Excitation spectra of the spin-12triangular-lattice Heisenberg antiferromagnet

Abstract

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-1/2 triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a threesublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find roton-like minima at special wave-vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [cond-mat/0608002]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a non-linear sigma model description of the finite-temperature properties is only applicable at extremely low temperatures.

Spin liquid phase of theS=12J1−J2Heisenberg model on the triangular lattice

“…Later, a variety of analytical and numerical studies [3][4][5][6] demonstrated that this system has three sublattice 120 • long range antiferromagnetic order. More recent numerical studies [7][8][9] have confirmed this result, and more accurately determined the magnetization, with M ∼ 0.2.…”

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

“…• antiferromagnetic order is found in the subsequent studies [36][37][38][39][40]. Although spin liquid does not exist in the NN model, both experimental and theoretical studies find that the additional interactions may open a new route for realizing such states.…”

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

“…For spins S = 1/2 (which is the case of interest here) quantum fluctuations are not strong enough to destroy the magnetic order and the 120 • structure survives. One should mention that this remains true at arbitrary J 2 0, as confirmed by spin-wave calculations, [25][26][27][28][29][30] Green's function Monte Carlo, 31 series expansions, 32 tower of states spectroscopy, 16 and recent DMRG calculations. 33 b.…”