Low-energy singlet sector in the spin-1/2 J1–J2 Heisenberg model on a square lattice

Abstract

Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin-\(\frac{1}{2}\) Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J₁ and J₂. It is well known that a nonmagnetic phase arises in this model for 0.4 ≲ J₂/J₁ ≲ 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J₂ ≈ 0.64 J₁ from the non-magnetic phase to the Néel one. A large gap (≳ 0.4J₁) is found in the singlet spectrum for J₂ < 0.64J₁, which excludes a gapless spin-liquid state for 0.4 ≲ J₂/J₁ ≲ 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J₂ ≈ 0.55J₁, presumably between two nonmagnetic phases.