Using a matrix product state algorithm with infinite boundary conditions, we compute high-resolution dynamic spin and quadrupolar structure factors in the thermodynamic limit to explore the low-energy excitations of isotropic bilinear-biquadratic spin-1 chains. Haldane mapped the spin-1 Heisenberg antiferromagnet to a continuum field theory, the non-linear sigma model (NL$σ$M). We find that the NL$σ$M fails to capture the influence of the biquadratic term and provides only an unsatisfactory description of the Haldane phase physics. But several features in the Haldane phase can be explained by non-interacting multi-magnon states. The physics at the Uimin-Lai-Sutherland point is characterized by multi-soliton continua. Moving into the extended critical phase, we find that these excitation continua contract, which we explain using a field-theoretic description. New excitations emerge at higher energies and, in the vicinity of the purely biquadratic point, they show simple cosine dispersions. Using block fidelities, we identify them as elementary one-particle excitations and relate them to the integrable Temperley-Lieb chain.
Magnetic excitations in the quasi-one-dimensional antiferromagnet IPA-CuCl3 are studied by cold neutron inelastic scattering. Strongly dispersive gap excitations are observed. Contrary to previously proposed models, the system is best described as an asymmetric quantum spin ladder. The observed spectrum is interpreted in terms of ``composite'' Haldane spin chains. The key difference from actual S=1 chains is a sharp cutoff of the single-magnon spectrum at a certain critical wave vector.
The antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling $J$ of the Heisenberg chain. We discuss recent results about the spin dependence of the Haldane gap and conjecture an analytical formula valid asymptotically for large spin values. We next study the robustness of the edge states of the spin one chain by studying by the DMRG algorithm a spin one ladder. We show that the peculiar hidden topological order of the spin one chain disappear…
We calculate the Haldane gap of the $\mathrm{SU}(3)$ spin $[3~0~0]$ Heisenberg model using variational uniform fully symmetric $\mathrm{SU}(3)$ matrix product states, and find that the minimal gap $Δ/J = 0.0263 $ is obtained in the $[2~1~0]$ sector at momentum $2π/3$. We also discuss the symmetry protected topological order of the ground state, and determine the full dispersion relation of the elementary excitations and the correlation lengths of the system.
A systematic method to construct the complete set of conserved quantities of the Haldane-Shastry type spin chains is proposed. The hidden relationship between the Yang-Baxter relation and the conservation laws of the long-range interacting integrable models is exposed explicitly. An integrable anisotropic Haldane-Shastry model is also constructed.
Long-range magnetic ordering in R_2 Ba Ni O_5 (R=magnetic rare earth) quasi-1-dimensional mixed-spin antiferromagnets is described by a simple mean-field model that is based on the intrinsic staggered magnetization function of isolated Haldane spin chains for the Ni-subsystem, and single-ion magnetization functions for the rare earth ions. The model is applied to new experimental results obtained in powder diffraction experiments on Nd_2 Ba Ni O_5 and Nd Y Ba Ni O_5, and to previously published diffraction data for Er_2 Ba Ni O_5. From this analysis we extract the bare staggered magnetization …
We present a new and simpler expression for the Hamiltonian of the partially isotropic (XXZ-like) version of the Haldane-Shastry model, which was derived by D. Uglov over two decades ago in an apparently little-known preprint. While resembling the pairwise long-range form of the Haldane-Shastry model our formula accounts for the multi-spin interactions obtained by Uglov. Our expression is physically meaningful, makes hermiticity manifest, and is computationally more efficient. We discuss the model's properties, including its limits and (ordinary and quantum-affine) symmetries. In particular we…
We have measured the thermal conductivity of the spin S=1 chain compound Y2BaNiO5. Analyzing the anisotropy of the thermal transport allows to identify a definite spin-mediated thermal conductivity κ_s along the chain direction. The calculated spin-related energy diffusion constant D_E(T) shows a broad peak around 120 K. Close to room temperature, D_E(T) approaches the theoretically predicted high-temperature value, while scattering of spin excitations by magnetic impurities seems to be the major limiting factor of κ_s at low temperature.
Linear-chain nickelates with the composition (Nd_x Y_{1-x})_2 Ba Ni O_5 (x=1, x=0.75, x=0.5, and x=0.25) are studied in a series of neutron scattering experiments. Powder diffraction is used to determine the temperature dependence of the magnetic structure in all four systems. Single-crystal inelastic neutron scattering is employed to investigate the temperature dependence of the Haldane-gap excitations and low-energy spin waves in the x=1 compound Nd_2 Ba Ni O_5. The results of these experiments are discussed in the context of the ``Haldane chain in a staggered field'' model for R_2 Ba Ni O_5…
We provide evidence of an intermediate Haldane phase in a spin-2 quantum chain. By combining effective field theory and numerical approaches, we show that the phase diagram of the proposed model includes SO(5) Haldane, intermediate Haldane, and large-D phases. We determine the characteristic properties of these phases, including edge states, string order parameters, and degeneracies in the entanglement spectrum. The symmetries responsible for the degeneracy patterns observed in the entanglement spectrum are also discussed.
We present a study of the magnetic field-dependent thermal transport in the spin S=1 chain material Ni(C2H8N2)2NO2(ClO4) (NENP). The measured thermal conductivity is found to be very sensitive to the field-induced changes in the spin excitation spectrum. The magnetic contribution to the total heat conductivity is analyzed in terms of a quasiparticle model, and we obtain a temperature and momentum independent mean free path. This implies that the motion of quasiparticles is effectively three dimensional despite the tiny interchain coupling.
We analyze the gaps in the excitation spectrum of a Haldane chain with single-ion anisotropy in a staggered field. We show that the gap along the direction of the field increases at a faster rate than the others, while its spectral weight decreases, being transferred to a two-magnon continuum.
We study a strong coupling expansion of the $ν=1/3$ fractional quantum Hall state away from the Tao-Thouless limit and show that the leading quantum fluctuations lead to an effective spin-1 Hamiltonian that lacks parity symmetry. By analyzing the energetics, discrete symmetries of low-lying excitations, and string order parameters, we demonstrate that the $ν=1/3$ fractional quantum Hall state is adiabatically connected to both Haldane and large-$D$ phases, and is characterized by a string order parameter which is dual to the ordinary one. This result indicates a close relation between (a gener…
Inelastic neutron scattering was used to probe edge states in a quantum spin liquid. The experiment was performed on finite length antiferromagnetic spin-1 chains in Y_2BaNi_{1-x}Mg_xO_5. At finite fields, there is a Zeeman resonance below the Haldane gap. The wave vector dependence of its intensity provides direct evidence for staggered magnetization at chain ends, which decays exponentially towards the bulk (xi = 8(1) at T=0.1K). Continuum contributions to the chain end spectrum indicate inter-chain-segment interactions. We also observe a finite size blue shift of the Haldane gap.
We consider spin-1 Haldane chains with single-ion anisotropy, which exists in known Haldane chain materials. We develop a perturbation theory in terms of anisotropy, where magnon-magnon interaction is important even in the low temperature limit. The exact two-particle form factor in the O(3) nonlinear sigma model leads to quantitative predictions on several dynamical properties including dynamical structure factor and electron spin resonance frequency shift. These agree very well with numerical results, and with experimental data on the Haldane chain material Ni(C$_5$H$_{14}$N$_2$)$_2$N$_3$(PF…
We use extensive DMRG calculations to show that a classification of SU(n) spin chains with regard to the existence of spinon confinement and hence a Haldane gap obtained previously for valence bond solid models applies to SU(n) Heisenberg chains as well. In particular, we observe spinon confinement due to a next-nearest neighbor interaction in the SU(4) representation 10 spin chain.
The one-dimensional Heisenberg antiferromagnets of large-integer-$S$ spins are studied; their Haldane gaps are estimated by the numerical diagonalization method for $S=5$ and $6$. We successfully obtain a monotonically increasing sequence of finite-size energy difference data corresponding to the Haldane gaps from the huge-scale parallel calculations of diagonalization under the twisted boundary condition and create a monotonically decreasing sequence within the range of system sizes treated in this study from the monotonically increasing sequence. Consequently, the gaps for $S=5$ and $6$ are …
Using the density matrix renormalization group (DMRG) technique, we carry out a large scale numerical calculation for the S=2 antiferromagnetic Heisenberg chain. Performing systematic scaling analysis for both the chain length $L$ and the number of optimal states kept in the iterations $m$, the Haldane gap $Δ(2)$ is estimated accurately as $(0.0876\pm0.0013)J$. Our systematic analysis for the S=2 chains not only ends the controversies arising from various DMRG calculations and Monte Carlo simulations, but also sheds light on how to obtain reliable results from the DMRG calculations for other c…
The ground state of spin-1 Haldane chains is characterized by the so-called string order. We show that the same hidden order is also present in ordinary one-dimensional band insulators. We construct a family of Hamiltonians which connects adiabatically band insulators to two topologically non-equivalent spin models, the Haldane chain and the antiferromagnetic spin-1/2 ladder. We observe that the localized spin-1/2 edge-state characteristic of spin-1 chains is smoothly connected to a surface-bound state of band insulators and its emergence is not related to any bulk phase transition. Furthermor…
The Haldane state is a typical quantum and topological state of matter, which exhibits an edge state corresponding to symmetry-protected topological order in a one-dimensional integer spin chain. This edge state can be utilized for a processing unit of quantum computation. Its realization, however, has difficulties with synthesis of integer spin compounds. In contrast, one-half spin systems are more designable due to recent progress on intended synthesis of organic materials, quantum dots, and optical lattices. Here we propose a concept to design the Haldane state with one-half spins by making…
The Haldane spin-chain compound, Tb2BaNiO5, has been known to order antiferromagnetically below (T_N= ) 63 K. The present magnetic studies on the polycrystals bring out that there is another magnetic transition at a lower temperature (T_2= ) 25 K, with a pronounced magnetic-field induced metamagnetic and metaelectric behavior. Multiferroic features are found below T_2 only, and not at T_N. The most intriguing observation is that the observed change of dielectric constant is intrinsic and largest (e.g., about 18% at 15 K) within this Haldane spin-chain family, R2BaNiO5. Taking into account that…
Magnetic excitations in the quasi-one-dimensional quantum antiferromagnets PbNi2V2O8 and SrNi2V2O8 are measured all the way up to the zone boundary energy using inelastic neutron scattering from powder samples. An estimate for next-nearest-neighbor in-chain interactions is obtained. The role played by these interactions in spin-vacancy induced magnetic ordering in PbNi2V2O8 is discussed.
We study the evolution of the dynamical spin structure factor in a spin-1 antiferromagnetic Heisenberg chain which is randomly doped with spin-1/2 moments. Using stochastic series expansion Quantum Monte Carlo simulations combined with the Maximum Entropy method, we monitor the crossover from the spin-1 chain, dominated by a single resonance at the Haldane energy, to the spin-1/2 chain with a continuum of spinon states which diverges at zero-frequency. Upon increasing the doping level, spectral weight is rapidly transferred from the Haldane peak to lower energies. If the exchange couplings bet…
We consider quasi one dimensional spin-1 Heisenberg chains with crystal field anisotropy in a uniform magnetic field. We determine the dynamical structure factor in various limits and obtain a fairly complete qualitative picture of how it changes with the applied field. In particular, we discuss how the width of the higher energy single magnon modes depends on the field. We consider the effects of a weak interchain coupling. We discuss the relevance of our results for recent neutron scattering experiments on the quasi-1D Haldane-gap compound NDMAP.
We present a functional renormalization group approach to interacting topological Green function invariants with a focus on the nature of transitions. The method is applied to chiral symmetric fermion chains in the Mott limit that can be driven into a Haldane phase. We explicitly show that the transition to this phase is accompanied by a zero of the fermion Green function. Our results for the phase boundary are quantitatively benchmarked against DMRG data.
Low-lying magnon dispersion in a S=1 Heisenberg antiferromagnetic (AF) chain is analyzed using the non-Abelian DMRG method. The scattering length $a_{\rm b}$ of the boundary coupling and the inter-magnon scattering length $a$ are determined. The scattering length $a_{\rm b}$ is found to exhibit a characteristic diverging behavior at the crossover point. In contrast, the Haldane gap $Δ$, the magnon velocity $v$, and $a$ remain constant at the crossover. Our method allowed estimation of the gap of the S=2 AF chain to be $Δ= 0.0891623(9)$ using a chain length longer than the correlation length $ξ…
Gapped quantum spin chains with symmetry PSU(N)=SU(N)/Z(N) are known to possess N distinct symmetry protected topological phases. Besides the trivial phase, there are N-1 Haldane phases which are distinguished by the occurrence of massless boundary spins. Motivated by the potential realization in alkaline-earth atomic Fermi gases, we explicitly construct previously unknown Hamiltonians for two classes of chiral AKLT states and we discuss their physical properties. We also point out a deep connection between symmetry protection in gapped and gapless 1D quantum spin systems and its implications …
Electron spin resonance (ESR), at 9, 94, and 190 GHz, and magnetization studies on polycrystalline, powder, and ultrafine powder samples of Ni(C3H10N2)2N3(ClO4) (NINAZ) have revealed several effects arising from the Haldane phase. Using the g value of the end-chain spin $S$ as determined by ESR, our results confirm that the end-chain spins are S=1/2 and show no evidence for S=1 end-chains. In addition, the ESR signals reveal spectral weight consistent with a model describing interactions between the end-chain spins on the shortest chains and between the magnetic excitations on the chains and t…
The Haldane-Shastry spin chain can be mapped to the infinite coupling limit of the SU(2) spin Calogero-Sutherland model. We use the $\mathfrak{gl}_2$ Jack polynomials' technology to compute the form factors of the spin operator on the multi-spinon spectrum. The spin structure factor is obtained through a form factor expansion. The expansion is proven to converge in the small momentum limit. Numerics based on two- and four-spinons contributions give an approximate result for the infinite temperature static and dynamic spin structure factor.
Inelastic neutron scattering experiments on the Haldane-gap quantum antiferromagnet \nd are performed at mK temperatures in magnetic fields of almost twice the critical field $H_c$ applied perpendicular to the spin cahins. Above $H_c$ a re-opening of the spin gap is clearly observed. In the high-field Néel-ordered state the spectrum is dominated by three distinct long-lived excitation branches. Several field-theoretical models are tested in a quantitative comparison with the experimental data.
We present a static, model-independent, experimental determination of the spin-spin correlation length ξin a quantum spin system. This is achieved in doped Haldane (i.e., S=1 Heisenberg antiferromagnetic) chain Y(2)BaNi(1-x)Mg(x)O(5) by Y NMR imaging of the staggered magnetization induced around the Mg-impurities (i.e., chain boundaries) by magnetic field. The magnitude of this magnetization is found to decay exponentially with ξequal to the theoretical prediction for an infinite S=1 chain, and the staggered magnetic moment at the edge site showing the Curie behavior of an effective S=1/2 spin…
The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Neel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Neel orders. The investigation of the model with longer period D-modulation also confirms this picture.
Two quasi-1-dimensional S=1 quantum antiferromagnetic materials, PbNi2V2O8 and SrNi2V2O8, are studied by inelastic neutron scattering on powder samples. While magnetic interactions in the two systems are found to be very similar, subtle differences in inter-chain interaction strengths and magnetic anisotropy are detected. The latter are shown to be responsible for qualitatively different ground state properties: magnetic long-range order in SrNi2V2O8 and disordered ``spin liquid'' Haldane-gap state in PbNi2V2O8.
The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, $D(S^z)^2$, and the rhombic-type, $E[(S^x)^2-(S^y)^2]$, single-ion anisotropies. Here, we provide a precise ground-state phase diagram for spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the $\mathbb{Z}_2$ symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on …
We introduce four types of SU(2M+1) spin chains which can be regarded as the BC_N versions of the celebrated Haldane-Shastry chain. These chains depend on two free parameters and, unlike the original Haldane-Shastry chain, their sites need not be equally spaced. We prove that all four chains are solvable by deriving an exact expression for their partition function using Polychronakos's "freezing trick". From this expression we deduce several properties of the spectrum, and advance a number of conjectures that hold for a wide range of values of the spin M and the number of particles. In particu…
For the Haldane phase, the magnetic field usually tends to break the symmetry and drives the system into a topologically trivial phase. Here, we report a novel reentrance of the Haldane phase at zero temperature in the spin-1 antiferromagnetic Heisenberg model on sawtooth chain. A partial Haldane phase is induced by the magnetic field, which is the combination of the Haldane state in one sublattice and a ferromagnetically ordered state in the other sublattice. Such a partial topological order is a result of the zero-temperature entropy due to quantum fluctuations caused by geometrical frustrat…
There was a slight error in calculating the nonlinear sigma-model prediction for the 2-magnon scattering continuum shown in Fig. 2 of cond-mat/0010049, and Phys. Rev. Lett. {\bf 87}, 017202 (2001). Present erratum explains what was incorrect, and shows a corrected version of the figure. The correction is minor and does not affect main conclusions drawn in the original paper.
We present analytical and numerical results regarding the magnetization full counting statistics (FCS) of a subsystem in the ground-state of the Haldane-Shastry chain. Exact Pfaffian expressions are derived for the cumulant generating function, as well as any observable diagonal in the spin basis. In the limit of large systems, the scaling of the FCS is found to be in agreement with the Luttinger liquid theory. The same techniques are also applied to inhomogeneous deformations of the chain. This introduces a certain amount of disorder in the system; however we show numerically that this is not…
The spin excitation continuum, expected to dominate the low-energy fluctuation spectrum in the Haldane spin chain around the Brillouin zone center, q=0, is directly observed by inelastic magnetic neutron scattering in the S=1 quasi-1D antiferromagnet CsNiCl3. We find that the single mode approximation fails, and that a finite energy width appears in the dynamic correlation function S(q,omega) for q < 0.5pi. The width increases with decreasing q, while S(q,omega) acquires an asymmetric shape qualitatively similar to that predicted for the 2-magnon continuum in the nonlinear sigma-model.
The $S=1$ Haldane state is constructed from a product of local singlet dimers in the bulk and topological states at the edges of a chain. It is a fundamental representative of topological quantum matter. Its well-known representative, the quasi-one-dimensional SrNi$_2$V$_2$O$_8$ shows both conventional as well as unconventional magnetic Raman scattering. The former is observed as one- and two-triplet excitations with small linewidths and energies corresponding to the Haldane gap $Δ_H$ and the exchange coupling $J_c$ along the chain, respectively. Well-defined magnetic quasiparticles are assume…
We apply field theory methods to $\mbox{SU}(3)$ chains in the symmetric representation, with $p$ boxes in the Young tableau, mapping them into a flag manifold non-linear $σ$-model with a topological angle $θ=2πp/3$. Generalizing the Haldane conjecture, we argue that the models are gapped for $p=3m$ but gapless for $p=3m\pm 1$ (for integer $m$), corresponding to a massless phase of the $σ$-model at $θ=\pm 2π/3$. We confirm this with Monte Carlo calculations on the $σ$-model.
We formulate the dynamics of local order parameters by extending the recently developed adiabatic spinwave theory involving the Berry curvature, and derive a formula showing explicitly the role of the Berry phase in determining the spectral form of the low-lying collective modes. For antiferromagnetic spin chains, the Berry phase becomes a topological invariant known as the Chern number. Our theory predicts the existence of the Haldane gap for a topologically trivial ground state, and a linear dispersion of low-lying excitations for a non-trivial ground state.
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…
Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-1/2 kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using th…
We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional geometries. Using large-scale numerical simulations, we map out the phase diagram for a realistic model applicable to experimental Haldane compounds. We also investigate the effect of different chain coupling geometries and confirm a general mean field universality of the critical coupling times the coordination number of the lattice. Inspired by the recent development of characterization of symmetry protected topological states, of which the Hal…
We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid similar to a $S=1/2$ Heisenberg antiferromagnetic chain. We furth…
A bosonized-field-theory representation of spin operators in the uniform-field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin-1 Haldane chains is formulated by means of the non-Abelian (Tsvelik's Majorana fermion theory) and the Abelian bosonizations and Furusaki-Zhang technique [Phys. Rev. B {\bf 60}, 1175 (1999)]. It contains massive magnon fields as well as massless boson fields. From it, asymptotic forms of spin correlation functions in the TLL phase are completely determined. Applying the formula, we further discuss effects of perturbations (bond alternation, single-ion anisotropy …
To begin with, we introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3bar of SU(3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon …
The $s=1/2$ chain-boundary excitations occurring in the Haldane phaseof $s=1$ antiferromagnetic spin chains are investigated. The bilinear-biquadratic hamiltonian is used to study these excitations as a function of the strength of the biquadratic term, $β$, between $-1\leβ\le1$. At the AKLT point, $β=-1/3$, we show explicitly that these excitations are localized at the boundaries of the chain on a length scale equal to the correlation length $ξ=1/\ln 3$, and that the on-site magnetization for the first site is $<S^z_1>=2/3$. Applying the density matrixrenormalization group we show that the cha…
Motivated by the recent generalization of the Haldane conjecture to $\mathrm{SU}(3)$ chains [M. Lajkó et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a multiple of three, we develop a density matrix renormalization group algorithm based on standard Young tableaus to study the model with three boxes directly in the representations of the global $\mathrm{SU}(3)$ symmetry. We show that there is a finite gap between the singlet and the symmetric $[3\,0\,0]$ sector $Δ_{[3\,0\,0]}/J …
The Haldane phase is the prototype of symmetry protected topological (SPT) phases of spin chain systems. It can be protected by several symmetries having in common the degeneracy of the entanglement spectrum. Here we explore in depth this degeneracy for the spin-1 AKLT and bilinear-biquadratic Hamiltonians and show the emergence of a bulk-edge correspondence that relates the low energy properties of the entanglement Hamiltonian of a periodic chain and that of the physical Hamiltonian of an open chain. We find that the entanglement spectrum can be described in terms of two spins-1/2 behaving as…
We use linked-cluster expansions to analyze the quantum phase transitions between symmetry unbroken trivial and topological Haldane phases in two different spin-one chains. The first model is the spin-one Heisenberg chain in the presence of a single-ion anisotropy while the second one is the dimerized spin-one Heisenberg chain. For both models we determine the ground-state energy and the one-particle gap inside the non-topological phase as a high-order series using perturbative continuous unitary transformations. Extrapolations of the gap series are applied to locate the quantum critical point…
We report the results of various measurements, namely magnetization, complex dielectric permittivity and electric polarization (P) on Dy2BaNiO5 as a function of temperature (T) and magnetic-field (H), apart from heat-capacity (C), with the primary motivation of exploring the existence of magnetoelectric (ME) coupling among Haldane spin-chain systems. The M(T) and C(T) data establish long range magnetic ordering at 58K. The most noteworthy observations are: (i) Distinct anomalies are observed in dielectric constant (ε') vs T and loss (tanδ) vs T at different temperatures, i.e. 12.5, 30, 50 and …
We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin, $S$, the magnetization curve can have plateaus and we argue that the magnetization per site $m$ is topologically quantized as $q (S - m)= integer$ at the plateaus, where $q$ is the period of the groundstate. We also discuss conditions for the presence of the plateau at those quantized values. For $S=3/2$ and $m=1/2$, we study several models and find two distinct types of massive phases at the plateau. One of them is argued to be a ``Haldane gap phase'' for half-in…
The bulk single crystals of $S = 1$ chain compound Ni(C$_3$H$_{10}$N$_2$)$_2$NO$_2$ClO$_4$ are grown by using a slow evaporation method at a constant temperature and a slow cooling method. It is found that the optimum condition of growing large crystals is via slow evaporation at 25 $^\circ$C using 0.015 mol Ni(ClO$_4$)$_2$$\cdot$6H$_2$O, 0.015 mol NaNO$_2$, and 0.03 mol 1,3-propanediamine liquid dissolved into 30 ml aqueous solvent. High-quality crystals with size up to $18 \times 7.5 \times 5$ mm$^3$ are obtained. The single crystals are characterized by measurements of x-ray diffraction, ma…
