一种等效于反铁磁海森伯混合自旋链的铁磁-反铁磁交替自旋链

利用严格对角化方法研究了一种自旋为1/2的铁磁-反铁磁交替自旋链的物理性质.计算了自旋关联函数、自旋z方向分量、自旋激发谱和磁化曲线等基本物理量,并将这些物理量和自旋为(1,1/2)的混合反铁磁自旋链对应的物理性质进行了比较.结果表明,当铁磁作用居于主导地位时,该模型的物理行为等效于混合自旋模型.因此,可以通过分析铁磁-反铁磁交替自旋链的物理性质研究混合自旋链的物理行为.     

Zero-point spin reduction in a two-dimensional Heisenberg antiferromagnet Cu(HCOO)2 · 4H2O

The copper NMR in a two-dimensional Heisenberg antiferromagnet Cu(HCOO)₂ ·4H₂O (T_N = 17 K) was observed using a standard spin- echo method at liquid He temperatures. The field-dependence of the ⁶³Cu NMR frequency was measured for H₀ (? 56 kOe) | b-axis. The result was interpreted by taking into account a zero-point spin reduction of about 35% in addition to the rotation of the antiferromagnetic spin axis. The amount of the observed spin reduction is in good agreement with the prediction of spin-wave theory.     

Quantum nonlinear sigma model for arbitrary spin Heisenberg antiferromagnets

We derive a quantum nonlinear sigma model (QNLSM) for quantum Heisenberg antiferromagnets (QHA) with arbitrary S (spin) values. A upper limit of the low temperature is naturally carried out for the reliability of the QNLSM. The S dependence of the effective coupling constant and the spin-wave velocity in the QNLSM are also obtained explicitly. The resulting spin-wave velocity for 2D spin-1/2 QHA highly concurs with the experimental data of high T(c) compound La(2)CuO(4). The predicted correlation lengths for 2D QHA and spin-gap magnitudes for 1D QHA also agrees with the accurate numerical results.     

Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.     

Spin frustration-related behavior of mixed spin diamond chain

The magnetization of mixed spin-1/2, 1 Ising diamond chain with antiferromagnetic spin exchange interaction has been investigated by using the Monte Carlo simulation. Magnetization behaviors with different antiferromagnetic interactions are simulated under magnetic field at low temperature. The behaviors are studied in two different cases. In one case the absolute value of the interaction between two spin-1/2 atoms is the largest and in the other case it is not the largest. Multiple plateaus of magnetization M, such as plateaus at M=±1, M=0 and M=±0.566 are obtained. The plateaus at M=±0.566 correspond to two metastable states. The M=0 plateau may disappear at some specific values of spin exchange interactions. The spin configurations were checked when the plateaus appear. The dimmer and trimmer states are found.     

Quantum spin liquid in the FCC lattice

The properties of the spin system in the FCC lattice described by the Heisenberg model (s=1/2) with antiferromagnetic interactions between the nearest neighbors were studied. It was shown within the framework of spin-wave theory that long-range antiferromagnetic order was absent because of frustration of exchange coupling and transverse quantum spin fluctuations. The system was in the quantum spin liquid state. A method for describing it within linear second-order theory with self-consistently calculated parameters was suggested. It was proved that the ground spin liquid state was singlet. The thermodynamic properties of the spin liquid in the whole temperature range and the character of spatial spin correlations, which had alternating signs and a finite correlation length, were determined. The theory was constructed based on the method of two-time Green temperature functions.     

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.     

High-temperature dynamics of the anisotropic Heisenberg chain studied by moment methods

The dynamics of the anisotropic spin-1/2 nearest-neighbour Heisenberg chain is studied at infinite temperature. Low-order coefficients of the short-time expansions are computed for spin-spin and energy-density-energy-density correlation functions for cyclical as well as for open-ended chains. The commutator algebra necessary to generate these coefficients may be performed by a computer. The series obtained for the spin correlation function (up to ordert ¹⁴ for a bulk spin and up to ordert ¹⁸ for a boundary spin) and for the energy density correlation function are the longest ones available up to now. The coefficients are used to construct rigorous upper and lower bounds to autocorrelation functions and near-neighbour correlation functions.     

The exact ground state and the origin of the spin gap in the distorted mixed spin (1, 1/2) diamond chain

By using the method of exact diagonalization, we investigated the properties of the distorted mixed spin (1, 1/2) diamond chain with antiferromagnetic interactions along the rung and leg. The ground states of this model contain the sawtooth chain state and the rung dimer plus Haldane state. The research on the origin of the spin gap of the model discloses that there are three different types of spin excitations at different parameter regimes due to the competition among the interactions J₁, J₂ and J₃.     

Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions

For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S = 1 and σ = 1/2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.     

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     

Effect of frustration on spin-wave excitation spectra and ground-state properties of the quasi-one-dimensional antiferromagnetic chain with asymmetrical sublattices

We investigate the effect of frustration on spin-wave excitation spectra and the properties of the quasi-one-dimensional Heisenberg chain using a spin-wave-wave analysis, the exact diagonalization method and the density matrix renormalization group method. The results show that frustration can cause the softening of the acoustic excitation spectrum ω₃, as well as the hardening of the optical excitation spectrum ω₁. As a function of the frustration parameter α, the phase diagram exhibits a ferromagnetic phase, a narrow canted phase and a singlet phase. The results obtained from numerical methods show that the spin gap obviously opens and the tetramer-dimer state dominates the properties of the ground state in the singlet phase.     

Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit

We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.     

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.     

Nonlocal conservation laws and supersymmetric Heisenberg spin chain

The role of nonlocal conservation laws and the corresponding charges are analyzed in the supersymmetric Heisenberg spin chain. It is observed that such nonlocal charges generate a graded-Yangian type algebra, by using the properties of the monodromy matrix and classicalr matrix.     

Alternating-spin S = 3/2 and <Emphasis Type="Italic">σ</Emphasis> = 1/2 Heisenberg chain with isotropic three-body exchange interactions

The promotion of collinear classical spin configurations as well as the enhanced tendencytowards nearest-neighbor clustering of the quantum spins are typical features of thefrustrating isotropic three-body exchange interactions in Heisenberg spin systems. Basedon numerical density-matrix renormalization group calculations, we demonstrate that theseextra interactions in the Heisenberg chain constructed from alternating S = 3/2 and σ = 1/2 site spins can generate numerous specific quantum spinstates, including some partially-polarized ferrimagnetic states as well as adoubly-degenerate non-magnetic gapped phase. In the non-magnetic region of the phasediagram, the model describes a crossover between the spin-1 and spin-2 Haldane-typestates.     

Phase diagram of the random Heisenberg antiferromagnetic spin-1 chain

We present a new perturbative real space renormalization group (RG) to study random quantum spin chains and other one-dimensional disordered quantum systems. The method overcomes problems of the original approach which fails for quantum random chains with spins larger than S=1/2. Since it works even for weak disorder, we are able to obtain the zero temperature phase diagram of the random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We find a random singlet phase for strong disorder. As the disorder decreases, the system shows a crossover from a Griffiths to a disordered Haldane phase.     

Anomalous spin excitation spectrum of the Heisenberg model in a magnetic field

Making the assumption that high-energy fermions exist in the two dimensional spin- 1/2 Heisenberg antiferromagnet, we present predictions based on the pi-flux ansatz for the dynamic structure factor when the antiferromagnet is subject to a uniform magnetic field. The main result is the presence of gapped excitations in a momentum region near (pi,pi) with energy lower than that at (pi,pi). This is qualitatively different from spin-wave theory predictions and may be tested by experiments or by quantum Monte Carlo.     

Effects of the single-ion anisotropy and dimerization on 1D spin-1 antiferromagnetic Heisenberg chain

One-dimensional quantum spin-1 antiferromagnetic Heisenberg chain (AFHC) with exchange anisotropy J_z, dimerization δ and single-ion anisotropy D∑_n(S_n^z)² was investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the excitation spectrum, phase order and the phase fluctuation φ were derived in a self-consistent-harmonic-field approach. We studied the effects of the single-ion anisotropy and dimerization on two gaps by taking the different momentum cutoff α_i in two scalar field spaces H_i (i=1,2). The occurrences of richer phase transitions were understood in the viewpoints of the phase fluctuation and the z polar spin fluctuation. And the Gaussian critical line was given as J_z−D−πα₁δ=0.