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arXiv:cond-mat/9508121 · Physical review. B, Condensed matter

Quantum solitons in the sawtooth lattice

Diptiman Sen, B. Sriram Shastry, Russel E. Walstedt, R. J. Cava

Published Mar 1, 1996• 107 citations
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Abstract

We study the sawtooth lattice of a coupled spin 1/2 Heisenberg system, a variant of the railroad-trestle lattice. The ground state of this system is twofold degenerate with periodic boundary conditions and supports kink-antikink excitations, which are distinct in this case, unlike the railroad-trestle lattice. The resulting low-temperature thermodynamics is compared with the recently discovered delafossites ${\mathrm{YCuO}}_{2.5}$. \textcopyright{} 1996 the American Physical Society.

DOI
10.1103/physrevb.53.6401

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We study the sawtooth lattice of a coupled spin 1/2 Heisenberg system, a variant of the railroad-trestle lattice. The ground state of this system is twofold degenerate with periodic boundary conditions and supports kink-antikink excitations, which are distinct in this case, unlike the railroad-trestle lattice. The resulting low-temperature thermodynamics is compared with the recently discovered delafossites YCuO2.5{\mathrm{YCuO}}_{2.5}YCuO2.5​. \textcopyright{} 1996 the American Physical Society.
Using an approximation method for eigenvalue distribution functions, we study the temperature dependence of specific heat of the antiferromagnetic Heisenberg model on the asymmetric railroad-trestle lattice. This model contains both the sawtooth-lattice and Majumdar-Ghosh models as special cases. Making extrapolations to the thermodynamic limit using finite size data up to 28 spins, it is found that specific heat of the Majumdar-Ghosh model has a two-peak structure in its temperature dependence and those of systems near the sawtooth-lattice point have a three-peak structure.
Abstract We consider the strongly anisotropic spin-1/2 XXZ model on the sawtooth-chain lattice with ferromagnetic longitudinal interaction Jzz = ΔJ and aniferromagnetic transversal interaction Jxx = Jyy = J > 0. At Δ = −1∕2 the lowest one-magnon excitation band is dispersionless (flat) leading to a massively degenerate set of ground states. Interestingly, this model admits a three-coloring representation of the ground-state manifold [H.J. Changlani et al., Phys. Rev. Lett. 120, 117202 (2018)]. We characterize this ground-state manifold and elaborate the low-temperature thermodynamics of the system. We illustrate the manifestation of the flat-band physics of the anisotropic model by comparison with two isotropic flat-band Heisenberg sawtooth chains. Our analytical consideration is complemented by exact diagonalization and finite-temperature Lanczos method calculations. Graphical abstract
We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain relation of the exchange (hopping) integrals. Although these eigenstates differ in details for the two models because of the different statistics, they share some characteristic features. The localized eigenstates are highly degenerate and become ground states in high magnetic fields (Heisenberg model) or at certain electron fillings (Hubbard model), respectively. They may dominate the low-temperature thermodynamics and lead to an extra low-temperature maximum in the specific heat. The ground-state degeneracy can be calculated exactly by a mapping of the manifold of localized ground states onto a classical hard-dimer problem, and explicit expressions for thermodynamic quantities can be derived which are valid at low temperatures near the saturation field for the Heisenberg model or around a certain value of the chemical potential for the Hubbard model, respectively.
We study the ground-state properties and dynamical response of the Heisenberg model on the sawtooth chain in and away from the exactly solvable valence-bond-solid (VBS) point. We employ U(1)-symmetric density-matrix renormalization group (DMRG) and time-dependent variational principle (TDVP) methods to compute equilibrium diagnostics and the zero-temperature dynamical structure factor (DSF) Szz(q,ω)S^{zz}(q,ω)Szz(q,ω) across the dimerized phase, a valence-bond-ordered state in which the two symmetry-equivalent apex--base bonds of each triangle develop unequal spin correlations, probing the approach to the continuous lower phase boundary, the exact VBS point, and the approach to the first-order upper boundary. In every regime, the DSF is a broad continuum dominated by a bright band at its lower edge, with the intensity at the one-triplon energy ω≃JABω\simeq J_{AB}ω≃JAB​ suppressed. We identify the spectrum as a deconfined two-spinon continuum of kink and antikink domain walls between the two degenerate singlet coverings. Closed-form spinon dispersions fix the continuum edges and track the dominant band across the zone in all three regimes, while an explicit finite-separation two-kink calculation in a constrained Hilbert space reproduces the measured intensity distribution. Our results provide a microscopic picture of fractionalized excitations in the dimerized sawtooth chain and are relevant to the recently discovered Ti3+^{3+}3+ kagome fluorides, where strongly anisotropic exchange interactions can generate sawtooth-chain building blocks.
We investigate the spin-1/2 Heisenberg model on the delta chain (sawtooth chain) with ferromagnetic nearest-neighbor and antiferromagnetic next-neighbor interactions. For a special ratio between these interactions there is a class of exact ground states formed by localized magnons and the ground state is macroscopically degenerate. The degree of this degeneration is found analytically. It is shown that the residual entropy per spin is s0=12ln2{s}_{0}=\frac{1}{2}ln\phantom{\rule{0.16em}{0ex}}2s0​=21​ln2. An important feature of this model is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the low-temperature thermodynamics. The corresponding thermodynamic quantities are calculated using full exact diagonalization of finite chains up to N=22N=22N=22. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions.
A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagom\'e lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like ``kink'' excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling.