Variational studies of the t-J model on the square lattice based on infinite projected-entangled pair states (iPEPS) confirm an extremely close competition between a uniform d-wave superconducting state and different stripe states. The site-centered stripe with an in-phase d-wave order has an equal or only slightly lower energy than the stripe with anti-phase d-wave order. The optimal stripe filling is not constant but increases with J/t. A nematic anisotropy reduces the pairing amplitude and the energies of stripe phases are lowered relative to the uniform state with increasing nematicity.
Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension $D$. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small $D$ the dimer state has a lower variational energy than the plaquette state, however, for large $D$ it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are non-chiral flux states.
The low temperature phase diagram of $^4$He adsorbed on a single graphene sheet is studied by computer simulation of a system comprising nearly thousand helium atoms. In the first layer, two commensurate solid phases are observed, with fillings 1/3 and 7/16 respectively, separated by a domain wall phase, as well as an incommensurate crystal at higher coverage. No evidence of a thermodynamically stable superfliuid phase is found for the first adlayer. Second layer promotion occurs at a coverage of 0.111(4) $AA^{-2}$. In the second layer two phases are observed, namely a superfluid and an incommensurate solid, with no commensurate solid intervening between these two phases. The computed phase diagram closely resembles that predicted for helium on graphite.
In a recent letter [D. Poletti et al., EPL 93, 37008 (2011)] a model of attractive spinless fermions on the honeycomb lattice at half filling has been studied by mean-field theory, where distinct homogenous phases at rather large attraction strength $V>3.36$, separated by (topological) phase transitions, have been predicted. In this comment we argue that without additional interactions the ground states in these phases are not stable against phase separation. We determine the onset of phase separation at half filling $V_{ps}approx 1.7$ by means of infinite projected entangled-pair states (iPEPS) and exact diagonalization.
