In this paper, we carry out a new technique named projection ED and indicate that it is applicable to the frustrated models, e.g., XXZ spin-1/2 Heisenberg and spinless fermion t-V models, in the strong coupling limit with highly degenerate ground states in a general way. As an example, we deal with a spinless fermion t-V model on a triangular lattice and show the usefulness of the method.
We describe the four kinds of behavior found in two-dimensional isotropic quantum antiferromagnets. Two of them display long range order at T=0: the Néel state and the Valence Bond Crystal. The last two are Spin-Liquids. Properties of these different states are shortly described and open questions are underlined.
Exact diagonalizations indicate that the effective 1-dimensional behavior (sliding Luttinger liquid phase) of the frustrated spin-1/2 crossed chain model, predicted by Starykh, Singh and Levine [Phys. Rev. Lett. 88, 167203 (2002)], persists for a wide range of transverse couplings. The extension of the other phases (plaquette valence bond crystal and Néel long range order) is precised. No clear indication of a coexistence of these two phases is found, at variance with a suggestion of Sachdev and Park (cond-mat/0108214).
The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature o…
Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J1 and next nearest-neighbor exchange coupling J2 we investigate the magnetic susceptibility of two-dimensional J1-J2 Heisenberg models with arbitrary spin quantum number s. We use exact diagonalization and high-temperature expansion up to order 10 to analyze the influence of the frustration strength J2/J1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on th…
We investigate the ground-state magnetic order of the spin-1/2 J1-J2 Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange J2>0. We use the coupled-cluster method to high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N=40 sites in order to calculate the ground-state energy, the spin-spin correlation functions, and the magnetic order parameter. We find that the transition point at which the ferromagnetic ground state disappears is given by J2^{c1}=0.393|J1|…
The phase diagram of a spin-1/2 $J-J'-J_2$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the $J_1-J_2$ model on the square lattice with two different nearest-neighbor couplings $J,J'$ and may be also viewed as an array of coupled Heisenberg chains. The results suggest that the resonnating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for $J_2=0.5J' \ll J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energ…
Quantum phase transition at the saturation field is studied for a class of frustrated quantum antiferromagnets. The considered models include (i) the $J_1$-$J_2$ frustrated square-lattice antiferromagnet with $J_2={1/2}J_1$ and (ii) the nearest-neighbor Heisenberg antiferromagnet on a face centered cubic lattice. In the fully saturated phase the magnon spectra for the two models have lines of degenerate minima. Transition into partially magnetized state is treated via a mapping to a dilute gas of hard core bosons and by complementary spin-wave calculations. Momentum dependence of the exact fou…
We predict that an external field can induce a spin order in highly frustrated classical Heisenberg magnets. We find analytically stabilization of collinear states by thermal fluctuations at a one-third of the saturation field for kagome and garnet lattices and at a half of the saturation field for pyrochlore and frustrated square lattices. This effect is studied numerically for the frustrated square-lattice antiferromagnet by Monte Carlo simulations for classical spins and by exact diagonalization for $S=1/2$. The field induced collinear states have a spin gap and produce magnetization platea…
We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. In the doped case, we find that static holes polarize their vicinity by a localization of singlets in order to reduce the frustration. This polarization induces short range …
We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size perio…
Exact diagonalization is a powerful numerical technique to analyze static and dynamical quantities in quantum many-body lattice models. It provides unbiased information concerning quantum numbers, energies and wave-functions of the low-energy eigenstates for almost any kind of microscopic model. The information about energies and quantum numbers is particularly useful to detect possible spontaneous symmetry breaking at T=0. We review some of the advances in the field of frustrated quantum magnets which have been possible thanks to detailed symmetry analysis of exact diagonalizations spectra. N…
A two-leg spin-1/2 ladder with diagonal interactions is investigated numerically. We focus our attention on the possibility of columnar dimer phase, which was recently predicted based on a reformulated bosonization theory. By using density matrix renormalization group technique and exact diagonalization method, we calculate columnar dimer order parameter, spin correlation on a rung, string order parameters, and scaled excitation gaps. Carefully using various finite-size scaling techniques, our results show no support for the existence of columnar dimer phase in the spin ladder under considerat…
Using both exact diagonalizations and diagonalizations in a subset of short-range valence bond singlets, we address the nature of the groundstate of the Heisenberg spin-1/2 antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (J1-J2-J3 model). A detailed comparison of the two approaches reveals a region along the line (J2+J3)/J1=1/2, where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore a careful analysis of dimer-di…
The Jordan-Wigner transformation is applied to study the ground state properties and dimerization transition in the $J_1-J_2$ $XXZ$ chain. We consider different solutions of the mean-field approximation for the transformed Hamiltonian. Ground state energy and the static structure factor are compared with complementary exact diagonalization and good agreement is found near the limit of the Majumdar-Ghosh model. Furthermore, the ground state phase diagram is discussed within the mean-field theory. In particular, we show that an incommensurate ground state is absent for large $J_2$ in a fully sel…
Correlated electrons often crystalize to the Mott insulator usually with some magnetic orders, whereas the "quantum spin liquid" has been a long-sought issue. We report numerical evidences that a nonmagnetic insulating (NMI) phase gets stabilized near the Mott transition with remarkable properties: The 2D Mott insulators on geometrically frustrated lattices contain a phase with gapless spin excitations and degeneracy of the ground state in the whole Brillouin zone of the total momentum. It has an interpretation for an unexplored type of a quantum liquid. The present concept is useful in analyz…
High degeneracy in ground states leads to the generation of exotic zero-energy modes, a representative example of which is the formation of molecular spin liquid-like fluctuations in a frustrated magnet. Here we present single-crystal inelastic neutron scattering results for the frustrated magnet MgCr$_2$O$_4$, which show that a common set of finite-energy molecular spin excitation modes is sustained in both the liquid-like paramagnetic phase and a magnetically ordered phase with an extremely complex structure. Based on this finding, we propose the concept of high degeneracy in excited states,…
Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose-Hubbard-Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.
Ultrasound velocity measurements of the orbital-degenerate frustrated spinel MgV$_2$O$_4$ are performed in the high-purity single crystal which exhibits successive structural and antiferromagnetic phase transitions, and in the disorder-introduced single crystal which exhibits spin-glass-like behavior. The measurements reveal that two-types of unusual temperature dependence of the elastic moduli coexist in the cubic paramagnetic phase, which are resolved by magnetic-field and disorder sensitivities: huge Curie-type softening with decreasing temperature, and concave temperature dependence with a…
We study the occurrence of plateaux and jumps in the magnetization curves of a class of frustrated ladders for which the Hamiltonian can be written in terms of the total spin of a rung. We argue on the basis of exact diagonalization of finite clusters that the ground state energy as a function of magnetization can be obtained as the minimum - with Maxwell constructions if necessary - of the energies of a small set of spin chains with mixed spins. This allows us to predict with very elementary methods the existence of plateaux and jumps in the magnetization curves in a large parameter range, an…
We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional…
Ground state properties of the S=1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and DMRG method. It is known that this model has a magnetization plateau at 1/3 of the saturation magnetization M_s. On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if frustration is strong. This …
We re-visit the phase diagram of the frustrated spin-1/2 ladder with two competing inter-chain antiferromagnetic exchanges, rung coupling J_\perp and diagonal coupling J_\times. We suggest, based on the accurate renormalization group analysis of the low-energy Hamiltonian of the ladder, that marginal inter-chain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line J_\perp = 2J_\times. Following this insight we then suggest that changing these competing inter-chain exchanges from the p…
We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg spin ladders with a transverse Hamiltonian that can involve frustration. Due to the variational nature of the algorithm, the accuracy can be arbitrarily improved enlarging the basis of eigenstates of the density matrix defined in the transverse direction. We observe that the precision of the algorithm is directly correlated to the binding of the chains. We al…
Starting from the archetypical geometrically frustrated magnetic objects -- equilateral triangle and tetrahedron -- we consider an imaginary object: a multidimensional tetrahedron with spins $1/2$ in the each vertex and equal Heisenberg magnetic exchange along each edge. Many-particle case is obtained by setting dimensionality $d$ to high numbers, hence providing likely the most geometrically frustrated magnetic system ever possible. This problem has an exact solution for each $d$, obtained by simple student-level approach. As a result, this imaginary object clearly demonstrates at $d\to{}\inf…
We consider the spin-1/2 antiferromagnetic Heisenberg model on two one-dimensional frustrated lattices, double-tetrahedral chain and octahedral chain, with almost dispersionless (flat) lowest magnon band in a strong magnetic field. Using the localized magnons picture, we construct an effective description of the one-dimensional chains with triangle and square traps within the strong coupling approximation. We perform extensive exact diagonalization and density matrix renormalization group calculations to check the validity of the obtained effective Hamiltonians by comparison with the initial m…
We investigate the properties of S=1/2 Heisenberg clusters with random frustration using exact diagonalizations. This is a model for a quantum spin glass. We show that the average ground state spin is $S \propto \sqrt{N}$, where N is the number of sites. We also calculate the magnetic susceptibility and the spin stiffness and low-energy excitations, and discuss these in terms of a semiclassical picture.
The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.
We study the magnetization process of the $S=1/2$ antiferromagnetic spin ladder in the presence of the second and the third-neighbor couplings which lead to frustration with the typical nearest-neighbor coupling. We use degenerate perturbation theory and level spectroscopy analysis of the numerical diagonalization data of the Hamiltonian for finite systems. We find two kinds of plateaux at half the saturation moment in the magnetization curve. One is mainly due to the second-neighbor couplings and the other to the third-neighbor couplings. The mechanisms of these two plateaux are quite differe…
Using exact numerical diagonalization and the conformal field theory approach, we study the effect of magnetic frustrations due to diagonal exchange bonds in a system of two coupled mixed-spin $(1,{1/2})$ Heisenberg chains. It is established that relatively moderate frustrations are able to destroy the ferrimagnetic state and to stabilize the critical spin-liquid phase typical for half-integer-spin antiferromagnetic Heisenberg chains. Both phases are separated by a narrow but finite region occupied by a critical partially-polarized ferromagnetic phase.
We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest and next-nearest neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S_1 > S_2, using 1/S spin-wave expansions, density-matrix renormalization group, and exact- diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate- incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of…
The ground state of a spin-1/2 Heisenberg chain with both frustration and long-range interactions is studied using Lanczos exact diagonalization. The evolution of the well known dimerization transition of the system with short-range frustrated interactions (the J1-J2 chain) is investigated in the presence of additional unfrustrated interactions decaying with distance as 1/r^a. It is shown that the continuous (infinite-order) dimerization transition develops into a first-order transition between a long-range ordered antiferromagnetic state and a state with coexisting dimerization and critical s…
Highly frustrated lattices yield a completely flat lowest single-electron band. Remarkably, exact many-body ground states can be constructed for the repulsive Hubbard model and the t-J model by filling this flat band with localized electron states. This construction leads to a macroscopic ground-state degeneracy. We discuss how to compute these ground-state degeneracies for a certain class of models, including in particular the sawtooth chain. Furthermore, we discuss generic consequences for low-temperature thermodynamic properties, like the appearance of a low-temperature peak in the specific…
We report the results of magnetization and specific heat measurements of Ba$_2$CoTeO$_6$ composed of two subsystems A and B, which are magnetically described as an $S\,{=}\,1/2$ triangular-lattice Heisenberg-like antiferromagnet and a $J_1-J_2$ honeycomb-lattice Ising-like antiferromagnet, respectively. These two subsystems were found to be approximately decoupled. Ba$_2$CoTeO$_6$ undergoes magnetic phase transitions at $T_{\rm N1}\,{=}\,12.0$ K and $T_{\rm N2}\,{=}\,3.0$ K, which can be interpreted as the orderings of subsystems B and A, respectively. Subsystem A exhibits a magnetization plat…
We consider the antiferromagnetic spin-1/2 $XXZ$ Heisenberg model on a frustrated diamond-chain lattice in a $z$- or $x$-aligned external magnetic field. We use the strong-coupling approach to elaborate an effective description in the low-temperature strong-field regime. The obtained effective models are spin-1/2 $XY$ chains which are exactly solvable through the Jordan-Wigner fermionization. We perform exact-diagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spin-chain compound…
We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in s…
As a simple model for spin-Peierls systems we study a frustrated Heisenberg chain coupled to optical phonons. In view of the anorganic spin-Peierls compound CuGeO3 we consider two different mechanisms of spin-phonon coupling. Combining variational concepts in the adiabatic regime and perturbation theory in the anti-adiabatic regime we derive effective spin Hamiltonians which cover the dynamical effect of phonons in an approximate way. Ground-state phase diagrams of these models are determined, and the effect of frustration is discussed. Comparing the properties of the ground state and of low-l…
The ground state phase diagram of the frustrated ferromagnetic spin-1/2 chain is investigated using the exact diagonalization technique. It is shown that there is a jump in the spontaneous magnetization and the ground state of the system undergos to a phase transition from a ferromagnetic phase to a phase with dimer ordering between next-nearest-neighbor spins. Near the quantum transition point, the critical behavior of the ground state energy is analyzed numerically. Using a practical finite-size scaling approach, the critical exponent of the ground state energy is computed. Our numerical res…
In the present paper we study the phase diagram of the Heisenberg model on the honeycomb lattice with antiferromagnetic interactions up to third neighbors along the line $J_2=J_3$ that include the point $J_2=J_3=J_1/2$, corresponding to the highly frustrated point where the classical ground state has macroscopic degeneracy. Using the Linear Spin-Wave, Schwinger boson technique followed by a mean field decoupling and exact diagonalization for small systems we find an intermediate phase with a spin gap and short range Néel correlations in the strong quantum limit (S=1/2). All techniques provide …
We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices -- sawtooth chain and two kagomé chains -- with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of {\em exact many-electron} ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential $μ_0$. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as …
We investigate the nature of a $Z_2$-invariant XY ring-exchange interaction with a frustrated Ising coupling on the triangular lattice. In the limit of pure XY ring-exchange interaction, we show that the classical ground state is degenerate resulting from the $Z_2$-invariance of the Hamiltonian. Quantum fluctuations lift these classical degenerate ground states and produce an unusual state whose excitation spectrum exhibits a gapped maximum quadratic dispersion near ${\bf k}=0$ and vanishes at the midpoints of each side of the Brillouin zone. This result is in contrast to a gapless quadratic d…
We study the spin-1/2 Heisenberg antiferromagnet on a bilayer honeycomb lattice including interlayer frustration. Using a set of complementary approaches, namely Schwinger bosons, dimer series expansion, bond operators, and exact diagonalization, we map out the quantum phase diagram. Analyzing ground state energies and elementary excitation spectra, we find four distinct phases, corresponding to three collinear magnetic long range ordered states, and one quantum disordered interlayer dimer phase. We detail, that the latter phase is adiabatically connected to an "exact" singlet product ground s…
The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation a…
Charge ordering (CO) with long-periodicities in a geometrically frustrated system, theta-(BEDT-TTF)2X, is numerically studied. We consider interacting fermion models on the anisotropic triangular lattice: the extended Hubbard model and the spinless fermion model, taking account of the inter-site Coulomb interactions on not only the nearest neighbor (NN) but also the next nearest neighbor (NNN) bonds. By applying Lanczos exact diagonalization method, we find that long-period charge correlations become dominant when NNN terms are included, in the charge-frustrated region. The calculated optical …
We study the XXZ spin-one quantum magnet on the kagome lattice as an example where quantum fluctuations on highly degenerate classical ground states lead to various exotic quantum ground states. Previous studies have predicted several quantum phases, but different analytical approaches do not necessarily lead to the same physical picture. In this work, we use Quantum Monte Carlo computations to critically examine some of the predictions made in the string-net mean-field theory and the degenerate perturbation theory combined with duality analysis and effective field theory. It is found that the…
Charge dynamics in an interacting fermionic model on a geometrically frustrated lattice are examined. We analyze a spinless fermion model on a paired triangular lattice, an electronic model for layered iron oxides, in zero and finite temperatures by the exact diagonalization methods. We focus on the two charge ordered (CO) phases, termed CO_1/2 and CO_1/3, which, respectively, are realized by the inter-site Coulomb interaction and the quantum/thermal fluctuations. The optical spectra in CO_1/3 show multiple components and their low-energy weights are survived even below the ordering temperatur…
Systems of strongly correlated fermions on certain geometrically frustrated lattices at particular filling factors support excitations with fractional charges $\pm e/2$. We calculate quantum mechanical ground states, low--lying excitations and spectral functions of finite lattices by means of numerical diagonalization. The ground state of the most thoroughfully studied case, the criss-crossed checkerboard lattice, is degenerate and shows long--range order. Static fractional charges are confined by a weak linear force, most probably leading to bound states of large spatial extent. Consequently,…
Frustration refers to competition between different interactions that cannot be simultaneously satisfied, a familiar feature in many magnetic solids. Strong frustration results in highly degenerate ground states, and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism are characterizing the fluctuating spin-liquid regime and determining the mechanism of eventual order at lower temperature. Here, we study a model of a diamond lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration a massive ground state degenera…
Motivated by recent inelastic neutron scattering experiment we examine magnetic properties of LiV2O4. We consider a model which describes the half-filled localized A1g spins interacting via frustrated antiferromagnetic Heisenberg exchange and coupled by local Hund's interaction with the 1/8-filled itinerant Eg band, and study it within an exact diagonalization scheme. In the present study we limited the analysis to the case of the cluster of two isolated tetrahedrons. We obtained that both the ground state structure and low-lying excitations depend strongly on the value of the Hund's coupling …
Using the coupled-cluster method for infinite lattices and the exact diagonalization method for finite lattices, we study the influence of an exchange anisotropy Delta on the ground-state phase diagram of the spin-1/2 frustrated J1-J2 XXZ antiferromagnet on the square lattice. We find that increasing Delta>1 (i.e. an Ising type easy-axis anisotropy) as well as decreasing Delta<1 (i.e. an XY type easy-plane anisotropy) both lead to a monotonic shrinking of the parameter region of the magnetically disordered quantum phase. Finally, at Delta~1.9 this quantum phase disappears, whereas in pure XY l…
We present a brief overview on some of the most significant achievements obtained by means of NMR and muSR techniques in highly frustrated magnets. First the basic quantities measured by the two techniques will be presented and their connection to the microscopic static and dynamical spin susceptibility recalled. Then the main findings will be outlined, starting from the most simple frustrated units, the molecular nanomagnets, to artificially built frustrated systems as $^{3}$He on graphite, to magnets with a macroscopically degenerate ground-state as the ones on a pyrochlore or kagomé lattice…
We present a theoretical study of the magnetic phase diagram of the frustrated coupled ladder structure realized recently in several materials. This system displays a nondegenerate spin-gap state in the dimer limit and an infinitely degenerate spin-gap state in the regime of weakly-coupled zig-zag chains. Between these we demonstrate the existence of gapless, magnetically ordered regions whose order is antiferromagnetic close to the honeycomb lattice limit, and incommensurate along the chains when all three magnetic interactions compete.
We study the competition between antiferromagnetic order and valence bond solid formation in a two-dimensional frustrated spin-1/2 model. The J1-J2 model on the square lattice is further frustrated by introducing products of three-spin projectors which stabilize four dimer-product states as degenerate ground states. These four states are reminiscent of the dimerized singlet ground state of the Shastry-Sutherland model. Using exact diagonalizations, we study the evolution of the ground state by varying theratio of interactions. For a large range of parameters (J2 > 0.25J1), our model shows a di…
We investigate the transverse field Ising model on a diamond chain using series expansions about the high-field limit and exact diagonalizations. For the unfrustrated case we accurately determine the quantum critical point and its expected 2d Ising universality separating the polarized and the Z2 symmetry broken phase. In contrast, we find strong evidences for a disorder by disorder scenario for the fully-frustrated transverse field Ising model, i.e. except for the pure Ising model, having an extensive number of ground states, the system is always in a quantum disordered polarized phase. The l…
Motivated by the recent discovery of the spin tube [(CuCl$_2$tachH)$_3$Cl]Cl$_2$, we investigate the properties of a frustrated three-leg spin tube with antiferromagnetic intra-ring and inter-ring couplings. We pay special attention to the evolution of the properties from weak to strong inter-ring coupling and show on the basis of extensive density matrix renormalization group and exact diagonalization calculations that the system undergoes a first-order phase transition between a dimerized gapped phase at weak coupling that can be described by the usual spin-chirality model and a gapless crit…
We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with $t_{2g}^4$ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor "triplon" operators describing the transitions between spin-orbit entangled $J=0$ ionic ground state and excited $J=1$ levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find clos…
We have found the exact ground state for two frustrated quantum spin-1/2 models on a linear chain. The first model describes ferromagnet- antiferromagnet transition point. The singlet state at this point has double-spiral ordering. The second model is equivalent to special case of the spin-1/2 ladder. It has non-degenerate singlet ground state with exponentially decaying spin correlations and there is an energy gap. The exact ground state wave function of these models is presented in a special recurrent form and recurrence technics of expectation value calculations is developed.
Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu$_2$(BO$_3$)$_2$ show an almost complete destruction of the one-triplet excitation band at a temper…
