For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S=1 and sigma=1/2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.
We discuss the transition strength between the disordered ground state and the basic low-lying triplet excitation for the Heisenberg chain with alternating exchange based on series expansions in the interdimer interaction up to tenth order. We demonstrate that the wave vector dependence of the simple dimer approximation is strongly modified in higher orders.
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.
We develop a low-temperature expansion for the finite temperature dynamical structure factor of the spin half Heisenberg chain with alternating nearest neighbour exchange in the limit of strong alternation of the exchange constants. We determine both the broadening of the low lying triplet lines and the contribution of the thermally activated intraband scattering.
We calculate dynamical structure factors of the S=1 bond-alternating Heisenberg chain with a single-ion anisotropy in transverse magnetic fields, using a continued fraction method based on the Lanczos algorithm. In the Haldane-gap phase and the dimer phase, dynamical structure factors show characteristic field dependence. Possible interpretations are discussed. The numerical results are in qualitative agreement with recent results for inelastic neutron-scattering experiments on the S=1 bond-alternating Heisenberg-chain compound $\rm{Ni(C_{9}D_{24}N_{4})(NO_{2})ClO_{4}}$ and the S=1 Haldane-gap…
An alternative triplet-wave expansion formalism for dimerized spin systems is presented, a modification of the 'bond operator' formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace, rather than constraint equations. The method is illustrated for the case of the alternating Heisenberg chain, and comparisons are made with the results of dimer series expansions and exact diagonalization. Some discussion is included of the phenomenon of 'quasiparticle breakdown', as it applies to the two-triplon bound states in this model.
The magnetic behaviors of a spin-1/2 alternating Heisenberg antiferromagnetic chain in a staggered transverse magnetic field is studied by means of the density-matrix renormalization group method and Jordan-Wigner transformation. Quantum phase transitions of different types are observed in the S=1 Neel and XY-like gapless phases, which result from the competitions between the staggered transverse field and magnetic orders induced by anisotropy and alternating interactions. The results are compared with the mean-field and some exactly resolved results.
The promotion of collinear classical spin configurations as well as the enhanced tendency towards nearest-neighbor clustering of the quantum spins are typical features of the frustrating isotropic three-body exchange interactions in Heisenberg spin systems. Based on numerical density-matrix renormalization group calculations, we demonstrate that these extra interactions in the Heisenberg chain constructed from alternating S=3/2 and sigma=1/2 site spins can generate numerous specific quantum spin states, including some partially-polarized ferrimagnetic states as well as a doubly-degenerate non-…
Dynamical structure factors of the S=1 bond-alternating spin chains in the dimer phase are calculated at finite temperature, using the pair dynamical correlated-effective-field approximation. At T=0, the delta-function-type peak of the one-magnon mode appears. When temperature is increased, such a sharp peak is broadened and the additional weak peak caused by the excitation from the triplet state to the quintet state emerges in the higher energy region. The results are discussed in comparison with those obtained by the exact diagonalization method.
We have studied the zero and low-temperature behavior of anisotropic alternating antiferromagnetic-ferromagnetic Heisenberg spin-1/2 chains in a transverse magnetic field. Using the analytical spinless fermion approach, the thermodynamic behavior of the model has been studied. We have introduced a new order parameter to distinguish the gapless Luttinger liquid phase from the other gapped phases. The exact diagonalization Lanczos results are also used to compare with the spinless fermion ones. We have found a double peak structure in the specific heat curves for the region between the two quant…
We present a study of the spin-1/2 Heisenberg chain with alternating ferro- and antiferromagnetic exchange, focusing on the role of the exchange couplings to cover both, dimer and Haldane limit. Employing a complementary combination of perturbation theory and quantum Monte Carlo simulation, we report results for the magnetic susceptibility as well as the dynamic structure factor over a wide range of coupling constants and for different temperatures to extract the spin gap. For a small ferromagnetic coupling, we find good agreement between perturbation theory and quantum Monte Carlo. For arbitr…
The ground state phase diagram of the alternating spin-1/2 chains with anisotropic ferromagnetic coupling under the influence of a symmetry breaking transverse magnetic field is studied. We have used the exact diagonalization technique. In the limit where the antiferromagnetic coupling is dominant, we have identified two Ising-type quantum phase transitions. We have calculated two critical fields $h_{c_{1}}$ and $h_{c_{2}}$, corresponding to the transition between different magnetic phases of the system. It is found that the intermediate state ($h_{c_{1}}<h<h_{c_{2}}$) is gapful, describing th…
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…
Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and s…
We study different phases of the one-dimensional bond-alternating spin-$1/2$ Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on …
In this paper, equations describing one-dimensional Non-Heisenberg model are studied by use of generalized coherent states in real parameterization and then dissipative spin wave equation for dipole and quadrupole branches is obtained if there is a small linear excitation from the ground state. Finally, it is shown that for such exchange-isotropy Hamiltonians, optical branch of spin wave is non-dissipative.
We present results for the dynamic structure factor of the S=1/2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $λ\approx 0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spi…
The fidelity and entanglement entropy in an antiferromagnetic-ferromagnetic alternating Heisenberg chain are investigated by using the method of density-matrix renormalization-group. The effect of anisotropy on fidelity and entanglement entropy are investigated. The relations between fidelity, entanglement entropy and quantum phase transition are analyzed. It is found that the quantum phase transition point can be well characterized by both the ground-state entropy and fidelity for large system.
The effect of the canting of local anisotropy axes on the ground-state phase diagram and magnetization of a ferrimagnetic chain with regularly alternating Ising and Heisenberg spins is exactly examined in an arbitrarily oriented magnetic field. It is shown that individual contributions of Ising and Heisenberg spins to the total magnetization basically depend on the spatial orientation of the magnetic field and the canting angle between two different local anisotropy axes of the Ising spins.
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 …
The ground state phase diagrams and thermodynamic properties of a spin-1 bond-alternating Heisenberg antiferromagnetic chain with a single-ion anisotropy in longitudinal and transverse magnetic fields are investigated jointly by means of the infinite time evolving block decimation, the linearized tensor renormalization group and the density matrix renormalization group methods. It is found that in the magnetic field-bond alternating ratio plane six phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2 magnetization plateau and spin polarized phases are identified in a longi…
A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the $Δ$-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and triv…
We have reanalyzed the microscopic origin of the isotropic deviations that are observed from the energy spacings predicted by the HDVV Hamiltonian. Usually, a biquadratic spin operator is added to the HDVV Hamiltonian to account for such deviations. It is shown here that this operator cannot describe the effect of the excited atomic non-Hund states which brought the most important contribution to the deviations. For systems containing more than two magnetic centers, non-Hund states cause additional interactions that are of the same order of magnitude as the biquadratic exchange and should have…
The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82, 064703 (2013) is confirmed using two kinds of entanglement spectra defined by different divisions of the whole chain. For the numerical calculation, the iDMRG method is used. The results are consistent with the valence bond solid picture proposed in the previous paper.
By using the coupled cluster method, the numerical exact diagonalization method, and the numerical density matrix renormalization group method, we investigated the properties of the one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions. In the classical limit, the ground state is in the collinear Neel state if a<1/2, while for a>1/2, there is an noncollinear canted state. For the quantum case, we found that, although the classical Neel state is absent, the canted state exists if the frustration parameter a exceeds a critical po…
Motivated by a novel bimetallic chain compound in which alternating magnetic centers are ferromagnetically coupled, we investigate thermodynamic properties of one-dimensional spin-$(S,s)$ Heisenberg ferromagnets both numerically and analytically. On the one hand, quantum Monte Carlo calculations illuminate the overall thermal behavior. The specific heat may exhibit a double-peaked structure at intermediate temperatures for $S\agt 3s$ in general. On the other hand, a modified spin-wave theory precisely describes the low-temperature properties. Expanding the specific heat and the magnetic suscep…
We make a matrix-product variational approach to spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chains with anisotropy on their ferromagnetic bonds, especially under the open boundary condition. The rich phase diagram containing the Haldane, large-D, and two types of Neel phases is well reproduced with only two variational parameters. The on-bond anisotropy has a significant effect on the ferromagnetic coupling between neighboring spins and induces novel edge states peculiar to spin-1/2 chains.
The low temperature magnetization process of the ferromagnetic-antiferromagnetic Heisenberg chain is studied using the interacting boson approximation. In the low field regime and near the saturation field, the spin wave excitations are approximated by the $δ$ function boson gas for which the Bethe ansatz solution is available. The finite temperature properties are calculated by solving the integral equation numerically. The comparison is made with Monte Carlo calculation and the limit of the applicability of the present approximation is discussed.
We successfully synthesized the zinc-verdazyl complex [Zn(hfac)$_2$]$\cdot$($o$-Py-V) [hfac = 1,1,1,5,5,5-hexafluoroacetylacetonate; $o$-Py-V = 3-(2-pyridyl)-1,5-diphenylverdazyl], which is an ideal model compound with an $S$ = 1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain (F-AF AHC). $Ab$ $initio$ molecular orbital (MO) calculations indicate that two dominant interactions $J_{\rm{F}}$ and $J_{\rm{AF}}$ form the $S=1/2$ F-AF AHC in this compound. The magnetic susceptibility and magnetic specific heat of the compound exhibit thermally activated behavior below approximately 1 …
The spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with ferromagnetic next-nearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact soluti…
$S=3/2$ system with general isotropic nearest-neighbor exchange within a mean-field approximation possesses a magnetically ordered ferromagnetic state and antiferromagnetic state, and two different spin nematic states, with zero spin expectation values. Both spin nematic phases display complicated symmetry break, including standard rotational break described by the vector-director $\vec {u}$ and specific symmetry break with respect to the time reversal. The break of time reversal is determined by non-trivial quantum averages cubic over the spin components and can be described by unit "pseudosp…
The mixture of bond-alternating and uniform S=1/2 antiferromagnetic Heisenberg chains is investigated by the density matrix renormalization group method. The ground state magnetization curve is calculated and the exchange parameters are determined by fitting to the experimentally measured magnetization curve of \CuCl$_{2x}$Br$_{2(1-x)}$($γ$-pic)$_2$. The low field behavior of the magnetization curve and low temperature behavior of the magnetic susceptibility are found to be sensitive to whether the bond-alternation pattern (parity) is fixed all over the sample or randomly distributed. The both…
Quantum phase transitions (QPTs) and the ground-state phase diagram of the spin-1/2 Heisenberg-Ising alternating chain (HIAC) with uniform Dzyaloshinskii-Moriya (DM) interaction are investigated by a matrix-product-state (MPS) method. By calculating the odd- and even-string order parameters, we recognize two kinds of Haldane phases, i.e., the odd- and even-Haldane phases. Furthermore, doubly degenerate entanglement spectra on odd and even bonds are observed in odd- and even-Haldane phases, respectively. A rich phase diagram including four different phases, i.e., an antiferromagnetic (AF), AF s…
The $J_1-J_3$ Heisenberg spin models with nearest-neighbor ($J_1$) and additional isotropic three-site ($J_3$) spin interactions remain relatively less explored, although such types of competing exchange terms can naturally emerge from different sources, including the strong-coupling expansion of the multiorbital Hubbard model. Below we present a short survey of the recently published research in this field, the emphasis being on the characteristics of the variety of quantum phases supported by a few generic uniform- and alternating-spin $J_1-J_3$ Heisenberg chains. For the reason that the pos…
Magnetization transport in a one-dimensional isotropic spin 1/2 Heisenberg model is studied. It is shown that in a nonequilibrium steady state at high temperature and constant small driving the magnetization current depends on the system length L as 1/L^{0.5}, meaning that the diffusion constant diverges as L^{0.5}. Spectral properties of a superoperator governing the relaxation towards a nonequilibrium steady state are also discussed.
We investigate string correlations in an infinite-size spin-1/2 bond-alternating Heisenberg chain. By employing the infinite matrix product state representation with the infinite time evolving block decimation method, a finite string correlation for extremely large lattice distances is directly observed, contrast to an extrapolated extreme value for finite size chains. We find that a topological quantum phase transition occurs between two different phases separated and characterized by two different long-range string orders in the space of bond-alternating interactions. Also, the critical expo…
We consider a mechanism for competing interactions in alternating Heisenberg spin chains due to the formation of local spin-singlet pairs. The competition of spin-1 and spin-0 states reveals hidden Ising symmetry of such alternating chains.
The ground-state phase diagram of $S=2$ antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-$D$, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the p…
We derive an effective spin Hamiltonian for the one-dimensional half-filled Alternating Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian is a spin $S=1/2$ Heisenberg chain with asymmetric next-nearest-neighbor (nnn) exchange.
The bulk properties and impurity effect in the one-dimensional S=1/2 Heisenberg model with dimerization and next-nearest-neighbor exchange are studied by the density matrix renormalization group (DMRG) and exact diagonalization methods. This model widely covers the S=1 Heisenberg model, two-leg ladders, bond-alternating chains and the S=1/2 Heisenberg model. Almost the whole parameter space belongs to the Haldane phase. In the non-dimerizing limit a transition to a kind of spin liquid takes place, characterized by the delocalized spin polarization. This transition causes the distinct impurity …
Composing higher auxiliary-spin transfer matrices and their derivatives, we construct a family of quasilocal conserved operators of isotropic Heisenberg spin 1/2 chain and rigorously establish their linear independence from the well-known set of local conserved charges.
The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim in describing available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave t…
We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from a given set of excited states. A linked cluster technique to obtain high order series expansions for these quantities is discussed. We apply these methods to the alternating Heisenberg chain around the dimerized limit ($λ=0$), where complete wavevector and frequency dependent spectral weights for one and two-particle excitations (continuum and bound-states)…
A classical-quantum chain composed of regularly alternating Ising and Heisenberg spins is rigorously solved by considering two distinct local anisotropy axes of the Ising spins. The ground-state phase diagram and magnetization curves are examined depending on a spatial orientation of the applied magnetic field. The phase diagram totally consists of four distinct phases and a few macroscopically degenerate points, where an outstanding coexistence of perfect order and complete disorder occurs within the so-called 'half-fire, half-ice' state. The zero-temperature magnetization curves generally ex…
We use recently developed strong-coupling expansion methods to study the two-particle spectra for the frustrated alternating Heisenberg model, consisting of an alternating nearest neighbor antiferromagnetic exchange and a uniform second neighbor antiferromagnetic exchange. Starting from the limit of weakly coupled dimers, we develop high order series expansions for the effective Hamiltonian in the two-particle subspace. In the limit of a strong applied dimerization, we calculate accurately various properties of singlet and triplet bound states and quintet antibound states. We also develop seri…
We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin $S=1/2$ anisotropic $XXZ$ Heisenberg chain with alternating next-nearest-neighbor and three-spin couplings in the presence of a uniform and a staggered magnetic field.
The ferrimagnetic spin-1/2 chain composed of alternating Ising and Heisenberg spins in an arbitrarily oriented magnetic field is exactly solved using the spin-rotation transformation and the transfer-matrix method. It is shown that the low-temperature magnetization process depends basically on a spatial orientation of the magnetic field. A sharp stepwise magnetization curve with a marked intermediate plateau, which emerges for the magnetic field applied along the easy-axis direction of the Ising spins, becomes smoother and the intermediate plateau shrinks if the external field is tilted from t…
Typically two particles (spins) could be maximally entangled at zero temperature, and for a certain temperature the phenomenon of entanglement vanishes at the threshold temperature. For the Heisenberg coupled model or even the Ising model with a transverse magnetic field, one can observe some rise of entanglement even for a disentangled region at zero temperature. So we can understand this emergence of entanglement at finite temperature as being due to the mixing of some maximally entangled states with some other untangled states. Here, we present a simple one-dimensional Ising model with alte…
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo si…
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is present due to the non-zero $J_2^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. For fixed $J_1^F$, the phase diagram in the space of $J_1^A-J_2^F$ is determin…
We use non-perturbative linked-cluster expansions to determine the ground-state energy per site of the spin-one Heisenberg model on the kagome lattice. To this end, a parameter is introduced allowing to interpolate between a fully trimerized state and the isotropic model. The ground-state energy per site of the full graph decomposition up to graphs of six triangles (18 spins) displays a complex behaviour as a function of this parameter close to the isotropic model which we attribute to divergencies of partial series in the graph expansion of quasi-1d unfrustrated chain graphs. More concretely,…
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 betw…
In the preprint cond-mat/0701060 we detected a factor two error in the coding of the Heisenberg term of the Hamiltonian. In the result the exchange term used in the paper was that of an anisotropic Heisenberg model with $J_x=J_y=J$ and $J_z=J/2$. Thus all results given for which J=0 was chosen, remain unchanged, whereas all results containing the exchange parameter remain true for the extended Hubbard model with anisotropic exchange. That model is of some interest by itself, due to the relation to the XXZ model. The differing results for isotropic exchange are given here.
We describe a method for calculating dynamical spin-spin correlation functions in the finite isotropic and anisotropic antiferromagnetic Heisenberg models. Our method is able to produce results with high accuracy over the full parameter space.
The one dimensional S=1/2 Heisenberg model with dimerization and quadrumerization is studied by means of the numerical exact diagonalization of finite size systems. Using the phenomenological renormalization group and finite size scaling law, the ground state phase diagram is obtained in the isotropic case. It exhibits a variety of the ground states which contains the S=1 Haldane state, S=1 dimer state and S=1/2 dimer state as limiting cases. The gap exponent $ν$ is also calculated which coincides with the value for the dimerization transition of the isotropic Heisenberg chain. In the XY limit…
The spin transport in isotropic Heisenberg model in the sector with zero magnetization is generically super-diffusive. Despite that, we here demonstrate that for a specific set of domain-wall-like initial product states it can instead be diffusive. We theoretically explain the time evolution of such states by showing that in the limiting regime of weak spatial modulation they are approximately product states for very long times, and demonstrate that even in the case of larger spatial modulation the bipartite entanglement entropy grows only logarithmically in time. In the limiting regime we der…
The effects of a magnetic field ($h$) and a space modulation ($δ$) on the magnetic properties of a one dimensional antiferromagnetic-ferromagnetic Heisenberg spin-1/2 model have been studied by means of numerical exact diagonalization of finite size systems, nonlinear sigma model and bosonization approach. The space modulation is considered on the antiferromagnetic couplings. At $δ=0$, the model is mapped to a gapless Lüttinger liquid phase by increasing the magnetic field. However, the space modulation induces a new gap in the spectrum of the system and the system experiences different quantu…
I use an improved version of the two-step density matrix renormalization group method to study ground-state properties of the 2D Heisenberg model on the checkerboard lattice. In this version the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as $J_2$ increases are: (i) Néel with $Q=(π,π)$, (ii) a valence bond crystal (VBC) of plaquettes, (iii) Néel with $Q=(π/2,π)$, and …
