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 journalArticle

3 Citations (Scopus)

Abstract

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
Volume2010
Issue number6
DOIs
StatePublished - Jul 6 2010

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Antiferromagnet
Square Lattice
Phase Diagram
Ground State
phase diagrams
Collinear
ground state
differential operators
Triple Point
free energy
Nearest Neighbor
expansion
First-order
y direction
x direction
Effective Field Theory
Diagrams
Critical value
Differential operator
Free Energy

Keywords

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

ASJC Scopus subject areas

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

Cite this

The ground state phase diagram of the quantum J1-J2 spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice. / Mendonça, Griffith; Lapa, Rodrigo; Ricardo De Sousa, J.; Neto, Minos A.; Majumdar, Kingshuk; Datta, Trinanjan.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2010, No. 6, P06022, 06.07.2010.

Research output: Contribution to journalArticle

Mendonça, Griffith ; Lapa, Rodrigo ; Ricardo De Sousa, J. ; Neto, Minos A. ; Majumdar, Kingshuk ; Datta, Trinanjan. / The ground state phase diagram of the quantum J1-J2 spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice. In: Journal of Statistical Mechanics: Theory and Experiment. 2010 ; Vol. 2010, No. 6.
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