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ZhETF, Vol. 150, No. 6, p. 1191 (December 2016)
(English translation - JETP, Vol. 123, No. 6, p. 1035, December 2016 available online at )

Low-energy singlet sector in the spin-1/2 J1-J2 Heisenberg model on a square lattice
Aktersky A.Yu., Syromyatnikov A.V.

Received: August 4, 2016

DOI: 10.7868/S0044451016120000

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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 J1 and J2. It is well known that a nonmagnetic phase arises in this model for 0.4\lesssim J_2/J_1\lesssim 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\approx 0.64J_1 from the nonmagnetic phase to the Néel one. A large gap (\gtrsim 0.4J_1) is found in the singlet spectrum for J2<0.64J1, which excludes a gapless spin-liquid state for 0.4\lesssim J_2/J_1\lesssim 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J_2\approx 0.55J_1, presumably between two nonmagnetic phases.

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