The ground state phase diagram of the quantum J1-J2 spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice

Griffith Mendonça, Rodrigo Lapa, J. Ricardo De Sousa, Minos A. Neto, Kingshuk Majumdar, Trinanjan Datta

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We have studied the ground state phase diagram of the quantum spin-1/2 frustrated Heisenberg antiferromagnet on a square lattice by using the framework of the differential operator technique. The Hamiltonian is solved by using an effective-field theory for a cluster with two spins (EFT-2). The model is described using the Heisenberg Hamiltonian with two competing antiferromagnetic interactions: nearest neighbor (NN) with different coupling strengths J 1 and J1′ along the x and y directions and next nearest neighbor (NNN) with coupling J2. We propose a functional for the free energy (similar to the Landau expansion) and using Maxwell construction we obtain the phase diagram in the (λ, α) space, where λ = J1′/J1 and α = J2/J1. We obtain three different states depending on the values of λ and α: antiferromagnetic (AF), collinear antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate region λ1 < λ < 1 we observe a QP state between the ordered AF and CAF phases, which disappears for λ above some critical value . We find a second-order phase transition between the AF and QP phases and a first-order transition between the CAF and QP phases. The boundaries between these ordered phases merge at the quantum triple point (QTP). Below this QTP there is again a direct first-order transition between the AF and CAF phases, with a behavior approximately described by the classical line .

Original languageEnglish (US)
Article numberP06022
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number6
StatePublished - 2010


  • phase diagrams (theory)
  • quantum phase transitions (theory)

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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