We analyze the possible existence of topological phases in two-legged spin ladders considering a staggered interaction in both chains. When the staggered interaction in one chain is shifted by one site with respect to the other chain, the model can be mapped, in the continuum limit, into a non linear sigma model NL$σ$M plus a topological term which is nonvanishing when the number of legs is two. This implies the existence of a critical point which distinguishes two phases. We perform a numerical analysis of energy levels, parity and string non-local order parameters, correlation functions between $x,y,z$ components of spins at the edges of an open ladder, the degeneracy of the entanglement spectrum and the entanglement entropy in order to characterize these two different phases. Finally, we identify one phase with a Mott insulator and the other one with a Haldane insulator.
We demonstrate the existence of an insulating phase in the three-legged Hubbard ladder at two-thirds filling. In this phase chargons are bound because the physics within a unit cell favors the formation of triplets. The resultant moments lead to a ground state in the Haldane phase, a symmetry protected topological state of matter. In this purely fermionic model, reflection is protecting but time reversal and dihedral symmetries are not, in contrast to spin models.
We study two-leg spin ladder systems analytically by using a t-J model which includes the interchain spin exchange and the interchain hopping term. The spin part is mapped to a quantum sine-Gordon model via a bosonization method that fully accounts for the phase fluctuation. The spin gap in the Luther-Emery phase evolves to gapless Luttinger liquid phases in even-ladders at certain doping concentration. This transition occurs as doping rate increases and/or the ratio of the interchain spin exchange and hopping to the intrachain couplings decreases. We also estimate the transition temperature a…
We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices, with an arbitrary number of legs. The method can be used to calculate bipartite as well as multipartite physical properties, including bipartite and multi-partite entanglement. We apply this technique to distinguish between even- and odd-legged ladders. Specifically, we show that while genuine multi-partite entanglement decreases with increasing system size …
We derive a path-integral expression for the effective action in the continuum limit of an AFM Heisenberg spin ladder with an arbitrary number of legs. The map is onto an $O(3)$ nonlinear $σ$-model (NL$σ$M) with the addition of a topological term that is effective only for odd-legged ladders and half-odd integer spins. We derive the parameters of the effective NL$σ$M and the behaviour of the spin gap for the case of even-legged ladders.
We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of these states. The variational ground state shows a finite energy gap with respect to the energies of states which span the Hilbert space and are orthogonal to it. This is the case for any size of the system. Under some justifiable approximations the argument can be extended to even-legged ladder systems in 2d and higher dimensional spaces. The Hamiltonian c…
We investigate finite-size scaling of genuine multisite entanglement in the ground state of quantum spin-1/2 Heisenberg ladders. We obtain the ground states of odd- and even-legged Heisenberg ladder Hamiltonians and compute genuine multisite entanglement, the generalized geometric measure (GGM), which shows that for even rungs, GGM increases for odd-legged ladder while it decreases for even ones. Interestingly, the ground state obtained by short-range dimer coverings, under the resonating valence bond (RVB) ansatz, encapsulates the qualitative features of GGM for both the ladders. We find that…
Magnetic properties and excitation spectrum of the S = 1/2 three-legged spin ladder, LiMoOP2O7
Diamond Light Source（钻石光源）；University of Birmingham（伯明翰大学）；Science and Technology Facilities Council（科学与技术设施委员会）；Leipzig University（莱比锡大学）；Institut Laue-Langevin（朗之万研究所）；University College London（伦敦大学学院）；University of Stavanger（斯塔万格大学）
本研究通过实验与密度泛函理论计算，明确了 S = 1/2 三腿自旋梯 LiMoOP2O7 的磁性基态与磁激发，确定其长程磁有序特征及自旋哈密顿量的交换参数，为该体系的磁性研究提供了关键微观模型。
Using the Lanczos method we determine the phase diagram of the 2-leg AF-Heisenberg ladder with alternating dimerization. It consists of a resonating valence bond phase and a dimer phase separated by a critical line. Our results are in good agreement with previous conjectures obtained with the non linear sigma model.
An interesting aspect of antiferromagnetic quantum spin ladders, with complete dimer coverings, is that the wave function can be recursively generated by estimating the number of coverings in the valence bond basis, which follow the fabled Fibonacci sequence. In this work, we derive generalized forms of this sequence for multi-legged and doped quantum spin ladders, which allow the corresponding dimer-covered state to be recursively generated. We show that these sequences allow for estimation of physically and information-theoretically relevant quantities in large spin lattices without resortin…
In this work, we analyze the nonsymmorphic symmetry group structures for a variety of generalized Kitaev spin chains and ladders with bond alternations, including Kitaev-Gamma chain, Kitaev-Heisenberg-Gamma chain, beyond nearest neighbor interactions, and two-leg spin ladders. The symmetry analysis is applied to determine the symmetry breaking patterns of several magnetically ordered phases in the bond-alternating Kitaev-Gamma spin chains, as well as the dimerization order parameters for spontaneous dimerizations. Our work is useful in understanding the magnetic phases in related models and ma…
We generalize the nonlinear sigma model treatment of quantum spin chains to cases including ferromagnetic bonds. When these bonds are strong enough, the classical ground state is no longer the standard Neel order and we present an extension of the known formalism to deal with this situation. We study the alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The smooth crossover between decoupled dimers and the Haldane phase is semi-quantitatively reproduced. We study also a spin ladder with diagonal exchange couplings that interpolates between the gapped phase of the two-l…
We study numerically the formation of magnetization plateaux with the Lanczos method in 2-leg ladders with mixed spins of magnitudes $(S_1,S_2)=(1,1/2)$ located at alternating positions along the ladder and with dimerization $γ$. For interchain coupling $J'>0$ and $γ=0$, we find normalized plateaux at $m=1/3$ starting at zero field and $m=1$ (saturation), while when $γ\ne 0$ is columnar, another extra plateau at $m=2/3$ shows up. For $J'<0$, when $γ<γ_c(J')$ we find no plateau while for $γ>γ_c(J')$ we find four plateaux at $m=0,1/3,2/3,1$. We also apply several approximate analytical methods (…
We have studied the ground state phase diagram of a spin ladder with alternating rung exchange $J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]$ in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an $XXZ$ Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is $\sim δ$. We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as $δ^ν$, where $ν=4/5$ in the case of ladder …
Employing mainly numerical methods, we explore the ground-state phase diagram of an anisotropic $S=1/2$ ladder, in which leg interactions are uniform and isotropic, while rung interactions are alternating and have a common Ising-type anisotropy. We determine the phase diagram in the case where $J_{\rm leg}=0.2$ (antiferromagnetic), $J_{\rm rung}=-1.0$ (ferromagnetic) and $|J_{\rm rung}'|\!\leq\!1.0$, the first one being the magnitude of the leg interaction and the second and third ones those of the rung interactions, which are alternating. It is emphasized that the system has a frustration whe…
We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite, with a non-equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order, while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The Density Matrix Renormalization Group (DMRG) method is used to obtain the ground state properties, e.g. excitation gaps, charge and spin d…
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 traslational 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 defect…
We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-1/2 rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-like non-degenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-1/2 ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization…
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/2 ladder, and a two-legged spin-1/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-c…
We study low-energy magnetic excitations of doped spin-ladders, based on an effective Hamiltonian describing interactions of mobile spin and background spins. The helicity modulus against fluctuations in the ladder plane as well as out-of-the-plane are calculated in terms of the doping concentration, the leg number and interaction strengths in the ladder. The doping range for spiral phase is computed and its relation to spin gap structure is discussed. The spiral order can enhance existing antiferromagnetic order at certain doping or reduce it at very low density of holes. For odd-legged ladde…
The ground state property of the alternating spin ladder is studied in the case that the system involves an antiferromagnetic intra-chain interaction as well as two kinds of inter-chain interactions; one is between spins of the same magnitude and the other is between spins with different magnitudes. The calculation has been carried out by the exact diagonalization method. As a consequence of the competition among interactions, the system is revealed to show an interesting variety of phases in the ground state property. Its phase diagram is exhibited in the parameter space of the system. We fin…
We study two-legged spin-1 ladder systems with $D_2\times σ$ symmetry group, where $D_2$ is discrete spin rotational symmetry and $σ$ means interchain reflection symmetry. The system has one trivial phase and seven nontrivial symmetry protected topological (SPT) phases. We construct Hamiltonians to realize all of these SPT phases and study the phase transitions between them. Our numerical results indicate that there is no direct continuous transition between any two SPT phases we studied. We interpret our results via topological nonlinear sigma model effective field theory, and further conject…
We obtain the phase diagram in the parameter space $(J'/J, γ)$ and an accurate estimate of the critical line separating the different phases. We show several measuments of the magnetization, dimerization, nearest neighbours correlation, and density of energy in the different zones of the phase diagram, as well as a measurement of the string order parameter proposed as the non vanishing phase order parameter characterizing Haldane phases. All these results will be compared in the limit $J'/J\gg 1$ with the behaviour of the $\textbf{S}=1$ Bond Alternated Heisenberg Chain (BAHC). The analysis of …
We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z2 symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the pr…
We investigate low-energy properties of a generalized spin ladder model with both of the spin alternation and the bond alternation, which allows us to systematically study not only ladder systems but also alternating spin chains. By exploiting non-linear $σ$ model techniques we study the model with particular emphasis on the competition between gapful and gapless states. Our approach turns out to provide a more consistent semi-classical description of alternating spin chains than that in the previous work. We also study a closely related model, i.e., a spin chain with plaquette structure, and …
Singlet quantum phases and magnetization of the frustrated spin-1/2 ladder with ferromagnetic (F) exchange in legs and alternating F-AF exchange in rungs
A two-legged ladder model, one dimensional, exhibiting the parity anomaly is constructed. The model belongs to the $C$ and $CI$ symmetry classes, depending on the parameters, but, due to reflection, it exhibits topological insulation. The model consists of two superimposed Creutz models with onsite potentials. The topological invariants for both cases are {\it mirror winding numbers,} which are nonzero individually in the topological phase, but sum to zero overall in both phases. We demonstrate the presence of edge states and quantized Hall response in the topological region. Our model exhibit…
We present a manifestly rotational invariant formulation of the matrix product method valid for spin chains and ladders. We apply it to 2 legged spin ladders with spins 1/2, 1 and 3/2 and different magnetic structures labelled by the exchange coupling constants, which can be ferromagnetic or antiferromagnetic along the legs and the rungs of the ladder We compute ground state energy densities, correlation lengths and string order parameters. We present numerical evidence of the duality properties of the 3 different non ferromagnetic spin 1/2 ladders. We show that the long range topological orde…
Spin-1/2 two-legged ladders respecting inter-leg exchange symmetry and D2 spin rotation symmetry have new symmetry protected topological (SPT) phases which are different from the Haldane phase. Three of the new SPT phases are tx,ty,tz, which all have symmetry protected two-fold degenerate edge states on each end of the open boundaries. However, the edge states in different phases have different response to magnetic field. For example, the edge states in the tz phase will be split by the magnetic field along the z-direction, but not by the fields in the x- and y-directions. We give the Hamilton…
The paper presents a computational study of the ground-state properties of a quantum nanomagnet possessing the shape of a finite two-legged ladder composed of 12 spins $S=1/2$. The system is described with isotropic quantum Heisenberg model with nearest-neighbour interleg and intraleg interactions supplemented with diagonal interleg coupling between next nearest neighbours. All the couplings can take arbitrary values. The description of the ground state is based on the exact numerical diagonalization of the Hamiltonian. The ground-state phase diagram is constructed and analysed as a function o…
A two-parameter family of quantum spin ladders with local bilinear and biquadratic interactions is shown to be solvable by a mapping onto fragments of integrable spin 1 chains. The phase diagram, consisting of four phases, and the ground state properties are discussed. In one novel phase, the ground state is made up of plaquette singlets and rung singlets, alternating with a three-rung periodicity.
In this paper, we construct a class of spin-1/2 antiferromagnetic (AFM) two-chain ladder models consisting of blocks of n-spin tetrahedral clusters alternating with two-spin rungs. For n=4 and 6 and in extended parameter regimes, the exact ground state of the ladder is shown to be a product of the ground states of the rungs and the n-spin blocks, in both zero and finite magnetic fields. In the latter case, magnetization/site (m) versus magenetic field (h) plot exhibits well-defined magnetization plateaus.
We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.
We apply the twisted order parameter (TOP) for dimerized quantum spin ladders to locate the critical phases that separate gapped phases representing quantum spin liquids of various types. Using the DMRG, method we find that the TOP is a good order parameter for these systems regardless the number of legs. As a check, we reproduce with DMRG and periodic boundary conditions the computations previously done with Quantum Montecarlo for one-dimensional S=1/2, S=1, S=3/2 and S=2 Heisenberg chains with alternating bonds.
Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between anyons has been well studied. However, unlike our understanding of the role of bosonic and fermionic statistics in the formation of different quantum phases of matter, little is known concerning the effect of non-Abelian anyonic statistics. We explore this physics using an anyonic Hubbard model on a two-legged ladder which includes braiding and nearest neigh…
We show that in double-chain Mott insulators (ladders), disordered alternating ionic potentials may locally destroy coherence of magnetic excitations and lead to the appearance of spontaneously dimerized islands inside the Haldane spin-liquid phase. We argue that a boundary between the dimerized and Haldane phases of a spin-1/2 ladder supports a localized zero-energy Majorana fermion mode. Based on these findings we suggest a realization of a generalized Kitaev model where Majorana fermions can propagate in more than one dimension.
We study ground-state properties and the low-lying excitations of Heisenberg spin ladders composed of two ferrimagnetic chains with alternating site spins $(S_1>S_2)$ by using the bosonic Dyson-Maleev formalism and Lanczos numerical techniques. The emphasis is on properties of the ferrimagnetic phase which is stable for antiferromagnetic interchain couplings $J_{\perp}\geq 0$. There are two basic implications of the underlying lattice structure: (i) the spin-wave excitations form folded acoustic and optical branches in the extended Brillouin zone and (ii) the ground state parameters (such as t…
We apply the Lanczos method to a 2-leg ladder with mixed spins of magnitudes $(S_1,S_2)=(1,1/2)$ located at alternating positions along the ladder. The effect of dimerization $γ$ is also considered according to two different patterns. A Spin Wave Theory (SWT) is applied to this model predicting one gapless branch with ferromagnetic properties and another gapful branch with antiferromagnetic nature as low energy excitations of the model. We compute the ground state energies, Ferro- and AF-excitation gaps, magnetizations and correlation functions as a function of $J'$ and $γ$ which results into …
The formation of domains comprising alternating 'hole rich' and 'hole poor' ladders recently observed by Scanning Tunneling Microscopy by Kohsaka et al., on lightly hole doped cuprates, is interpreted in terms of an attractive mechanism which favors the presence of doped holes on Cu sites located each on one side of an oxygen atom. This mechanism leads to a geometrical pattern of alternating hole-rich and hole-poor ladders with a periodicity equal to 4 times the lattice spacing in the CuO plane, as observed experimentally. To cite this article: G. Deutscher, P.-G. de Gennes, C. R. Physique 8 (…
Employing a method of exact diagonalization for finite-size systems, we investigate the magnetization curve in the ground state of an antiferromagnetic spin-1/2 ladder with additional exchange interactions on diagonal bonds, which is equivalent to an antiferromagnetic spin-1/2 chain with bond-alternating nearest-neighbor and uniform next-nearest-neighbor interactions. It is found that a half-plateau appears in the magnetization curve in a certain range of the interaction constants. This result is discussed in connection with the necessary condition for the appearance of the plateau, recently g…
We use the variational matrix-product ansatz to study elementary excitations in the S=1/2 ladder with additional diagonal coupling, equivalent to a single S=1/2 chain with alternating exchange and next-nearest neighbor interaction. In absence of alternation the elementary excitation consists of two free S=1/2 particles ("spinons") which are solitons in the dimer order. When the nearest-neighbor exchange alternates, the "spinons" are confined into one S=1 excitation being a soliton in the generalized string order. Variational results are found to be in a qualitative agreement with the exact dia…
We have measured the specific heat of an S=1/2 antiferromagnetic alternating Heisenberg chain pentafulorophenyl nitronyl nitroxide under magnetic fields up to H>H_C2. This compound has the field-induced magnetic ordered (FIMO) phase between H_C1 and H_C2. Characteristic behaviors are observed depending on the magnetic field up to above H_C2 outside of the H-T boundary for the FIMO. Temperature and field dependence of the specific heat are qualitatively in good agreement with the theoretical calculation on an S=1/2 two-leg ladder. [Wang et al. Phys. Rev. Lett 84 5399 (2000)] This agreement sugg…
We perform a systematic investigation of an asymmetric zig-zag spin ladder with inter-leg exchange $J_1$ and different exchange integrals $J_2 \pm δ$ on both legs. In the weak limit of frustration, the spin model can be mapped to a revised double frequency Sine-Gorden model by using bosonization. Renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer liquid is realized. Fixing $J_2 = J_1 /2$, we find, as a function of…
It is shown, using asymptotically exact methods, that the two dimensional repulsive Hubbard model with strongly modulated interactions exhibits ``high temperature superconductivity". Specifically, the explicit modulation, which has the same symmetry as period 4 bond-centered stripes, breaks the system into an alternating array of more and less heavily hole doped, nearly decoupled two-leg ladders. It is shown that this system exhibits a pairing scale determined by the spin-gap of the undoped two-leg ladder, and a phase ordering temperature proportional to a low positive power of the inter-ladde…
The ground-state magnetic phase diagram of a spin $S=1/2$ two-leg ladder with alternating rung exchange $J_{\perp}(n)=J_{\perp}[1 + (-1)^{n} δ]$ is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We hav…
We present a microscopic model for alpha'-NaV2O5. Using an extended Hubbard model for the vanadium layers we derive an effective low-energy model consisting of pseudospin Ising chains and Heisenberg chains coupled to each other. We find a ``spin-Peierls-Ising'' phase transition which causes charge ordering on every second ladder and superexchange alternation on the other ladders. This transition can be identified with the first transition of the two closeby transitions observed in experiment. Due to charge ordering the effective coupling between the lattice and the superexchange is enhanced. T…
Magnetic excitations in an array of (VO)2P2O7 single crystals have been measured using inelastic neutron scattering. Until now, (VO)2P2O7 has been thought of as a two-leg antiferromagnetic Heisenberg spin ladder with chains running in the a-direction. The present results show unequivocally that (VO)2P2O7 is best described as an alternating spin-chain directed along the crystallographic b-direction. In addition to the expected magnon with magnetic zone-center energy gap DE = 3.1$ meV, a second excitation is observed at an energy just below 2DE. The higher mode may be a triplet two-magnon bound …
The mineral malachite, Cu2(OD)2CO3, has a quantum spin-liquid ground state and no long-range magnetic order down to at least T=0.4 K. Inelastic neutron scattering measurements show that the excitation spectrum consists of dispersive gapped singlet-triplet excitations, characteristic of spin-1/2 dimer-forming Heisenberg antiferromagnets. We identify a new two-dimensional dimerized coupling scheme with strong interdimer coupling J'/J1~0.3 that places malachite between strongly coupled alternating chains, square lattice antiferromagnets, and infinite-legged ladders. The geometry of the interactio…
Two-leg spin-$\frac12$ ladders with anisotropy and two different dimerization patterns are analyzed at zero temperature. This model is equivalent to a modulated interacting (Kitaev) ladder. The Hartree-Fock mean-field approximation reduces the model to a sum of two quadratic effective Majorana Hamiltonians, which are dual to a sum of two (even/odd) XY quantum chains in the alternating transverse fields. The mapping between the effective Hamiltonian of the ladder and the pair of the dual XY chains considerably simplifies calculations the order parameters and analysis of the hidden symmetry brea…
We study the ground-state magnetic phase diagram of a spin S=1/2 antiferromagnetic two-leg ladder in the presence of period two lattice units modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto the effective spin $σ=1/2$ XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes int…
The dynamical structure factor of the S=1/2 bond-alternating spin chain with a next-nearest-neighbor interaction in magnetic field is investigated using the continued fraction method based on the Lanczos algorithm. When the plateau exists on the magnetization curve, the longitudinal dynamical structure factor shows a large intensity with a periodic dispersion relation, while the transverse one shows a large intensity with an almost dispersionless mode. The periodicity and the amplitude of the dispersion relation in the longitudinal dynamical structure factor are sensitive to the coupling const…
Ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed to the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg-Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the 'classical' Ising chain in a longitudinal field or th…
We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated $J_1-J_2$ chain with alternating (1,1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase tra…
The interplay between Kondo effect, indirect magnetic interaction and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group (DMRG), the ground state and various short- and long-range spin- and density-correlation functions are calculated for the model at half-filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$ where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limi…
Experimental studies of magnetoresistance in thin superconducting strips subject to a perpendicular magnetic field B exhibit a multitude of transitions, from superconductor to insulator and vice versa alternately. Motivated by this observation, we study a theoretical model for the transport properties of a ladder--like superconducting device close to a superconductor--insulator transition. In this regime, strong quantum fluctuations dominate the dynamics of the vortex chain forming along the device. Utilizing a mapping of the vortex system at low energies to one-dimensional (1D) Fermions at a …
