4p-Q-8 Short range order for the two dimensional Heisenberg model on a triangular lattice

Pavel Rubin, A. Sherman

Dariush Heidarian, Sandro Sorella, Federico Becca

We investigate the anisotropic triangular lattice that interpolates from decoupled one-dimensional chains to the isotropic triangular lattice and has been suggested to be relevant for various quasi-two-dimensional materials such as ${\text{Cs}}_{2}{\text{CuCl}}_{4}$ or $\ensuremath{\kappa}\text{\ensuremath{-}}{(ET)}_{2}{\text{Cu}}_{2}{(\text{CN})}_{3}$. We obtain an excellent accuracy by means of a representation for the resonating valence-bond wave function with both singlet and triplet pairings. This approach allows us to establish that the magnetic order is rapidly destroyed away from the pure triangular lattice and incommensurate spin correlations are short range. A nonmagnetic spin liquid naturally emerges in a wide range of the phase diagram with strong one-dimensional character.

F. W. O. da Silva, Antonio S. T. Pires

Biao Hao, Chang-De Gong

J. Schulenburg, Johannes Richter, Donald D. Betts

Based on the triangular lattice and its depletions there are three simple frustrated antiferromagnetic Heisenberg models in two dimensions.The first two, the triangular and kagοmé lattices, have been examined in the recent past.The triangular lattice seems to have a łong range order whereas the kagomé does not show the long range order.But these results are still con-' troversial.This work is concentrated on a third type of this lattice family in order to improve the understanding of the connection between the long range order and coordination number in low dimensional systems.Bets has described the geometric properties of this lattice.It has a coordination number 5, which lies precisely between coordination numbers 6 and 4 of the other two lattices.The low-lying spectra and the correlation functions of finite lattices have been examined to discuss the possibility of a long range ordered ground state in the I/7-depleted triangular lattice.The low-lying spectrum is generated by an exact diagonalization, and the tower of states behavior points to a long range ordered ground state.

Tao Xie, Jie Xing, Stanislav E. Nikitin +7 more

A layered triangular lattice with spin-1/2 ions is an ideal platform to explore highly entangled exotic states like quantum spin liquid (QSL). Here, we report a systematic in-field neutron scattering study on a perfect two-dimensional triangular-lattice antiferromagnet, CsYbSe$_2$, a member of the large QSL candidate family rare-earth chalcogenides. The elastic neutron scattering measured down to 70 mK shows that there is a short-range 120$^{\circ}$ magnetic order at zero field. In the field-induced ordered states, the spin-spin correlation lengths along the $c$ axis are relatively short, although the heat capacity results indicate long-range magnetic orders at 3 T $-$ 5 T. The inelastic neutron scattering spectra evolve from highly damped continuum-like excitations at zero field to relatively sharp spin wave modes at the plateau phase. Our extensive large-cluster density-matrix renormalization group calculations with a Heisenberg triangular-lattice nearest-neighbor antiferromagnetic model reproduce the essential features of the experimental spectra, including continuum-like excitations at zero field, series of sharp magnons at the plateau phase as well as two-magnon excitations at high energy. This work presents comprehensive experimental and theoretical overview of the unconventional field-induced spin dynamics in triangular-lattice Heisenberg antiferromagnet and thus provides valuable insight into quantum many-body phenomena.