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arXiv:cond-mat/9612014 · Physical Review Letters

One-Dimensional Spin-Liquid without Magnon Excitations

A. A. Nersesyan, Alexei M. Tsvelik

Published May 19, 1997• 160 citations
arXivHTMLPDF

Abstract

It is shown that a sufficiently strong four-spin interaction in the spin-1/2 spin ladder can cause dimerization. Such interaction can be generated either by phonons or (in the doped state) by the conventional Coulomb repulsion between the holes. The dimerized phases are thermodynamically undistinguishable from the Haldane phase, but have dramatically different correlation functions: the dynamical magnetic susceptibility, instead of displaying a sharp single magnon peak near $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}$, shows only a two-particle threshold separated from the ground state by a gap.

DOI
10.1103/physrevlett.78.3939

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It is shown that a sufficiently strong four-spin interaction in the spin-1/2 spin ladder can cause dimerization. Such interaction can be generated either by phonons or (in the doped state) by the conventional Coulomb repulsion between the holes. The dimerized phases are thermodynamically undistinguishable from the Haldane phase, but have dramatically different correlation functions: the dynamical magnetic susceptibility, instead of displaying a sharp single magnon peak near q=\ensuremathπq\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}q=\ensuremathπ, shows only a two-particle threshold separated from the ground state by a gap.
We present a family of spin-ladder models which can be solved exactly for the ground state and exhibit non-Haldane spin-liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. 78, 3939 (1997)], and study their excitation spectra using a simple variational Ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.
We present a family of spin ladder models which admit exact solution for the ground state and exhibit non-Haldane spin liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. v.78, 3939 (1997)], and study their excitation spectrum using a simple variational ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.
We have numerically investigated the doped t-J ladder using exact diagonalization. We have studied both the limit of strong interchain coupling and isotropic coupling. The ladder scales to the Luther-Emery liquid regime in the strong interchain coupling limit. In this strong coupling limit there is a simple picture of the excitation spectrum that can be continued to explain the behavior at isotropic coupling. At J=0 we have indications of a ferromagnetic ground state. At a large J/t the ladder is phase separated into holes and a Heisenberg ladder. At intermediate coupling the ground state shows hole pairing with a modified d-wave symmetry. The excitation spectrum separates into a limited number of quasiparticles which carry charge +\ensuremath{\Vert}e\ensuremath{\Vert} and spin 1/2 and a triplet magnon mode. At half filling the former vanish but the latter evolves continuously into the magnon band of the spin liquid. At low doping the quasiparticles form a dilute Fermi gas with a strong attraction but simultaneously the Fermi wave vector, as would be measured in photoemission, is large. The dynamical structure factors are calculated and are found to be very similar to calculations on two-dimensional clusters. \textcopyright{} 1996 The American Physical Society.
This thesis describes the neutron scattering measurements of magnetic excitations in \nspin-chains and ladders. The first part discusses an experimental investigation of the copper oxide family Srâ â Cuâ â Oâ â composed of edge-sharing chains and spin-ladders. \nThe study of Laâ Srâ â Cuâ â Oâ â comprises a slightly hole-doped chain and an undoped ladder structure where the chain can be modeled by a ferromagnetic nearest and an \nantiferromagnetic next-nearest neighbor coupling. The hole effects are apparent in gaps in the dispersion relation and can be described by a charge-density wave agreeing with the commensuration of the dispersion. Investigating the undoped ladder establishes \nthe exchange constants including a cyclic exchange manifested by the two-magnon \ncontinuum and the suppression of the S = 1 bound mode. An orbital consideration \nprovides an explanation for the exchanges including the different sizes of rung and \nleg coupling. The excitation spectrum of the doped ladder in Caâ .â Srâ â .â Cuâ â Oâ â can be \ndescribed by a direct comparison with the undoped ladder and the differences consisting \nof a higher energy mode and subgap scattering can be successfully modeled by the charge spectrum of the ladder calculated from the free electron model. The second part of the thesis investigates the alternating chain material Cu(NOâ )â · 2.5D2O and establishes the gapped one-magnon dispersion, the two-magnon continuum and for the first time the S =1 bound mode. Applying magnetic field drives the system through two critical field transitions, condensation of magnons into the ground state and saturation. The modes beyond saturation can be modeled by spin wave theory and the excitations at the first critical field follow Luttinger Liquid behavior. Additionally investigated are the temperature effects with the excitations being of a different nature but containing the signature of a strong correlated system. For an outlook the measurements including temperature and field are provided with further theoretical descriptions necessary.
We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest-neighbor hopping t, we also include a next-to-nearest-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$. For strong enough on-site repulsion, this model has a transition at half filling from a magnetic insulator with gapless spin excitations at small ${\mathit{t}}^{\ensuremath{'}}$/t to a dimerized insulator with a spin gap at larger ${\mathit{t}}^{\ensuremath{'}}$/t. We show that upon doping this model exhibits quite interesting features, which include the presence of a metallic phase with a spin gap and dominant superconducting fluctuations, in spite of the repulsive interaction. More interestingly, we find that this superconducting phase can be reached upon hole doping the magnetic insulator. The connections between this model and the two chain models, recently object of intensive investigations, are also discussed. \textcopyright{} 1996 The American Physical Society.