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arXiv:1806.06907 · Journal of Physics Condensed Matter

Heisenberg–Ising delta-chain with bond alternation

D V Dmitriev, V Ya Krivnov

Published Aug 20, 2018• 9 citations
arXivHTMLPDF

Abstract

The spin-[Formula: see text] delta-chain (sawtooth chain) with antiferromagnetic Heisenberg basal chain and Ising apical-basal interactions is studied. The basal-apical interactions involve the bond alternation. The limiting cases of the model include the symmetrical delta-chain and the antiferromagnetic chain in the staggered magnetic field. We study ground state properties of the model by the exact diagonalization and density matrix renormalization group methods. The ground state phase diagram as a function of the bond alternation consists of magnetic and various non-magnetic phases. All phases excluding the ferrimagnetic phase are gapped and an origin of the gaps is cleared.

DOI
10.1088/1361-648x/aadb72

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The spin-[Formula: see text] delta-chain (sawtooth chain) with antiferromagnetic Heisenberg basal chain and Ising apical-basal interactions is studied. The basal-apical interactions involve the bond alternation. The limiting cases of the model include the symmetrical delta-chain and the antiferromagnetic chain in the staggered magnetic field. We study ground state properties of the model by the exact diagonalization and density matrix renormalization group methods. The ground state phase diagram as a function of the bond alternation consists of magnetic and various non-magnetic phases. All phases excluding the ferrimagnetic phase are gapped and an origin of the gaps is cleared.
We consider analytically and numerically an anisotropic spin-[Formula: see text] delta-chain (sawtooth chain) in which exchange interactions between apical and basal spins are ferromagnetic and those between basal spins are antiferromagnetic. In the limit of strong anisotropy of exchange interactions this model can be considered as the Ising delta chain with macroscopic degenerate ground state perturbed by transverse quantum fluctuations. These perturbations lift the ground state degeneracy and the model reduces to the basal XXZ spin chain in the magnetic field induced by static apical spins. We show that the ground state of such a model is ferrimagnetic. The excitations of the model are formed by ferrimagnetic domains separated by domain walls with a finite energy. At low temperatures the system is effectively divided into two independent subsystems, the apical subsystem described by the Ising spin-[Formula: see text] chain and the basal subsystem described by the XXZ chain with infinite zz interactions.
Abstract We study the delta-chain with spin-1 on basal sites and spin- 1 2 on apical sites. The Heisenberg interaction between neighbor basal spins is antiferromagnetic (AF) and the interaction between basal and apical spins is ferromagnetic (F). We show that the magnetization curve of this model is the same as that of the spin- 1 2 kagome-like chain with competing Heisenberg interactions. The ground state phase diagram of the latter as a function of the ratio between the AF and F interaction, α, consists of the ferromagnetic, ferrimagnetic and singlet phases. We study the magnetic properties in each ground state phase and analyze the magnetization curves. We show that there are magnetization plateaus and jumps in definite regions of value α. We compare the magnetic properties of considered models with those of the spin- 1 2 delta chain.
The antiferromagnetic sawtooth chain is a prototypical example of a frustrated spin system with vertex-sharing triangles, giving rise to complex quantum states. Depending on the interaction parameters, this system has three phases, of which the gapless noncollinear phase (for strongly coupled basal spins and loosely attached apical spins) has received little theoretical attention so far. In this work, we comprehensively investigate the properties of the noncollinear phase using large-scale tensor network computations which exploit the full SU(2) symmetry of the underlying Heisenberg model. We study the ground state both for finite systems using the density-matrix renormalization group (DMRG) as well as for infinite chains via the variational uniform matrix-product state (VUMPS) formalism. Finite temperatures and correlation functions are tackled via imaginary or real time evolutions, which we implement using the time-dependent variational principle (TDVP). We find that the noncollinear phase is characterized by a low-momentum peak and a diffuse tail for the apex-apex correlations. Deep into the phase, the pattern sharpens into a peak indicating a 90 ∘ spiral. The apical spins are soft and highly susceptible to external perturbations; they give rise to a large number of gapless magnetic states that are polarized by weak fields and cause a long low-temperature tail in the specific heat. The dynamic spin-structure factor exhibits additive contributions from a two-spinon continuum (excitations of the basal chain) and a gapless peak at k = π / 2 (excitations of the apical spins). Small temperatures excite the gapless states and smear the spectral weight of the k = π / 2 peak out into a homogeneous flat-band structure. Our results are relevant, e.g., for the material atacamite Cu 2 Cl ( OH ) 3 in high magnetic fields.
The ground-state phase diagram of S=2S=2S=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-DDD, 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 presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
The successive phase transitions of the Heisenberg spin chain with bond alternation, H = ∑ i =1 L -1 [1-(-1) i δ] S i · S i +1 , for the spin S =3/2 case under the open boundary condition are investigated by the density-matrix renormalization-group method proposed by White. Besides the Heisenberg point, we find that another gapless point exists at δ c = 0.42 ±0.02. This result qualitatively supports the field-theoretical prediction by Affleck and Haldane. However, our estimation of δ c deviates from the field-theoretical prediction, δ c = 2/3. We also find a fourfold degeneracy of the ground state in the region 0 <δ< δ c in the thermodynamic limit. Our results show that the degeneracy is described by the edge excitations, which is essentially similar to the one in the S =1 case. We calculate the string correlation function and find that its behavior is consistent with the valence-bond-solid (VBS) picture.