Gapless spin liquid and valence-bond solid in the J1-J2 Heisenberg model on the square lattice: Insights from singlet and triplet excitations

The spin-1/2 J(1)-J(2) Heisenberg model on the square lattice represents one of the simplest examples in which the effects of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for J(2)/J(1) approximate to 0.54. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for 0.48 less than or similar to J(2)/J(1) less than or similar to 0.54) and a valence-bond solid (for 0.54 less than or similar to J(2)/J(1) less than or similar to 0.6), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)], reconcile the contradicting results obtained within different approaches over the years.