Frustrated Spin Chain Research Articles

Doped coupled frustrated spin-1/2 chains with four-spin exchange.

The role of various magnetic interchain couplings is investigated by numerical methods in doped frustrated quantum spin chains. A nonmagnetic dopant introduced in a gapped spin chain releases a free spin-1/2 soliton. The formation of a local magnetic moment is analyzed in terms of soliton confinement. A four-spin coupling which might originate from cyclic exchange is shown to produce such a confinement. Dopants on different chains experience an effective space-extended nonfrustrating pairwise spin interaction.

Absence of effective spins12induced by nonmagnetic impurities in a class of low-dimensional magnets

We show that doping a Majumdar--Ghosh chain with non-magnetic impurities does {\it not} produce almost free spins 1/2. The difference between this system and other spin liquids, such as unfrustrated spin ladders, is illustrated in the context of the general dimerized, frustrated spin chain. By detailed analysis of the excitation spectra of finite chains with two impurities, we investigate the evolution of the screening affecting impurity-induced free spins, and of the sign and magnitude of their effective interactions. We comment on a possible connection to impurity-doping experiments in CuGeO_3.

New type of frustrated spin chains in KMg xCu 5− xV 3O 13 ( x=0–1)

We synthesized the powder samples of KMg x Cu 5− x V 3O 13 ( x=0.1∼1) and investigated their magnetic susceptibilities and the magnetization curves up to 47 T. The Curie constant and the Weiss temperature of KMgCu 4V 3O 13 change markedly around 20 K. From the Curie constant estimated from the data between 5 and 10 K, the number of spins in the low-temperature region was estimated to be n low=8.13%, assuming all the copper spins have S=1/2 and g=2. The magnetization curve of KMgCu 4V 3O 13 at 1.7 K is bent around 20 T and shows a linear increase between 20 and 30 T. The magnetization, M linear( H→0), estimated by extrapolating the linear part to 0 T is 0.306 μ B/f.u. Furthermore, all the x dependences of the Néel temperature T N, n low, θ low, the magnetic field at spin–flop transition H sf and M linear( H→0) change continuously with x. This indicates that there is no quantum critical region between the frustrated spin chains of KCu 5V 3O 13 and KMgCu 4V 3O 13. The ground states of KCu 5V 3O 13 and KMgCu 4V 3O 13 have been deduced.

Large-SApproach to Chiral Phases in Frustrated Spin Chains

A large-S approach to the description of chiral phases in frustrated antiferromagnetic spin-S chains with easy-plane anisotropy is proposed. The approach is valid in the vicinity of the classical Lifshitz point j=1/4, where j is the relative strength of the frustrating next-nearest-neighbor coupling. The effective theory turns out to be the nonlinear sigma-model with the additional fourth-order term in spatial derivatives. The topological term persists for j>1/4, which leads to disappearance of the chiral gapped phase for half-integer S, in accordance with the recent numerical results.

First-Order Phase Transitions in Frustrated Spin Systems

We give a short review of our recent works on the first-order quantum phase transitions in frustrated spin chains with orthogonal-dimer structure. When the ratio of the competing antiferromagnetic exchange couplings is varied, a first-order transition occurs between the dimer phase and the plaquette phase, which is accompanied by the discontinuity in the spin excitation gap. We further show that strong frustration triggers the phase transitions in a magnetic field, which exhibit plateaus and jumps in the magnetization curve. The hole-doping effect is also addressed for the orthogonal-dimer chain with linked-tetrahedra structure. It is found that the competing antiferromagnetic interactions result in a first-order metal-insulator transition upon hole doping.

Novel Frustrated Spin Chain System in KCu5V3O13

A powder sample of KCu 5 V 3 O 13 was synthesized and is expected to represent a novel frustrated spin chain system based on its characteristic crystal structure. The magnetic susceptibility and the high-field magnetization process were investigated in order to elucidate the ground state of this spin chain system. From the results, the ground state of this compound appears to be an antiferromagnetically ordered state. The transition temperature was determined to be T N =7.8 K. However, there are some anomalous behaviors evident in both the susceptibility and the magnetization curves: the Curie constant and the Weiss temperature change markedly around 75 K, the gradient of the magnetization curve becomes small after a spin-flop transition, and the number of the ordered spins is only 1/5 of all the copper spins. Assuming that the other spins vanish by forming a spin-singlet state, the energy gap was estimated to be 44.3 K from the magnetization curve. Thus, the classical renormalized ordered state may coexi...

Single-hole dynamics in dimerized and frustrated spin chains

We present a unified account for the coupled single-hole and spin dynamics in the spin-gap phase of dimerized and frustrated spin chains and two-leg spin ladders. Based on the strong dimer limit of a one-dimensional ${t}_{1,2,3}$-${J}_{1,2,3}$ model a diagrammatic approach is presented that employs a mapping of the spin Hamiltonian onto a pseudofermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasiparticle weight is observed and studied for a variety of system parameters. A comparison with existing exact-diagonalization data is performed and good agreement is found.

Phase diagram of the quarter-filled extended Hubbard model on a two-leg ladder

We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion V using the Density Matrix Renormalization Group technique. The ground-state is homogeneous at small V, a ``checkerboard'' charge--ordered insulator at large V and not too small on-site Coulomb repulsion U, and is phase-separated for moderate or large V and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper, we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling charge-ordered regime which maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.

Phase Diagram of a Heisenberg Spin-Peierls Model with Quantum Phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

: A quantum mechanical picture is presented to describe the behavior of confined spinons in a variety of S =1/2 chains. The confinement is due to dimerization and frustration and it manifests itself as a nonlinear potential , centered at chain ends () or produced by modulation kinks (b > 1). The calculation extends to weak or zero frustration some previous ideas valid for spinons in strongly frustrated spin chains. The local magnetization patterns of the confined spinons are calculated. A (minimum) enhancement of the local moments of about 11/3 over a single S =1/2 is found. Estimates for excitation energies and binding lengths are obtained.

Frustrated antiferromagnetic quantum spin chains for spin lengthS>1

We investigate frustrated antiferromagnetic Heisenberg quantum spin chains at $T=0$ for $S=\frac{3}{2}$ and $S=2$ using the DMRG method. We localize disorder and Lifshitz points, confirming that quantum disorder points can be seen as quantum remnants of classical phase transitions. Both in the $S=\frac{3}{2}$ and the $S=2$ chain, we observe the disappearance of effectively free $S=\frac{1}{2}$ and $S=1$ end spins, respectively. The frustrated spin chain is therefore a suitable system for clearly showing the existence of free end spins ${S}^{\ensuremath{'}}=[S/2]$ also in half-integer antiferromagnetic spin chains with $S>\frac{1}{2}.$ We suggest that the first-order transition found for $S=1$ in our previous work [A. K. Kolezhuk, R. Roth, and U. Schollw\"ock, Phys. Rev. Lett. 77, 5142 (1996); Phys. Rev. B 55, 8928 (1997)] is present in all frustrated spin chains with $S>\frac{1}{2},$ characterized by the disappearance of effectively free end spins with ${S}^{\ensuremath{'}}=[S/2].$

Critical properties of frustrated spin chain with bond alternation in magnetic fields

Abstract The critical exponents of spin correlation functions of the frustrated S = 1 2 antiferromagnetic Heisenberg chain with bond alternation are investigated numerically by the exact diagonalization method combined with finite-size-scaling analysis. The magnetization curve in the thermodynamic limit is also presented.

Field theories for frustrated antiferromagnetic spin chains

We study the antiferromagnetic spin chain with both dimerization and frustration. The classical ground state has three phases, a Néel phase, a spiral phase and a collinear phase, which we study through a nonlinear sigma-model approach. In the spiral phase, the field theory becomes and Lorentz invariant at long distances, a model which is exactly solvable. The low-energy spectrum is doubly degenerate with massive `elementary' spin-1/2 particles and `two-particle' triplet and singlet physical excitations. The field theory also supports solitons which lead to a double degeneracy of the ground state for half-integer spins (when there is no dimerization).