Global phase diagram and quantum spin liquids in a spin-12triangular antiferromagnet

Abstract

We study the spin-1/2 Heisenberg model on the triangular lattice with the nearest-neighbor J1 > 0, the nextnearest-neighobr J2 > 0 Heisenberg interactions, and the additional scalar chiral interaction Jχ( Si × Sj) · S k for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing J2 (J2/J1 ≤ 0.3) and Jχ (Jχ/J1 ≤ 1.0) interactions, we establish a quantum phase diagram with the magnetically ordered 120 • phase, stripe phase, and non-coplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a ν = 1/2 bosonic fractional quantum Hall state with possible spontaneous rotational symmetry breaking. By switching on the chiral interaction, we find that the previously identified spin liquid in the J1 − J2 triangular model (0.08 J2/J1 0.15) shows a phase transition to the CSL phase at very small Jχ. We also compute spin triplet gap in both spin liquid phases, and our finite-size results suggest large gap in the odd topological sector but small or vanishing gap in the even sector. We discuss the implications of our results to the nature of the spin liquid phases.

Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study

“…Recent numerical investigations of a spin-1/2 chiral Heisenberg antiferromagnetic model (HAFM) on the kagomé lattice [17,18] suggest that a scalar chiral interaction on all triangular units can indeed stabilize a spin liquid of the ν = 1/2 KL type. Similar Abelian CSL were also uncovered in spin-1/2 chiral antiferromagnets on the triangular lattice [19,20]. Interestingly, the CSL can also emerge in spin-1/2 time-reversal invariant frustrated magnets [18,21].…”

Dirac Spin Liquid on the Spin- 1/2 Triangular Heisenberg Antiferromagnet

“…For the J 1 -J 2 triangular spin liquid, one can obtain two "groundstates" on the YC2n-0 geometry. Previous works [16][17][18]21] call these two "groundstates" the even and odd sectors, which pictorially corresponds to the number of valence bonds which cross a cut through the system. Their entanglement spectrum is one-fold or two-fold degenerate respectively, related to whether the SO(3) spin rotation symmetry is realized projectively (two-fold) or not (one-fold).…”

“…Historically, it has been proposed that geometric frustrations on the spin-1/2 triangular antiferromagnetic Heisenberg model (TAFM) could lead to a spin disordered ground state [5]. Although the nearest neighbor TAFM turns out to exhibit a 120 • magnetic order [6][7][8][9][10], the possibility of increasing the frustration by adding next-nearest-neighbor (NNN) interactions has captured much interest in the literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for the J 1 -J 2 TAFM…”

“…where i, j and i, j respectively denote NN and NNN bonds. So far, the general consensus is that an intermediate region (0.07 J 2 /J 1 0.15) without magnetic ordering [11][12][13][14][15][16][17][18][19][20][21][22][23][24] is sandwiched between a stripe ordered phase (J 2 /J 1 0.15) [25,26] and a 120 • magnetically ordered phase (0.0 ≤ J 2 /J 1 0.07) [6][7][8][9][10]. However, the underlying physics and precise nature of this intermediate phase is under an intense debate.…”

Finite-temperature properties of the extended Heisenberg model on a triangular lattice

“…Recently, the focus shifted to generalized HM where SL can become the stable g.s.. Recent numenical studies reveal that the J 1 − J 2 HM on TL with additional AFM next-neighbor coupling J 2 > 0 introduces further frustration which favours SL [17][18][19][20][21][22]. The same state might be stable also by introducing ringexchange [23,24] or similar terms obtained by downfolding the Hubbard model in the Mott insulating phase [25,26].…”