Motivated by recent numerical discovery of a gapped spin liquid phase in spin-
1/2 triangular-lattice ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, we classify symmetric
Z2 spin liquids on triangular lattice in the Abrikosov-fermion representation. We find 20 phases with distinct spinon symmetry quantum numbers, eight of which have their counterparts in the Schwinger-boson representation. Among them we identify two promising candidates (#1 and #20), which can realize a gapped
Z2 spin liquid with up to next nearest neighbor mean-field amplitudes. We analyze their neighboring magnetic orders and valence bond solid patterns, and find one state (#20) that is connected to 120-degree Neel order by a continuous quantum phase transition. We also identify gapped nematic
Z2 spin liquids in the neighborhood of the symmetric states and find three promising candidates (#1, #6, and #20).
The nature of the quantum spin liquid (QSL) phase in the frustrated
J1-
J2 Heisenberg model on the triangular lattice remains an open and actively debated problem. In this work, we employ the infinite projected entangled-pair state (PEPS) to systematically investigate the model under different symmetry constraints. Our simulations reveal a direct transition from the
120∘ Néel state to a putative QSL at
J2/J1≈0.08, signaled by the collapse of magnetic order. We further show that, through either an appropriate unitary rotation or spontaneous spin long-range order, the stripe antiferromagnetic phase can also be accurately captured within the infinite PEPS framework. A central focus of our study is the role played by the PEPS symmetry in approximating the QSL ground-state sandwiched between the two magnetic phases. We first found that a fully-symmetric topological
Z2 Resonating Valence Bond state, which can be written as a simple PEPS with bond dimension
D=3, exhibits a reasonably good variational energy. Motivated by this finding, we have further constructed generic
Z2-symmetric PEPS of larger bond dimension (up to
D=7). We found that, under wavefunction optimization, spinons condense and, simultaneously, topological vison excitations get confined, hence precluding
Z2 topological order. This strongly indicates the gapless (or critical) nature of the QSL phase, which is most naturally consistent with a U(1) Dirac spin liquid scenario.