Dynamics of Alternating Spin Chains

We consider the dimerised spin- isotropic XY chain in a transverse field and study the xx and zz dynamic structure factors for different values of the Hamiltonian parameters and temperature.     

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T/J=10^-24) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given. Received: 12 February 1998 / Received in final form: 15 March 1998 / Accepted: 17 March 1998     

Exact results of a mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies Dz and Dx is solved exactly by means of a mapping to the spin-1/2 Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles' spectra Λk, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δh for exciting a hole, and the ground state energy are obtained. The phase diagram of the ground state is also given. The results show that when Dz?0 for any finite value of Dx, there is no quantum critical point and the ground state is always in a spin ordered phase disregard of the boundary condition in the present system.     

Quantum phase transitions in alternating spin-(1/2, 5/2) Heisenberg chains

The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim of describing the available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature versus magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger liquid phase, the ferrimagnetic plateau and the fully polarized phase, and the respective quantum critical points and crossover lines.     

Triplet superconductivity vs. easy-plane ferromagnetism in a 1D itinerant electron system with transverse spin anisotropy

In this paper we study the ground state phase diagram of a one-dimensional t-U-J model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin- XY model takes place.Received: 6 February 2004, Published online: 9 April 2004PACS: 71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.Pq Spin chain modelsG.I. Japaridze: Permanent address: Andronikashvili Institute of Physics, Georgian Academy, Tamarashvili 6, Tbilisi 380077, Georgia     

Exactly Solvable su(N) Mixed Spin Ladders

It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin- spin-1 ladder, a mixed spin- spin- ladder and a spin-1 ladder with biquadratic interactions.     

Mixed spin transverse Ising model with longitudinal random crystal field interactions

The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory. In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators. We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features resulting from the fluctuation of the crystal field interactions. Received: 13 February 1998 / Accepted: 17 March 1998     

Exact solution and magnetic properties of an anisotropic spin ladder

We study an integrable two-leg spin-1/2 ladder with an XYZ-type rung interaction. The exact rung states and rung energies are obtained for the anisotropic rung coupling in the presence of a magnetic field. The magnetic properties are analyzed at both zero and finite temperatures via the thermodynamic Bethe ansatz and the high-temperature expansion. According to different couplings in the anisotropic rung interaction, there are two cases in which a gap opens, where the ground state involves one or two components in the absence of a magnetic field. We obtain the analytic expressions of all critical fields for the field-induced quantum phase transitions (QPT). The anisotropic rung interaction leads to such effects as separated magnetizations and susceptibilities in different directions, lowered inflection points, and remnant weak variation of the magnetization after the last QPT.Received: 21 May 2004, Published online: 30 September 2004PACS: 75.10.Jm Quantized spin models - 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)     

Ground state phase diagram of the 1D XXZ model in a transverse magnetic field

The Ground state phase diagram of the 1D spin-1/2 XXZ model in a transverse magnetic field is studied by the numerical Lanczos method. Also by computing the energy gap and different spin-spin structure factors, quantum phase transitions in whole range of the anisotropy parameter are determined.     

Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains

The free energy and correlation lengths of the spin-1/2XYZ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the criticalXXZ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-criticalXXZ chain and the related spin-1 biquadratic chain at arbitrary temperature.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Exact results on spin dynamics and multiple quantum NMR dynamics in alternating spin-1/2 chains with <Emphasis Type="Italic">XY</Emphasis> Hamiltonian at high temperatures

We extend the picture of a transfer of nuclear spin-1/2 polarization along a homogeneous one-dimensional chain with the XY Hamiltonian to the inhomogeneous chain with alternating nearest neighbor couplings and alternating Larmor frequencies. To this end, we exactly calculate the spectrum of the spin-1/2 XY Hamiltonian of the alternating chain with an odd number of sites. The exact spectrum of the XY Hamiltonian is also applied to study the multiple quantum (MQ) NMR dynamics of the alternating spin-1/2 chain. MQ NMR spectra are shown to have the MQ coherences of zero and ± second orders just as in the case of a homogeneous chain. The intensities of the MQ coherences are calculated.     

The anisotropic multichannel spin-$\mathsf{S}$ Kondo model: Calculation of scales from a novel exact solution

A novel exact solution of the multichannel spin-S Kondo model is presented, based on a lattice path integral approach of the single channel spin-1/2 case. The spin exchange between the localized moment and the host is of XXZ-type, including the isotropic XXX limit. The free energy is given by a finite set of non-linear integral equations, which allow for an accurate determination of high- and low-temperature scales.Received: 9 June 2004, Published online: 3 August 2004PACS: 72.15.Qm Scattering mechanisms and Kondo effect - 04.20.Jb Exact solutions - 75.20.Hr Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions - 75.10.Lp Band and itinerant models     

Exact and numerical results for a dimerized coupled spin- 1/2 chain

We establish exact results for coupled spin-1/2 chains for special values of the four-spin interaction V and dimerization parameter delta. The first exact result is at delta = 1/2 and V = -2. Because we find a very small but finite gap in this dimerized chain, this can serve as a very strong test case for numerical and approximate analytical techniques. The second result is for the homogeneous chain with V = -4 and gives evidence that the system has a spontaneously dimerized ground state. Numerical diagonalization and bosonization techniques indicate that the interplay between dimerization and interaction could result in gapless phases in the regime 0相似文献   

Thermal Entanglement in 2 × 3 Heisenberg Chains via Distance Between States

Most of the work involving entanglement measurement focuses on systems that can be modeled by two interacting qubits. This is due to the fact that there are few studies presenting entanglement analytical calculations in systems with spins s >?1/2. In this paper, we present for the first time an analytical way of calculating thermal entanglement in a dimension 2 ? 3 Heisenberg chain through the distance between states. We use the Hilbert-Schmidt norm to obtain entanglement. The result obtained can be used to calculate entanglement in chains with spin-1/2 coupling with spin-1, such as ferrimagnetic compounds as well as compounds with dimer-trimer coupling.

     

Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets

It is shown for a class of antiferromagnetic Hamiltonians how one can get lower bounds for the energy gap above the ground state by diagonalizing a finite system. This method is applied to certain spin chains (including a spin-1 chain). Trial wave functons are proposed for the elementary excitations and are tested in the case of the spin-1 chain.     

Thermodynamics of a model for valence fluctuations between two magnetic configurations

The thermodynamic Bethe-Ansatz equations of a model describing valence fluctuations between two magnetic configurations are derived. The model includes a spin-1/2 and a spin-1 configurations hybridized through the promotion of an electron to a conduction band.Thes–d like limits are reproduced. An expression for the specific heat at low temperatures is obtained.ConicetGuggenheim fellow     

Improved Bounds on the Spectral Gap Above Frustration-Free Ground States of Quantum Spin Chains

Nachtergaele obtained explicit lower bounds for the spectral gap above many frustration free quantum spin chains by using the martingale method. We present simple improvements to his main bounds which allow one to obtain a sharp lower bound for the spectral gap above the spin-1/2 ferromagnetic XXZ chain. As an illustration of the method, we also calculate a lower bound for the spectral gap of the AKLT model, which is about 1/3 the size of the expected gap.     

Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: high-order coupled-cluster calculations

We investigate the ground-state magnetic long-range order of quasi-one-dimensional quantum Heisenberg antiferromagnets for spin quantum numbers s = 1/2 and s = 1. We use the coupled cluster method to calculate the sublattice magnetization and its dependence on the inter-chain coupling J_⊥. We find that for the unfrustrated spin-1/2 system, an infinitesimal inter-chain coupling is sufficient to stabilize magnetic long-range order, in agreement with results obtained by other methods. For s = 1, we find that a finite inter-chain coupling is necessary to stabilize magnetic long-range order. Furthermore, we consider a quasi one-dimensional spin-1/2 system, where a frustrating next-nearest neighbor in-chain coupling is included. We find that for stronger frustration as well, a finite inter-chain coupling is necessary to have magnetic long-range order in the ground state, and that the strength of the inter-chain coupling necessary to establish magnetic long-range order is related to the size of the spin gap of the isolated chain.     

In-plane anisotropy of the electronic structure for the charge- and orbital-ordered state in half-doped manganite with layered structure

We report on the in-plane anisotropy of the electronic response in the spin-, charge-, and orbital-ordered phase of a half-doped layered-structure manganite. The optical conductivity spectra for a single domain of Eu1/2Ca3/2MnO4 unambiguously show the anisotropic charge dynamics which well corresponds to the theoretical calculation: the optical conductivity with the polarization along the zigzag ferromagnetic chain direction exhibits a smaller gap and a larger intensity at lower energies than that of the perpendicular polarization mostly due to the charge and orbital ordering and the associated quantum interference effect.     

Finite-size scaling for correlations of quantum spin chains at criticality

We study the finite-size scaling behavior of two-point correlation functions of translationally invariant many-body systems at criticality. We propose an efficient method for calculating the two-point correlation functions in the thermodynamic limit from numerical data of finite systems. Our method is most effective when applied to a two-dimensional (classical) system which possesses a conformal invariance. By using this method with numerical data obtained from exact diagonalizations and Monte Carlo simulations, we study the spin-spin correlations of the quantum spin-1/2 and-3/2 antifierromagnetic chains. In particular, the logarithmic corrections to power-law decay of the correlation of the spin-1/2 isotropic Heisenberg antiferromagnetic chain are studied thoroughly. We clarify the cause of the discrepancy in previous calculations for the logarithmic corrections. Our result strongly supports the field-theoretic prediction based on the mappings to the Wess-Zumino-Witten nonlinear -model or the sine-Gordon model. We also treat logarithmic corrections and crossover phenomena in the spin-spin correlation of the spin-3/2 isotropic Heisenberg antiferromagnetic chain. Our results are consistent with the Affleck-Haldane prediction that the correlation of the spin-3/2 chain exhibits a crossover to the same asymptotic behavior as in the spin-1/2 chain.