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AIP Advances

A low-energy effective model for the S=1/2 Kagome-triangular-strip Heisenberg model

Kouichi Okunishi, Yoshitaka Onozato, Kouichi Seki

Published Aug 28, 2018• 0 citations
Publisher

Abstract

We study low-energy properties of the S=1/2 kagome-triangular-strip Heisenberg model. Using exact diagonalization, we calculate magnetization curves of the model in the ferromagnetic kagome coupling regime, where the singlet ground state and 1/3 plateau emerge. In order to analyze formation of the singlet ground state, we further derive a low-energy effective ladder model, focusing on the parity degrees of freedom for the two degenerating doublets of the unit triangle. We then discuss the entanglement between the spin and parity degrees of freedom.

DOI
10.1063/1.5042702

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We study low-energy properties of the S=1/2 kagome-triangular-strip Heisenberg model. Using exact diagonalization, we calculate magnetization curves of the model in the ferromagnetic kagome coupling regime, where the singlet ground state and 1/3 plateau emerge. In order to analyze formation of the singlet ground state, we further derive a low-energy effective ladder model, focusing on the parity degrees of freedom for the two degenerating doublets of the unit triangle. We then discuss the entanglement between the spin and parity degrees of freedom.
The Spin-1/2 Heisenberg Model (HM) is investigated using a block-spin renormalization approach on Kagome and triangular lattices. In both cases, after coarse graining the triangles on original lattice and truncation of the Hilbert space to the triangular ground state subspace, HM reduces to an effective model on a triangular lattice in terms of the triangular-block degrees of freedom i.e. the spin and the chirality quantum numbers. The chirality part of the effective Hamiltonian captures the essential difference between the two lattices. It is seen that simple eigenstates can be constructed for the effective model whose energies serve as upper bounds on the exact ground state energy of HM, and chiral-ordered variational states have high energies compared to the other variational states.
Using exact numerical diagonalizations as well as the semiclassical spin-wave approach, we study the quantum phase diagram of the spin-12 Heisenberg kagome strip, which is a particular cut-out from the kagome lattice. The unit cell contains five spins placed on the central cite and on the four end sites building two spin-12 along the strip. The model can be characterized by three different constants for the nearest-neighbor exchange bonds between (i) the central and chain spins (J1), (ii) the end spins in a cluster (J2 > 0), and (ii) the spins of neighboring clusters (J′2>0) In the present work we extend the previous studies of the model, which were restricted to antiferromagnetic J1 bonds (J1 > 0), by including the region with ferromagnetic J1 couplings (J1<0). It is demonstrated that for dominating ferromagnetic J1 couplings there is another gapless phase, which can be related to the critical ground state of the spin-52 Heisenberg chain. The phase boundaries separating the discussed critical phases, as well as the behavior of their low-lying excitations close to these boundaries, are examined as well.
The spin half Heisenberg antiferromagnet on the Kagome lattice, is mapped by Contractor Renormalization to a Spin-Pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low energy singlets observed numerically, and the non magnetic T-squared specific heat observed experimentally.
The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.
Derivation of a reduced effective model allows for a unified treatment and discussion of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{4pt}{0ex}}S=1/2$ Heisenberg model on triangular and kagome lattices. Calculating thermodynamic quantities, i.e., the entropy s(T)s(T)s(T) and uniform susceptibility ${\ensuremath{\chi}}_{0}(T)$, numerically on systems up to effectively N=42N=42N=42 sites, we show by comparing to full-model results that low-TTT properties are qualitatively well represented within the effective model. Moreover, we find in the spin-liquid regime similar variation of s(T)s(T)s(T) and ${\ensuremath{\chi}}_{0}(T)$ in both models down to $T\ensuremath{\ll}{J}_{1}$. In particular, studied spin liquids appear to be characterized by the Wilson ratio vanishing at low TTT, indicating that the low-lying singlets are dominating over the triplet excitations.
We investigate the quantum phases of a frustrated antiferromagnetic Heisenberg spin-1/2 model Hamiltonian on a kagom\'e-strip chain (KSC), a one-dimensional analog of the kagom\'e lattice, and construct its phase diagram in an extended exchange-parameter space. The isolated unit cell of this lattice comprises of five spin-1/2 particles, giving rise to several types of magnetic ground states in a unit cell: a spin-3/23/23/2 state as well as spin-1/21/21/2 states with and without additional degeneracies. We explore the ground-state properties of the fully connected thermodynamic system using exact diagonalization and density matrix renormalization group methods, identifying several distinct quantum phases. All but one of the phases exhibit gapless spin excitations. The exception is a dimerized spin-gapped phase that covers a large part of the phase diagram and includes the uniformly exchange coupled system. We argue that this phase can be understood by perturbing around the limit of decoupled unit cells where each unit cell has six degenerate ground states. We use degenerate perturbation theory to obtain an effective Hamiltonian, a Kugel-Khomskii model with an anisotropic spin-one orbital degree of freedom, which helps explain the origin of dimerization.