Frustrated Quantum Spin Systems Research Articles

Frustration-induced phase transitions in the spin-Sorthogonal-dimer chain

We investigate quantum phase transitions in the frustrated orthogonal-dimer chain with an arbitrary spin $S \geq 1/2$. When the ratio of the competing exchange couplings is varied, first-order phase transitions occur 2S times among distinct spin-gap phases. The introduction of single-ion anisotropy further enriches the phase diagram. The phase transitions described by the present model possess most of the essential properties inherent in frustrated quantum spin systems.

Competing Spin-Gap Phases in a Frustrated Quantum Spin System in Two Dimensions

We investigate quantum phase transitions among the spin-gap phases and the magnetically ordered phases in a two-dimensional frustrated antiferromagnetic spin system, which interpolates several important models such as the orthogonal-dimer model as well as the model on the 1/5-depleted square lattice. By computing the ground state energy, the staggered susceptibility and the spin gap by means of the series expansion method, we determine the ground-state phase diagram and discuss the role of geometrical frustration. In particular, it is found that a RVB-type spin-gap phase proposed recently for the orthogonal-dimer system is adiabatically connected to the plaquette phase known for the 1/5-depleted square-lattice model.

Sign problem in Monte Carlo simulations of frustrated quantum spin systems

We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and antiferromagnetic couplings $J_{xy}(r)=-J_z(r)$ in the $xy$-plane, for arbitrary distances $r$) the sign problem present for algorithms operating in the $z$-basis can be solved within a recent ``operator-loop'' formulation of the stochastic series expansion method (a cluster algorithm for sampling the diagonal matrix elements of the power series expansion of ${\rm exp}(-\beta H)$ to all orders). The solution relies on identification of operator-loops which change the configuration sign when updated (``merons'') and is similar to the meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for solving the sign problem for a class of fermion models (Phys. Rev. Lett. {\bf 83}, 3116 (1999)). Some important expectation values, e.g., the internal energy, can be evaluated in the subspace with no merons, where the weight function is positive definite. Calculations of other expectation values require sampling of configurations with only a small number of merons (typically zero or two), with an accompanying sign problem which is not serious. We also discuss problems which arise in applying the meron concept to more general quantum spin models with frustrated interactions.

Ground State Properties of a Fully Frustrated Quantum Spin System

We find that ground states of the quantum Heisenberg antiferromagnet on the geometrically frustrated pyrochlore checkerboard lattice are singlets and can be expressed in terms of positive matrices. The magnetization at zero external field vanishes for each frustrated tetrahedral unit separately and there is an upper bound of 1/8 in natural units on the susceptibility both for the ground state and at finite temperature. These results are the first exact ones in this field and generalize to some other lattices; the approach is also of interest for other spin systems.

Rotational invariance and order-parameter stiffness in frustrated quantum spin systems

We compute, within the Schwinger-boson scheme, the Gaussian-fluctuation corrections to the order-parameter stiffness of two frustrated quantum spin systems: the triangular-lattice Heisenberg antiferromagnet and the J1-J2 model on the square lattice. For the triangular-lattice Heisenberg antiferromagnet we found that the corrections weaken the stiffness, but the ground state of the system remains ordered in the classical 120 spiral pattern. In the case of the J1-J2 model, with increasing frustration the stiffness is reduced until it vanishes, leaving a small window 0.53 < J2/J1 < 0.64 where the system has no long-range magnetic order. In addition, we discuss several methodological questions related to the Schwinger-boson approach. In particular, we show that the consideration of finite clusters which require twisted boundary conditions to fit the infinite-lattice magnetic order avoids the use of ad hoc factors to correct the Schwinger-boson predictions.

Vanishing of the negative-sign problem of quantum Monte Carlo simulations in one-dimensional frustrated spin systems

The negative-sign problem in one-dimensional frustrated quantum spin systems is solved. We can remove negative signs of the local Boltzmann weights by using a dimer basis that has the spin-reversal symmetry. Validity of this new basis is checked in a general frustrated double-spin-chain system, namely the J_0-J_1-J_2-J_3 model. The negative sign vanishes perfectly for $J_0 + J_1 \leq J_3$.

Partial order in frustrated quantum spin systems

Partial order in frustrated quantum spin systems

Thermodynamic Property of theΔ-Chain

A one-dimensional fully frustrated quantum spin system called the Δ -chain is investigated, particularly with respect to the low-temperature structure of the specific heat, by quantum Monte Carlo simulations using the restructuring method. Sizes of the systems we considered are N =32,48 and 64. The simulation results together with the diagonalization results for N =10 and 16 show that the size dependence of the data is very weak, and thus the second peak of the specific heat stably exists at T <0.1, which corresponds to less than half the spin gap. Locality of excitations is seen in the Monte Carlo snapshot. We consider that the low-temperature properties of this system are governed by the local elementary excitations which generate the Schottky-type specific heat peak in the background of the ordinary thermal specific heat.

Cluster-effective-field approximations in frustrated quantum spin systems: CAM analysis of Neel-dimer transition in the S= 1/2 frustrated XXZ chain at the ground state

How to impose boundary conditions is crucial to finite-cluster calculations of quantum spin systems, but only open-boundary clusters have been used in cluster-effective-field approximations up to now. In the present paper, periodic-boundary clusters are also considered for the formulation of cluster-effective-field approximations in frustrated quantum spin systems. Namely, the open-boundary-condition double-cluster approximation (OBC-DCA) and the periodic-boundary-condition double-cluster approximation (PBC-DCA) are applied to the one-dimensional S= 1/2 frustrated XXZ model at the ground state. These two approximations are compared using the coherent-anomaly method (CAM). Within the limitation of cluster sizes in exact-diagonalization calculations, the PBC-DCA can reproduce the true phase boundary of the Neel-dimer transition. On the other hand, the OBC-DCA severely underestimates the existence of magnetic orders as quantum fluctuation is increased. These findings suggest that previous cluster-effective-field studies based on open-boundary clusters should be reconsidered.

Perturbation theory for the triangular Heisenberg antiferromagnet with Ising-like anisotropy

It has been argued that the case of strong uniaxial anisotropy is especially favourable for the formation of a spin-liquid state in theS=1/2 triangular Heisenberg antiferromagnet [77]. We reconsider the old arguments using up-to-date numerical techniques, and extend the study to general values ofS. Recent progress in the understanding of this frustrated quantum spin system sheds light on the question why the original arguments in favour of an RVB state can not be conclusive. Our present results indicate that the tendency towards three-sublattice ordering is much stronger than it had been thought. However, the caseS=1/2 is still seen to be set apart from the casesS>1/2, and forS=1/2 the existence of true longrange order in the ground state remains debatable.

Reply to "Comment on 'Chiral ordering in a frustrated quantum spin system' "

We discuss different definitions of chiral order parameters for spin systems. For the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ frustrated Heisenberg model on a finite square lattice, we calculate the vector chirality in the ground state. Unlike the ``spiral'' order parameter, the vector chiral order parameter shows a significant enhancement for strong frustration ${\mathit{J}}_{2}$\ensuremath{\approxeq}0.5${\mathit{J}}_{1}$ in comparison to its corresponding high-temperature expectation value. That indicates different finite-size contributions for both types of order parameters. Thus, we argue that we found some evidence for enhanced vector chiral correlations in the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ model.

Comment on "Chiral ordering in a frustrated quantum spin system"

The symmetry properties of an operator recently introduced by Richter, Gros, and Weber in the context of the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ frustrated Heisenberg model in two dimensions are studied. Richter et al. claimed that the enhancement of this operator with ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$ indicates the existence of strong ``chiral'' correlations in the model. However, we show that this operator transforms identically as a previously analyzed ``spiral'' operator and thus their physical content, including energy gaps in the spectrum, are the same. Thus, we argue that there are no clear numerical indications of chiral order in the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ model.

A modified Holstein-Primakoff approach to frustrated quantum spin systems

A simple modification of conventional spin-wave theory based on the Holstein-Primakoff transformation is investigated. On the basis of a comparison with exact results on finite lattices it is shown to give substantially improved results, especially for highly frustrated systems.

Chiral ordering in a frustrated quantum spin system.

We examine the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$, spin-1/2 Heisenberg model on a square lattice with 16 and 20 sites. We evaluate the ground-state correlations of an operator, measuring the handiness of plaquettes. We find a strong, physically relevant enhancement in these chiral correlations for intermediate values of ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$. We compare with the known results for correlations between column-wise-ordered singlets. We find both types of correlations to be viable candidates for the ground-state correlations in the thermodynamic limit.

New class of frustrated quantum spin systems with an exactly known ground state.

We present a new class of quantum systems whose ground state can be found exactly. This construction involves an assembly of finite frustrated clusters connected by fixed spins. By contrast to solvable dimerized models, our systems exhibit long-range magnetic order, providing a striking example of ordering by quantum fluctuations in the presence of frustration.

Frustrated quantum spin systems

The problem of quantum fluctuations in a number of quantum spin systems showing a spin glass transition is investigated. To deal with the quantum nature of the spins the Trotter-Suzuki method is used. Physical quantities like freezing temperature and phase diagrams are calculated exactly and the results are compared with other approaches.

Spin waves in frustrated quantum spin systems

The author presents a general Green function formalism to study the spin wave excitations in frustrated spin systems which are periodically defined. He gives an expression for the spin wave spectrum omega k and self-consistent equations for the local order parameter. He finds that omega k is linear in k for long wavelengths except for the ferromagnetic ground state and that the classical gauge invariance is broken by quantum fluctuations. The author applies the formalism to the fully frustrated simple cubic lattice. The zero-point motion is found to be rather small and the gauge invariance is restored at a temperature T0 below the transition. Comparison with Monte Carlo results is made.