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.
We study the nature of the ground state of the frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ model and the ${J}_{1}\ensuremath{-}{J}_{3}$ model using a variational algorithm based on projected entangled pair states. By investigating spin-spin correlation functions, we observe a separation in parameter regions with long- and short-range order. A direct comparison with exact diagonalizations in the subspace of short-range valence bond singlets reveals that the system is well described by states within this subset in the short-range order regions. We discuss the question whether the system forms a spin liquid, a plaquette valence bond crystal, or a columnar dimer crystal in these parameter regions.
Using infinite projected entangled-pair states, we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and not to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu2(BO3)2, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a localized bound state with Sz=2. Finally, we discuss the role of competing domain-wall and supersolid phases, as well as that of additional anisotropic interactions.
The frustrated Heisenberg ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model on a square lattice is numerically investigated by variational Monte Carlo simulations. We propose an antiferromagnetic fermion resonating-valence-bond (AF-fRVB) state that has the ability to examine the entire phase diagram in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. Two phase transition points, the second order around
J2/J1=0.45 and the first order around
J2/J1=0.6, can be extracted more clearly than the conventional bosonic RVB state. At the maximally frustrated point
(J2/J1=0.5), the AF-fRVB state shows the variational ground-state energy in the thermodynamic limit very close to the one estimated by the projected entangled pair state at the largest bond dimension available. On the other hand, in the frustrated regime $0.4\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$, AF-fRVB states with
exts2 (using the terminology in the field of iron-based superconductors) and
dxy pairing symmetries are degenerate in the thermodynamic limit, implying the existence of gapless Dirac excitations in the spinon spectrum.
The Shastry-Sutherland model is an effective model of the layered material SrCu_{2}(BO_{3})_{2}, which exhibits an extremely rich phase diagram as a function of pressure and magnetic field. Motivated by the recent controversy regarding its phase diagram at zero magnetic field, we perform large-scale simulations based on infinite projected entangled-pair states, a two-dimensional tensor network Ansatz to represent the ground state directly in the thermodynamic limit. By employing the latest optimization techniques, we obtain variational states with lower energy than previous results obtained from other methods. Using systematic extrapolations to the exact infinite bond dimension limit, our simulations reveal a narrow quantum spin liquid phase between the plaquette and antiferromagnetic phases in the range 0.785(5)≤J^{'}/J≤0.82(1).
A simple spin-
21 frustrated antiferromagnetic Heisenberg model (AFHM) on the square lattice---including chiral plaquette cyclic terms---was argued [A. E. B. Nielsen, G. Sierra, and J. I. Cirac, Nat. Commun. 4, 2864 (2013)] to host a bosonic Kalmeyer-Laughlin (KL) fractional quantum Hall ground state [V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett. 59, 2095 (1987)]. Here, we construct generic families of chiral projected entangled pair states (chiral PEPS) with low bond dimension (
D=3,4,5) which, upon optimization, provide better variational energies than the KL Ansatz. The optimal
D=3 PEPS exhibits chiral edge modes described by the Wess-Zumino-Witten
SU(2)1 model, as expected for the KL spin liquid. However, we find evidence that, in contrast to the KL state, the PEPS spin liquids have power-law dimer-dimer correlations and exhibit a gossamer long-range tail in the spin-spin correlations. We conjecture that these features are genuine to local chiral AFHM on bipartite lattices.