Gapless Spin-Liquid Phase in an Extended Spin 1/2 Triangular Heisenberg Model

Abstract

We numerically study Heisenberg models on modified triangular lattices, and show that a weak nextnearest-neighbor exchange interaction added to a simple triangular lattice, namely, the equilateral triangular lattice with only the nearest-neighbor exchange is sufficient to stabilize a quantum spin liquid against the antiferromagnetic order widely accepted as the ground state of the simple triangular model. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic and spin-liquid phases as well as inside the spin-liquid phase, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents z + η ∼ 1. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.KEYWORDS: triangular lattice, next nearest neighbor interaction, J1-J2 Heisenberg model, many-variable variational Monte Carlo method, gapless quantum spin liquid, spin gap, spinon Fermi surface

Phase diagram of thespin−12triangularJ1−J2Heisenberg model on a three-leg cylinder

“…4(b)], which is also gapless. This is consistent with the 2D model, which has long-range columnar order [30][31][32]. However, this ordering is forbidden in one dimension for the same reason as the 120 • state.…”

“…Quantum fluctuations break this degeneracy, and the quantum model has a two-sublattice columnar (collinear) Néel state [30][31][32]. It is worth mentioning that the selection of the collinear order from the four-sublattice classical order can be understood analytically using groupsymmetry analysis [51].…”

“…The J 1 -J 2 THM in two dimensions has been previously studied using semiclassical spin-wave theories (SWTs) and exact diagonalization (ED) [18,19,[26][27][28][29], but these studies did not cover the physics of the whole phase diagram. Recently, a coupled cluster method (CCM) study [30] and quantum Monte Carlo (QMC) studies [31,32] have identified a phase in this model that is a candidate for a spin liquid. Magnetically ordered states in a variety of classical O(3) models with J 1 -J 2 -J 3 interactions have been studied by Messio, Lhuillier, and Misguich [33], finding several different "regular magnetic orders" relevant to the triangular lattice, including planar and nonplanar 120 • states.…”

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

“…Overall, our results strongly support a fully gapped SL state, instead of the gapless SL state in Ref. [14].…”

“…The limited number of studies on this question, which have usually relied on approximations with uncertain reliability, have given conflicting results, particularly on the nature of a possible disordered phase and the location of the phase boundaries. [12][13][14][15] Here, we try to resolve the nature of this possible intermediate state using DMRG methods. [16] We do find a spin liquid intermediate phase, gapped with fairly large singlet and triplet gaps, which is bordered by the expected magnetic phases, the √ 3 × √ 3 ordered state (120 • classical Need order pattern) at J 2 < 0.05 ∼ 0.07 and a two sub-lattice collinear ordered state at J 2 0.17.…”