Bond-operator Mean-field Theory Research Articles

Dynamic Structure Factor of Disordered Quantum Spin Ladders.

We investigate the impact of quenched disorder on the zero-temperature dynamic structure factor of two-leg quantum spin ladders. Using linked-cluster expansions and bond-operator mean-field theory, huge effects on individual quasiparticles but also on composite bound states and two-quasiparticle continua are observed. This leads to intriguing quantum structures in dynamical correlation functions well observable in spectroscopic experiments.

Interlayer coupling effect on a bilayer Kitaev model

We investigate a bilayer Kitaev model, where two honeycomb layers are coupled by the Heisenberg interactions, to discuss effects of an interlayer coupling against the Kitaev quantum spin liquids (QSLs). In this model, there exists a local conserved quantity, which results in no long-range spin correlations in the system. Using the exact diagonalization, bond operator mean-field theory, and cluster expansion techniques, we study ground state properties in the system. The obtained results suggest the existence of a first-order quantum phase transition between the Kitaev QSL and singlet-dimer states. We find that one-triplet excitation from the singlet-dimer ground state is localized owing to the existence of the local conserved quantity. To examine finite-temperature properties, we make use of the thermal pure quantum state approach. We clarify that double-peak structure in the specific heat inherent in the Kitaev QSL is maintained even above the quantum phase transition. The present results suggest that the Kitaev QSL is stable against the interlayer interference. Magnetic properties of multilayer Kitaev models are also addressed.

Stripe phases in a frustrated spin-1/2 dimer Heisenberg model

We use a bond-operator mean-field theory and a generalized spin-wave theory to study the frustrated spin-1/2 dimer Heisenberg model on a square lattice with frustrations in both cardinal and corner directions. We establish the ground state phase diagram with very rich phases. It has been disclosed that the frustrations in cardinal directions can induce exotic superfluid (SF) and supersolid (SS) phases. By introducing the frustrations in corner directions, we found more interesting phases, such as the striped superfluid (S-SF) and the striped supersolid (S-SS). We also investigate the excitation spectra and analyze the anisotropic spin-wave velocities of the stripe phases.

Magnetic responses of randomly depleted spin ladders

The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work of Sigrist and Furusaki [J. Phys. Soc. Jpn. 65, 2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions are also analyzed. First, the magnetic profile around a single impurity and effective interactions between impurities are analyzed within the bond-operator mean-field theory and compared to density-matrix renormalization group calculations. Then, the temperature behavior of the Curie constant is studied in details. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattice and compute exactly the distribution of ladder cluster due to chain breaking effects. Using exact diagonalization and quantum Monte-Carlo methods on the effective model, the temperature dependence of the Curie constant is compared to a random dimer model and a real-space renormalization group scenario. Next, the low-part of the magnetic curve corresponding to the contribution of impurities is computed using exact diagonalization. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from the Brillouin response. At zero-temperature, the effective model prediction agrees relatively well with density-matrix renormalization group calculations. Finite-temperature effects are displayed within the effective model and for large depleted ladder models using quantum Monte-Carlo simulations. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly discussed.

Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-12deformed kagome lattice antiferromagnet

Motivated by the recent neutron-scattering experiment on Rb${}_{2}$Cu${}_{3}$SnF${}_{12}$ [Nature Phys. 6, 865 (2010)], we investigate the effect of Dzyaloshinskii-Moriya interactions in a theoretical model for the magnetic structure of this material. Considering the valence bond solid ground state, which has a 12-site unit cell, we develop the bond operator mean-field theory. It is shown that the Dzyaloshinskii-Moriya interactions significantly modify the triplon dispersions around the $\ensuremath{\Gamma}$ point and cause a shift of the spin-gap (the minimum triplon gap) position from the $K$ to $\ensuremath{\Gamma}$ point in the first Brillouin zone. The spin gap is also evaluated in exact diagonalization studies on a 24-site cluster. We discuss a magnetic transition induced by the Dzyaloshinskii-Moriya interactions in the bond operator framework. Moreover, the magnetization process under external magnetic fields is studied within the exact diagonalization approach. We find that the results of both approaches are consistent with the experimental findings.

Néel to dimer transition in spin-Santiferromagnets: Comparing bond operator theory with quantum Monte Carlo simulations for bilayer Heisenberg models

We study the N\'eel to dimer transition driven by interlayer exchange coupling in spin-S Heisenberg antiferromagnets on bilayer square and honeycomb lattices for S=1/2, 1, 3/2. Using exact stochastic series expansion quantum Monte Carlo (QMC) calculations, we find that the critical value of the interlayer coupling, J_{\perp c}[S], increases with increasing S, with clear evidence that the transition is in the O(3) universality class for all S. Using bond operator mean field theory restricted to singlet and triplet states, we find J_{\perp c}[S] ~ S(S+1), in qualitative accord with QMC, but the resulting J_{\perp c} [S] is significantly smaller than the QMC value. For S=1/2, incorporating triplet-triplet interactions within a variational approach yields a critical interlayer coupling which agrees well with QMC. For higher spin, we argue that it is crucial to account for the high energy quintet modes, and show that including these within a perturbative scheme leads to reasonable agreement with QMC results for S=1,3/2. We discuss the broad implications of our results for systems such as the triangular lattice S=1 dimer compound Ba_3Mn_2O_8 and the S=3/2 bilayer honeycomb material Bi_3Mn_4O_{12}(NO_{3}).

Quantum paramagnetic ground states on the honeycomb lattice and field-induced Néel order

Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), and a broader interest arising from numerical work on the honeycomb lattice Hubbard model, we have studied the effect of a magnetic field on honeycomb lattice spin models with quantum paramagnetic ground states. For a model with frustrating second-neighbor exchange, $J_2$, we use a Lindemann-like criterion within spin wave theory to show that N\'eel order melts beyond a critical $J_2$. The critical $J_2$ increases with a magnetic field, implying the existence of a field-induced paramagnet-N\'eel transition over a range of $J_2$. We also study bilayer model using a spin-$S$ generalization of bond operator mean field theory. We show that there is a N\'eel-dimer transition for various spin values with increasing bilayer coupling, and that the resulting interlayer dimer state undergoes a field induced transition into a state with transverse N\'eel order. Finally, we study a spin-3/2 model which interpolates between the Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki (AKLT) parent Hamiltonian. Using exact diagonalization, we compute the fidelity susceptibility to locate the Neel-AKLT quantum critical point, obtain the spin gap of the AKLT parent Hamiltonian, and argue that AKLT state also undergoes field-induced Neel ordering.

Bond operators and triplon analysis for spin-Sdimer antiferromagnets

The mean-field triplon analysis is developed for spin-S quantum antiferromagnets with dimerized ground states. For the spin-1/2 case, it reduces to the well known bond-operator mean-field theory. It is applied to a coupled-dimer model on square lattice, and to a model on honeycomb lattice with spontaneous dimerization in the ground state. Different phases in the ground state are investigated as a function of spin. It is found that under suitable conditions (such as strong frustration) a quantum ground state (dimerized singlet phase in the present study) can survive even in the limit $S\rightarrow \infty$. Two quick extensions of this representation are also presented. In one case, it is extended to include the quintet states. In another, a similar representation is worked out on a square plaquette. A convenient procedure for evaluating the total-spin eigenstates for a pair of quantum spins is presented in the appendix.

Phase transition of spin–orbital models with a four-spin ring exchange

We extend the bond-operator mean-field theory to study the rung singlet phase and its phase boundary, the triplet excitation, and the spin gap of the spin–orbital models with four-spin exchanges. The theory gives a well description of the rung singlet phase and phase boundaries in two-dimensional (2D) and three-dimensional (3D) cases are predicted. It is shown that consideration of the ring exchange suppresses the excitation spectrum and decreases the spin gap. For 2D and 3D spin–orbital models, positive ring and leg coupling tend to collaborate with each other to break the rung singlet phase. On the boundary line J l e g = J r i n g < J r u n g / 4 , the rung singlet density is one and a second-order phase transition occurs.

Fermionic representation of a symmetrically frustrated SU(3) model: Application to the Haldane-gap antiferromagnets

The one-dimensional spin 1 bilinear–biquadratic model is re-expressed in a symmetrically frustrated SU(3) model, which facilitates us to introduce a fermionic representation and related bond-operator mean-field theory. By analyzing the gap and the static spin susceptibility, we shows that this treatment can easily capture the commensurate and incommensurate Haldane gap phases.

Valence bond solid phases on deformed kagome lattices: Application toRb2Cu3SnF12

Motivated by a recent experiment on ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$, where spin-1/2 ${\text{Cu}}^{2+}$ moments reside on the layers of kagome-like lattices, we investigate quantum ground states of the antiferromagnetic Heisenberg model on a series of deformed kagome lattices. The deformation is characterized by a weaker exchange coupling $\ensuremath{\alpha}J$ on certain lattice links appropriate for ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ with $\ensuremath{\alpha}=1$ corresponding to the ideal kagome lattice. In particular, we study possible valence bond solid phases using the perturbation theory around isolated dimer limits, dimer series expansion, and self-consistent bond operator mean-field theory. It is shown that the valence bond solid phase with a 36-site unit cell of the ideal kagome lattice is quite sensitive to a small lattice distortion as the kind discovered in ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$. As a result, we find that a more likely quantum ground state in ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ is the valence bond solid phase with a 12-site unit cell, where six dimers form a pinwheel structure, leading to strong modification of the elementary triplet and singlet excitation spectra in the deformed kagome lattices.

Spin triplet excitations for a valence bond solid on the kagome lattice

One of the most promising candidate ground states for the quantum antiferromagnetic Heisenberg model on the kagome lattice is the valence bond solid (VBS) with a 36-site unit cell. We present a theory of triplet excitation spectra about this ground state using bond operator formalism. In particular we obtain dispersions of all 18 triplet modes in the reduced Brillouin zone. In the bond operator mean-field theory, it is found that a large number of triplet modes are nondispersive. In particular, the lowest triplet excitation is nondispersive and degenerate with a dispersive mode at the zone center. Away from the zone center, the lowest triplet is separated from two other flat modes by a small energy gap. Quantum fluctuations are considered by taking into account scattering processes of two triplets and their bound-state formation, which leads to a downward renormalization of the lowest spin triplet gap. The dispersion of the lowest triplet excitation in the VBS state is compared with the dispersive lower bound of the triplet continuum expected in competing spin liquid phases. Implications to future neutron-scattering experiments are discussed.

Fourfold degenerate columnar-dimer ground state in square lattice antiferromagnets

We construct and study the two frustrated quantum spin-$1∕2$ models on square lattice, which are like the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model with some additional four-spin exchange interactions. These models admit an exactly solvable case in which the ground state consists of four degenerate columnar-dimer singlet (CDS) configurations. Away from the exact case, we employ bond-operator mean-field theory to investigate the evolution of the ground state by varying the interaction parameters. The mean-field calculation reveals a quantum phase diagram in which the CDS phase undergoes a continuous phase transition to either N\'eel or collinear ordered antiferromagnetic phases.

SU(3) bosons and the spin nematic state on the spin-1 bilinear-biquadratic triangular lattice

A bond-operator mean-field theory in the SU(3) bosons representation is developed to describe the antiferronematic phase of the spin-1 bilinear-biquadratic model. The quadruplar order of this phase is delicately shown by the calculated static structure factors. The result shows the quadruple operators may be divided into two nonequivalent types. The type exhibiting both the ferroquadruple and antiferroquadruplar long-range orders is reminiscent of the ferrimagnets or the canted antiferromagnets. To address the possible relevance of this unconventional state to the quasi-two-dimensional triangular material $\mathrm{Ni}{\mathrm{Ga}}_{2}{\mathrm{S}}_{4}$, we calculated the quasiparticle density of states, the specific heat, and the uniform magnetic susceptibility. We discussed the coincidences and discrepancies between our results and others.

Numerical study of magnetic field induced ordering inBaCuSi2O6and related systems

Thermodynamics of spin dimer system $\mathrm{Ba}\mathrm{Cu}{\mathrm{Si}}_{2}{\mathrm{O}}_{6}$ is studied using a quantum Monte Carlo calculation (QMC) and a bond-operator mean field theory. We propose that a new type of boson, which, rather than being hard core, allows up to two occupancies at each site, is responsible for the Bose-Einstein condensation of field induced ordering. Its superfluid density is identified as the square of the in-plane staggered magnetization ${m}_{xy}$ in the ordered phase. We also compare our QMC result of the spin Heisenberg model to those predicted by the mean field theory as well as by the simple hard-core boson model for both large and small intradimer coupling $J$. The asymmetry of the phase diagram of ${m}_{xy}(h)$ of small coupling $J$ in related systems such as $\mathrm{Ni}{\mathrm{Cl}}_{2}\text{\ensuremath{-}}4\mathrm{S}\mathrm{C}(\mathrm{N}{\mathrm{H}}_{2})$ is explained with our new boson operator.

Single-hole dynamics in the half-filled two-dimensional Kondo-Hubbard model

We consider the Kondo lattice model in two dimensions at half filling. In addition to the fermionic hopping integral $t$ and the superexchange coupling $J$ the role of a Coulomb repulsion $U$ in the conduction band is investigated. We find the model to display a magnetic order-disorder transition in the U-J plane with a critical value of J_c which is decreasing as a function of U. The single particle spectral function A(k,w) is computed across this transition. For all values of J > 0, and apart from shadow features present in the ordered state, A(k,w) remains insensitive to the magnetic phase transition with the first low-energy hole states residing at momenta k = (\pm \pi, \pm \pi). As J -> 0 the model maps onto the Hubbard Hamiltonian. Only in this limit, the low-energy spectral weight at k = (\pm \pi, \pm \pi) vanishes with first electron removal-states emerging at wave vectors on the magnetic Brillouin zone boundary. Thus, we conclude that (i) the local screening of impurity spins determines the low energy behavior of the spectral function and (ii) one cannot deform continuously the spectral function of the Mott-Hubbard insulator at J=0 to that of the Kondo insulator at J > J_c. Our results are based on both, T=0 Quantum Monte-Carlo simulations and a bond-operator mean-field theory.

Bond-operator mean-field theory of the half-filled Kondo lattice model

We present a bond-operator mean field theory for the Kondo lattice model at half filling in two (2D) and three (3D) dimensions. A continuous quantum phase transition from an antiferromagnetic to a spin-gapped singlet ground state is found at J/t=1.505 (1.833) in 2D (3D). Additionally we evaluate the quasiparticle dispersions as well as the staggered magnetic moment and provide a comparison with complementary numerical approaches.

Disordered Ground‐State Properties of the Double‐Layer Antiferromagnetic Quantum XXZ Model

The double-layer antiferromagnetic quantum XXZ model is studied by the bond-operator mean-field theory. The transverse and longitudinal modes in excited spectra, and the phase diagram for disorder-order phase transition about Δ and J/J⊥, which are the relative strength of spin anisotropy and the ratio of the intralayer coupling to the interlayer coupling, respectively, are obtained. It is found that the critical ratio of (J/J⊥) c is 0.174 for XY model (Δ = 0), and is 0.430 for isotropic model (Δ = 1). In the disordered phase and on the critical points, the excitation spectra are analyzed. The spin gap from the condensed spin singlets to the first excited states, the ground state energy and the spin wave velocities in the disordered state are calculated as functions of parameters Δ and J/J⊥.

Order-disorder transitions in bilayer Heisenberg models on the triangular lattice

The triangular-lattice bilayer Heisenberg model with antiferromagnetic interlayer coupling ${J}_{0}$ is studied using strong-coupling perturbation theory and bond-operator mean-field theory. It is found that the model with ferromagnetic intralayer coupling $J&lt;0$ undergoes a quantum order-disorder transition at a strong-${J}_{0}$ critical point ${J}_{0c}=\ensuremath{-}3.83J.$ While for the model with $J&gt;0,$ the transition point is very small, ${J}_{0c}=0.15J.$ The result implies that the single-layer triangular Heisenberg antiferromagnet only has small long-range order parameter (if ordered) so that it is very sensitive to the interlayer perturbation.

Bond-operator approach to the bilayer Heisenberg antiferromagnet

The bilayer spin-$1/2$ antiferromagnetic Heisenberg model is studied by the bond-operator mean-field theory and perturbation theory. From both methods, the zero-temperature quantum phase transition occurs at a critical ratio of ${(J}_{2}{/J}_{1}{)}_{c}\ensuremath{\approx}2.3,$ where ${J}_{1}$ and ${J}_{2}$ are the intralayer and interlayer coupling constants. Under the mean-field method, the obtained spin-wave mass, uniform susceptibility, and inverse correlation length at the critical point show good linear behavior versus temperature at low temperatures, in agreement with results of the nonlinear $\ensuremath{\sigma}$ model and quantum Monte Carlo simulations. On the other hand, the finite temperature perturbation theory gives a good description of the disordered phase in quite a large temperature range. The specific heat and uniform susceptibility exhibit broad maxima versus temperature, consistent with series expansion results.