Low-energy singlet sector in the spin-1/2 J 1- J 2 Heisenberg model on a square lattice

Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin-1/2 Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J ₁ and J ₂. It is well known that a nonmagnetic phase arises in this model for 0.4 ≲ J ₂/ J ₁ ≲ 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J ₂ ≈ 0.64 J ₁ from the non-magnetic phase to the Néel one. A large gap (≳ 0.4 J ₁) is found in the singlet spectrum for J ₂ < 0.64 J ₁, which excludes a gapless spin-liquid state for 0.4 ≲ J ₂/ J ₁ ≲ 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J ₂ ≈ 0.55 J ₁, presumably between two nonmagnetic phases.