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arXiv:1711.08471 · Physical review. B./Physical review. B

One dimensionalization in the spin-1 Heisenberg model on the anisotropic triangular lattice

M. G. Gonzalez, E. A. Ghioldi, C. J. Gazza, L. O. Manuel, A. E. Trumper

Published Nov 17, 2017• 16 citations
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Abstract

We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-1 Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains $({J}^{\ensuremath{'}}\ensuremath{\ll}J)$ and the isotropic triangular lattice $({J}^{\ensuremath{'}}=J)$. We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at ${({J}^{\ensuremath{'}}/J)}_{c}\ensuremath{\sim}0.42$, signaled by the sudden closing of the spin gap. Coming from the magnetically ordered side, the computation of the spin stiffness within Schwinger boson theory predicts the instability of the spiral magnetic order toward a magnetically disordered phase with one-dimensional features at ${({J}^{\ensuremath{'}}/J)}_{c}\ensuremath{\sim}0.43$. The agreement of these complementary methods, along with the strong difference found between the intra- and the interchain DMRG short spin-spin correlations for sufficiently large values of the interchain coupling, suggests that the interplay between the quantum fluctuations and the dimensional crossover effects gives rise to the one-dimensionalization phenomenon in this frustrated spin-1 Hamiltonian.

DOI
10.1103/physrevb.96.174423

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Frustrated spin-1/2 model with all-antiferromagnetic exchange on Shastry-Sutherland lattice (SSL) has been extensively explored, and in this work we study the quantum phase diagram of isotropic Heisenberg spin- 1 / 2 model on the SSL with ferromagnetic exchange interactions along leg, and antiferromagnetic couplings along the diagonal bonds ( J ). Using density matrix renormalization group (DMRG) and exact diagonalization calculations, we identify four distinct ground-state (gs) phases for this frustrated spin-1/2 model: stripe ( π , 0 ) , stripe ( 0 , π ) , ferromagnetic, and spiral-dimer phases. In the spiral-dimer phase the gs can exhibit dimer formation along the diagonal bonds with or without spins spiral along the x axis or y axis in different parameter regime and these states are connected through crossovers. There is a continuous transition between stripe with a long-range spin-spin correlations and spiral-dimer phase with a short-range correlations. An effective spin parameter is introduced to accurately determine the phase boundaries. Our DMRG results differ significantly from previous Schwinger boson mean-field theory predictions. The spiral phase occurs in a narrow range of the parameter space and shows short-range correlations in the system.
The spin-1/21/21/2 anisotropic triangular model, which is believed to describe the materials Cs2CuCl4{\mathrm{Cs}}_{2}{\mathrm{CuCl}}_{4}Cs2​CuCl4​ and Cs2CuBr4{\mathrm{Cs}}_{2}{\mathrm{CuBr}}_{4}Cs2​CuBr4​, among others, is dominated by incommensurate spiral physics and is thus extremely resistant to numerical analysis on small system sizes. In this paper, we use twisted boundary conditions and exact diagonalization techniques to study the ground state of this model as a function of exchange parameter strength. With these boundary conditions we are able to extract the inter- and intrachain ordering qqq vectors for the $\frac{{J}^{\ensuremath{'}}}{J}<1$ region finding very close agreement with recent DMRG results on much larger systems. Our results suggest a phase transition between a long-range incommensurate spiral ordered phase, and a more subtle phase with short-range spiral correlations with the qqq vector describing the incommensurate correlations varying smoothly through the transition. In the latter phase correlations between next-nearest chains exhibit an extremely close competition between predominantly antiferromagnetic and ferromagnetic correlations. Further analysis suggests that the antiferromagnetic next-nearest chain correlations may be slightly stronger than the ferromagnetic ones. This difference is found to be slight but in line with previous renormalization group predictions of a collinear antiferromagnetic ordering in this region.
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