Magnetic Properties of XXZ Heisenberg Antiferromagnetic and Ferrimagnetic Nanotubes

The spin-1/2 antiferromagnetic and spin-(1/2, 1) ferrimagnetic single-walled nanotubes are described by XXZ Heisenberg model. The sublattice magnetization and the critical temperature of the system are calculated by using the double-time spin Green's function method. At zero temperature, with the increase of the exchange interaction in the circumferential direction, a maximum value appears in the sublattice magnetization curves of antiferromagnetic and ferrimagnetic systems. As the diameter of the tube increases, the spin quantum fluctuations and thermal fluctuations are suppressed. In addition, the spin quantum fluctuation of the spin-1/2 antiferromagnetic system is greater than that of the spin-(1/2, 1) ferrimagnetic system. The critical temperature of the system increases firstly and then tends to a constant with the increase of the diameter of tube, and it decreases to zero as the exchange anisotropy of the system disappears.     

Ising phases of Heisenberg ladders in a magnetic field

We show that Dzyaloshinskii-Moriya (DM) interactions can substantially modify the phase diagram of spin-1/2 Heisenberg ladders in a magnetic field provided they compete with exchange. For nonfrustrated ladders, they induce a local magnetization along the DM vector that turns the gapless intermediate phase into an Ising phase with broken translational symmetry, while for frustrated ladders, they extend the Ising order of the half-integer plateau to the surrounding gapless phases of the purely Heisenberg case. Implications for experimental ladder and dimer systems are discussed.     

Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet

We present a density matrix renormalization group study of the ground-state properties of spin-1/2 frustrated J1-J3 Heisenberg n(l)-leg ladders (with n(l) up to 8). For strong frustration (J(3)/J(1) approximately 0.5), both even-leg and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.     

0- and 2/3-magnetization plateaus in three-leg antiferromagnetic Heisenberg spin-1/2 ladders with leg-dimerization

Magnetic properties of three-leg antiferromagnetic Heisenberg spin-1/2 ladders with different dimerization patterns have been studied using the bond mean-field theory. Our results show that rung-columnar ladders are thermodynamically stable states for large rung-to-leg coupling ratios. Magnetization curves of leg-columnar and leg-staggered ladders always exhibit 0- and 2/3-magnetization plateaus, which do not appear in rung-columnar and rung-staggered ladders. In leg-dimerized ladders, the formation of spin dimers in the three legs results in the appearance of the 0- and 2/3-magnetization plateaus. Spin configuration in the 2/3-magnetization plateau can be understood from the mean-field bond parameters.     

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.     

一维亚铁磁混合自旋链的磁特性的Monte Carlo模拟

基于一维自旋链模型，采用Monte Carlo方法对具有反铁磁相互作用的自旋一I和自旋-3／2交替混合的亚铁磁系统进行模拟计算，研究单离子各向异性对系统磁特性的影响．模拟结果发现：基态时系统的磁化强度在外加磁场作用下呈现出阶梯状，并获得了自旋-1和自旋-3／2交替混合的亚铁磁系统相图．最后，通过对系统能量和自旋组态的研究，解释了该系统中出现的阶梯效应和相图．     

Green's function study of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system

The magnetic properties of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system on a square lattice are investigated by using the double-time temperature-dependent Green's function technique. In order to decouple the higher order Green's functions, Anderson and Callen's decoupling and random phase approximations have been used. The nearest- and next-nearest-neighbor interactions and the single-ion anisotropies are considered and their effects on compensation and critical temperature are studied.     

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.     

Long-range spin-pairing order and spin defects in quantum spin- $${1 \over 2}$$ ladders

For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range spin pairing order can be identified which enables the separation of the space spanned by finite-range (covalent) valence-bond configurations into w +1 subspaces. Since every subspace has an equivalent counter subspace connected by translational symmetry, twofold degeneracy, breaking translational symmetry is found except for the subspace where the ground state of w = even belongs to. In terms of energy ordering, (non)degeneracy and the discontinuities introduced in the long-range spin pairing order by topological spin defects, the differences between even and odd ladders are explained in a general and systematic way. Received 19 July 1999 and Received in final form 8 October 1999     

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.

     

Ferromagnetic Lieb-Mattis theorem

We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains with spins of arbitrary magnitude, thus extending our previous result for the spin-1/2 chain. Ferromagnetic ordering means that the minimum energies in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin. This result provides a ferromagnetic analogue of the well-known theorem by Lieb and Mattis about ordering of energy levels in antiferromagnetic and ferrimagnetic systems on bipartite graphs.     

Magnetic Properties of a Mixed Spin-2 and Spin-5/2 Heisenberg Ferrimagnetic System on a Two-Dimensional Honeycomb Lattice： Green＇s Function Approach

The multisublattice Green＇s function technique is applied to study the magnetic properties of a mixed spin-2 and spin-5/2 Heisenberg ferrimagnetic system on a two-dimensional honeycomb lattice. The role of the different interactions in the Hamiltonian is explored. When only the nearest-neighbor interaction and the single-ion anisotropy are included, our results indicate that there are compensation points at finite temperatures. When the next-nearest-neighbor interaction exceeds a minimum value that depends on the other parameters in the Hamiltonian, the compensation point disappears. The next-nearest-neighbor interaction has the effect of changing the compensation temperature.     

Magnetization and spin gap in two-dimensional organic ferrimagnet BIPNNBNO

A magnetization process in the two-dimensional ferrimagnet BIPNNBNO is analyzed. The compound consists of ferrimagnetic (1,1/2) chains coupled by two sorts of antiferromagnetic interaction. Whereas the behavior of the magnetization curve in higher magnetic fields can be understood within a process for the separate ferrimagnetic chain, the appearance of the singlet plateau at lower fields is an example of non-Lieb-Mattis type ferrimagnetism. By using the exact diagonalization technique for finite clusters of size 4 × 6, 4 × 8 and 4 × 10 we show that the interchain frustration coupling plays an essential role in stabilization of the singlet phase. These results are complemented by an analysis of four cylindrically coupled ferrimagnetic (1,1/2) chains via an Abelian bosonization technique and an effective theory based on the XXZ spin-1/2 Heisenberg model when the interchain interactions are sufficiently weak/strong, respectively.     

Controlling Luttinger liquid physics in spin ladders under a magnetic field

We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate T1(-1) at 250 mK and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and the Luttinger liquid model tested in detail over the whole fermion band.     

Magnetic properties of zig-zag ladders

We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZchains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling. Received 11 February 1999 and Received in final form 16 June 1999     

Concurrence and entanglement entropy in a dimerised spin-1/2 two-leg ladder

We consider isotropic spin-1/2 two-leg ladders with dominant spatially-modulated rung exchanges. We study the effect of a uniform magnetic field on the ground state phase diagram of the model using perturbation theory and the numerical Lanczos method. The ground state phase diagram consists of two gapless Luttinger liquid (LL) and three gapped phases. Numerically, we calculate the concurrence between two spins and the entanglement entropy between legs. Numerical experiment shows that the gapless LL phases are fundamentally different. In the first LL phase, only spins on rungs are entangled, but in the second LL phase the spins on legs are long-distance entangled. Therefore, the concurrence between spins on legs can be considered as a function to distinguish the LL phases.     

Spin Bose-metal and valence bond solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder

We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states and a possible phase diagram in two dimensions.     

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.     

Spin-driven jahn-teller distortion in a pyrochlore system

The ground-state properties of the spin-1 antiferromagnetic Heisenberg model on the corner-sharing tetrahedra, the pyrochlore lattice, are investigated. By breaking up each spin into a pair of 1/2-spins, the problem is reduced to the equivalent one of the spin-1/2 tetrahedral network in analogy with the valence bond solid state in one dimension. The twofold degeneracy of the spin singlets of a tetrahedron is lifted by a Jahn-Teller mechanism, leading to a cubic to tetragonal structural transition. It is proposed that the present mechanism is responsible for the phase transition observed in the spin-1 spinel compounds ZnV2O4 and MgV2O4.     

Exact ground states with deconfined gapless excitations for the three-leg spin-1/2 tube

We consider a spin-1/2 tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators-one on the triangles and the other on the square plaquettes on the side of the tube-that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i)?for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet bonds between nearest triangles; (ii)?for ferromagnetic exchange on the triangles, we recover the phase of the spin-3/2 Heisenberg chain; (iii)?between these two phases, a gapless incommensurate phase exists. We construct an exact ground state with two deconfined domain walls and a gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phases.