renormalization of fidelity in terms of quantum renormalization group without the need to know the ground state. We calculate the fidelity susceptibility and its scaling behavior close to quantum critical point (QCP) to find the critical exponent which governs the divergence of correlation length. The model consists of a long range antiferromagnetic order with n…
A recent density functional theory (DFT) based analysis, complemented with Quantum Monte Carlo calculations revealed a highly spin-frustrating nature of the one-dimensional spin-$\frac{1}{2}$ compound $Cs_2CuAl_4O_8$ that comprises of unique bond alternations and relatively strong next nearest neighbor interactions. This article gives a brief account on possible magnon excitations that can appear in the ground state of such systems. We find that the spin waves obtained on top of coplanar helical reference states show multiple magnon modes (both acoustic and optical). However, those magnon mode…
High intensity inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 (NTENP) are performed in magnetic fields of up to 14.8~T. Excitation in the high field magnetized quantum spin solid (ordered) phase are investigated. In addition to the previously observed coherent long-lived gap excitation [M. Hagiwara et al., Phys. Rev. Lett 94, 177202 (2005)], a broad continuum is detected at lower energies. This observation is consistent with recent numerical studies, and helps explain the suppression of the lowest-energy gap mode …
The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the Néel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times Z_2 symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Ha…
We have proposed the plaquette-singlet solid (PSS) ground state for the spin-1 antiferromagnetic Heisenberg two-leg ladder. Based on the PSS picture, we discuss the correspondence of the PSS state to the valence-bond solid (VBS) state of the ground state of spin-2 chain by introducing an appropriate composite spin picture. When the bond alternation is introduced, there occur quantum phase transitions and each phase can be identified with that in the dimerized spin-2 chain. Furthermore, we argue that the VBS picture of spin-2S chain can be applied to the ground state of spin-S two-leg ladder.
We calculate the dynamical structure factors of the magnetization-plateau state in the $S=1/2$ bond-alternating spin chain with a next-nearest-neighbor interaction. The results show characteristic behaviors depending on the next-nearest-neighbor interaction $α$ and the bond-alternation $δ$. We discuss the lower excited states in comparison with the exact excitation spectrums of an effective Hamiltonian. From the finite size effects, characteristics of the lowest excited states are investigated. The dispersionless mode of the lowest excitation appears in adequate sets of $α$ and $δ$, indicating…
We present variational results for the ground state of the antiferromagnetic quantum Heisenberg model with frustrating next-nearest-neighbour interactions. The trial wave functions employed are of resonating-valence-bond type, elaborated to account for various geometric motifs of adjacent bond pairs. The calculation is specialized to a square-lattice cluster consisting of just sixteen sites, large enough that the system can accommodate nontrivial singlet dimer correlations but small enough that exhaustive enumeration of states in the total spin zero sector is still feasible. A symbolic computa…
We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.
We develop a generalization of the singlet sector valence bond basis projection algorithm of Sandvik, Beach, and Evertz (A. W. Sandvik, Phys. Rev. Lett. 95, 207203 (2005); K. S. D. Beach and A. W. Sandvik, Nucl. Phys. B750, 142 (2006); A. W. Sandvik and H. G. Evertz, arXiv:0807.0682, unpublished.) to cases in which the ground state of an antiferromagnetic Hamiltonian has total spin $S_{tot} = 1/2$ in a finite size system. We explain how various ground state expectation values may be calculated by generalizations of the estimators developed in the singlet case, and illustrate the power of the m…
The fidelity and entanglement entropy in an antiferromagnetic-ferromagnetic alternating Heisenberg chain are investigated by using the method of density-matrix renormalization-group. The effect of anisotropy on fidelity and entanglement entropy are investigated. The relations between fidelity, entanglement entropy and quantum phase transition are analyzed. It is found that the quantum phase transition point can be well characterized by both the ground-state entropy and fidelity for large system.
The ground state phase diagrams and thermodynamic properties of a spin-1 bond-alternating Heisenberg antiferromagnetic chain with a single-ion anisotropy in longitudinal and transverse magnetic fields are investigated jointly by means of the infinite time evolving block decimation, the linearized tensor renormalization group and the density matrix renormalization group methods. It is found that in the magnetic field-bond alternating ratio plane six phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2 magnetization plateau and spin polarized phases are identified in a longi…
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…
A molecular Mott insulator $κ$-(ET)$_2$B(CN)$_4$ [ET = bis(ethylenedithio)tetrathiafulvalene] with a distorted triangular lattice exhibits a quantum disordered state with gapped spin excitation in the ground state. $^{13}$C nuclear magnetic resonance, magnetization, and magnetic torque measurements reveal that magnetic field suppresses valence bond order and induces long-range magnetic order above a critical field $\sim 8$ T. The nuclear spin-lattice relaxation rate $1/T_1$ shows persistent evolution of antiferromagnetic correlation above the transition temperature, highlighting a quantum spin…
A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the $Δ$-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and triv…
We make a matrix-product variational approach to spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chains with anisotropy on their ferromagnetic bonds, especially under the open boundary condition. The rich phase diagram containing the Haldane, large-D, and two types of Neel phases is well reproduced with only two variational parameters. The on-bond anisotropy has a significant effect on the ferromagnetic coupling between neighboring spins and induces novel edge states peculiar to spin-1/2 chains.
We report on the magnetic structures of Tb3RuO7 and Nd3RuO7 determined from powder neutron-diffraction experiments. In Tb3RuO7, alternating-bond spin-3/2 Ru1-Ru2 chains are formed. The Ru1 and Ru2 moments are ordered and disordered (paramagnetic), respectively, below 15 K. This result indicates the appearance of a partially disordered (PD) state, although the two Ru sites are very similar to each other. In Nd3RuO7, the Ru1 and Ru2 ions form independent uniform chains. Both the Ru1 and Ru2 moments are ordered below 17.5 K. Probably, the main source of the PD state in Tb3RuO7 is the magnetic fru…
We analyze the logarithmic corrections due to ferromagnetic impurity ending bonds of open spin 1/2 antiferromagnetic chains, using the density matrix renormalization group technique. A universal finite size scaling $\sim {\frac 1 {L \log L}}$ for impurity contributions in the quasi-degenerate ground state energy is demonstrated for a zigzag spin 1/2 chain at the critical next nearest neighbor coupling and the standard Heisenberg spin 1/2 chain, in the long chain limit. Using an exact solution for the latter case it is argued that one can extract the impurity contributions to the entropy and sp…
The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82, 064703 (2013) is confirmed using two kinds of entanglement spectra defined by different divisions of the whole chain. For the numerical calculation, the iDMRG method is used. The results are consistent with the valence bond solid picture proposed in the previous paper.
The spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with ferromagnetic next-nearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact soluti…
We present results for the dynamic structure factor of the S=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 $λ\approx 0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spi…
By using the coupled cluster method, the numerical exact diagonalization method, and the numerical density matrix renormalization group method, we investigated the properties of the one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions. In the classical limit, the ground state is in the collinear Neel state if a<1/2, while for a>1/2, there is an noncollinear canted state. For the quantum case, we found that, although the classical Neel state is absent, the canted state exists if the frustration parameter a exceeds a critical po…
We extend to magnetically ordered phases a recently developed expansion in 1/d for coupled-dimer Heisenberg magnets, where d is the number of space dimensions. This extension utilizes generalized bond operators describing spin excitations on top of a reference state involving triplet condensates. We explicitly consider a model of dimers on a hypercubic lattice which displays, in addition to the paramagnetic singlet phase, a collinear antiferromagnetic phase for which we calculate static and dynamic observables at zero temperature. In particular, we show that the 1/d expansion smoothly connects…
We obtain the phase diagram in the parameter space $(J'/J, γ)$ and an accurate estimate of the critical line separating the different phases. We show several measuments of the magnetization, dimerization, nearest neighbours correlation, and density of energy in the different zones of the phase diagram, as well as a measurement of the string order parameter proposed as the non vanishing phase order parameter characterizing Haldane phases. All these results will be compared in the limit $J'/J\gg 1$ with the behaviour of the $\textbf{S}=1$ Bond Alternated Heisenberg Chain (BAHC). The analysis of …
The ground-state phases of alternating-bond spin-1 diamond chains are investigated. Each ground state consists of an array of spin clusters separated by singlet dimers owing to an infinite number of local conservation laws. If no singlet dimers are present, the ground state is equivalent to that of a spin chain with infinite length.For strong frustration, we find a series of quantum phase transitions as in the case of alternating-bond mixed diamond chains with spins 1 and 1/2. For intermediate frustration, we find the nonmagnetic Haldane or dimer phases according to whether the bond alternatio…
We study the impact of a weak bond disorder on the spinon heat transport in the S=1/2 antiferromagnetic (AFM) Heisenberg chain material Sr_{1-x}Ca_xCuO_2. We observe a drastic suppression in the magnetic heat conductivity kappa_mag even at tiny disorder levels (i.e., Ca-doping levels), in stark contrast to previous findings for kappa_mag of S=1/2 two-dimensional square lattice and two-leg spin-ladder systems, where a similar bond disorder has no effect on kappa_mag. Hence, our results underpin the exceptional role of integrability of the S=1/2 AFM Heisenberg chain model and suggest that the bo…
The low temperature magnetization process of the ferromagnetic-antiferromagnetic Heisenberg chain is studied using the interacting boson approximation. In the low field regime and near the saturation field, the spin wave excitations are approximated by the $δ$ function boson gas for which the Bethe ansatz solution is available. The finite temperature properties are calculated by solving the integral equation numerically. The comparison is made with Monte Carlo calculation and the limit of the applicability of the present approximation is discussed.
By the analytical coupled cluster method (CCM), we study both the ground state and lowest-lying excited-state properties of the alternating bond diamond chain. The numerical exact diagonalization (ED) method is also applied to the chain to verify the accuracy of CCM results. The ED results show that the ground-state phase diagram contains two exact spin cluster solid ground states, namely, the tetramer-dimer (TD) state and dimer state, and the ferrimagnetic long-range-ordered state. We prove that the two exact spin cluster solid ground states can both be formed by CCM. Moreover, the exact spin…
Nuclear magnetic resonance (NMR) of 31P and 51V nuclei has been measured in a spin-1/2 alternating-chain compound (VO)_2P_2O_7. By analyzing the temperature variation of the 31P NMR spectra, we have found that (VO)_2P_2O_7 has two independent spin components with different spin-gap energies. The spin gaps are determined from the temperature dependence of the shifts at 31P and 51V sites to be 35 K and 68 K, which are in excellent agreement with those observed in the recent inelastic neutron scattering experiments [A.W. Garrett et al., Phys. Rev. Lett. 79, 745 (1997)]. This suggests that (VO)_2P…
We formulate a real-space renormalization scheme that allows the study of the effects of bond randomness in the Heisenberg antiferromagnetic spin-1 chain. There are four types of bonds that appear during the renormalization flow. We implement numerically the decimation procedure. We give a detailed study of the probability distributions of all these bonds in the phases that occur when the strength of the disorder is varied. Approximate flow equations are obtained in the weak-disorder regime as well as in the strong disorder case where the physics is that of the random singlet phase.
The ground state phase diagram of the alternating spin-1/2 chains with anisotropic ferromagnetic coupling under the influence of a symmetry breaking transverse magnetic field is studied. We have used the exact diagonalization technique. In the limit where the antiferromagnetic coupling is dominant, we have identified two Ising-type quantum phase transitions. We have calculated two critical fields $h_{c_{1}}$ and $h_{c_{2}}$, corresponding to the transition between different magnetic phases of the system. It is found that the intermediate state ($h_{c_{1}}<h<h_{c_{2}}$) is gapful, describing th…
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 …
The mixture of bond-alternating and uniform S=1/2 antiferromagnetic Heisenberg chains is investigated by the density matrix renormalization group method. The ground state magnetization curve is calculated and the exchange parameters are determined by fitting to the experimentally measured magnetization curve of \CuCl$_{2x}$Br$_{2(1-x)}$($γ$-pic)$_2$. The low field behavior of the magnetization curve and low temperature behavior of the magnetic susceptibility are found to be sensitive to whether the bond-alternation pattern (parity) is fixed all over the sample or randomly distributed. The both…
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 $Γ$ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-$1/2$ $g_x$-$g_y$ $K$-$Γ$ 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 t…
In order to clarify the origin of the enhancement of the thermal conductivity in the Bose-Einstein Condensed (BEC) state of field-induced triplons, we have measured the thermal conductivity along the [101] direction parallel to spin-chains, $kappa_{\|[101]}$, and perpendicular to spin-chains, $kappa_{\perp[101]}$, of the S=1/2 bond-alternating spin-chain system Pb2V3O9 in magnetic fields up to 14 T. With increasing field at 3 K, it has been found that both $kappa_{\|[101]}$ and $kappa_{\perp[101]}$ are suppressed in the gapped normal state in low fields. In the BEC state of field-induced tripl…
The antiferromagnetic (AF) model is generalized for the quasielectron system composed of identical ionic-covalent dimers. The density-fluctuation and covalent-correlation operators are constructed based on the extended AF density matrices, and the quasielectron system is decomposed into 4-level subsystems for the electron ionization and affinity. By considering the nearest-neighbor hopping near the covalent limit, we can see the importance of the bonding coefficients to the effective mass of the excited carrier in the crystal of the zincblende structure.
We study the frustration-induced enhancement of the incommensurate correlation for a bond-alternating quantum spin chain in a magnetic field, which is associated with a quasi-one-dimensional organic compound F5PNN. We investigate the temperature dependence of the staggered susceptibilities by using the density matrix renormalization group, and then find that the incommensurate correlation becomes dominant in a certain range of the magnetic field. We also discuss the mechanism of this enhancement on the basis of the mapping to the effective S=1/2 XXZ chain and a possibility of the field-induced…
Quasi-one-dimensional antiferromagnetic (AF) quantum spin systems show a wide range of interesting phenomena such as the spin-Peierls transition and disorder driven long range ordering. While there is no magnetic long range order in strictly one-dimensional systems, in real systems some amount of interchain coupling is always present and AF long range order may appear below a Neel ordering temperature T_N. We study the effect of bond randomness on Neel ordering in weakly coupled random AF S=1/2 chains both with and without dimerization (or spin-Peierls order). We use the real space renormaliza…
We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|λ|J$ as a power series in $λ$. For small $|λ|$, the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|λ|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$, the one particle states merge with the bottom of the continuum near $k=0$, and the spectral weigh…
We investigate the critical properties of the $S=1/2$ bond-alternating spin chain with a next-nearest-neighbor interaction in magnetic fields. By the numerical calculation and the exact solution based on the effective Hamiltonian, we show that there is a parameter region where the longitudinal incommensurate spin correlation becomes dominant around the half-magnetization of the saturation. Possible interpretations of our results are discussed. We next investigate the effects of the interchain interaction ($J^{\prime}$). The staggered susceptibility and the uniform magnetization are calculated …
We report novel effects of randomness in the S=1 bond-alternating antiferromagnetic chain compound with a dimer-singlet ground state [Ni(N,N'-bis(3-aminopropyl)propane-1,3-diamine(mu-NO2]ClO4 abbreviated as NTENP. The 15N NMR spectra develop a continuum with sharply peaked edges at low temperatures, indicating an inhomogeneous staggered magnetization induced by magnetic field. We attribute this to random anisotropic interactions due to disorder of NO2 groups in the chains. The field-induced antiferromagnetic transition exhibits remarkably anisotropic behavior. We propose that a field-induced i…
Coexistence of antiferromagnetism and d-wave superconductivity within a CuO_2 plane was recently observed in a wide doping region for multilayer high-temperature cuprate superconductors. We find that the experimental phase diagram is well reproduced in the slave-boson mean-field scheme of the two-dimensional t-J model by including antiferromagnetic order. We argue that weak three dimensionality coming from a multilayer structure is sufficient to stabilize antiferromagnetic order and its coexistence with superconductivity.
