### 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 J_{1}′ along the x and y directions and next nearest neighbor (NNN) with coupling J_{2}. 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 = J_{1}′/J_{1} and α = J_{2}/J_{1}. 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 λ_{1} < 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 language | English (US) |
---|---|

Article number | P06022 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2010 |

Issue number | 6 |

DOIs | |

State | Published - Jul 6 2010 |

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### 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

_{1}-J

_{2}spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice.

*Journal of Statistical Mechanics: Theory and Experiment*,

*2010*(6), [P06022]. https://doi.org/10.1088/1742-5468/2010/06/P06022

**The ground state phase diagram of the quantum J _{1}-J_{2} 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.

Research output: Contribution to journal › Article

_{1}-J

_{2}spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice',

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2010, no. 6, P06022. https://doi.org/10.1088/1742-5468/2010/06/P06022

_{1}-J

_{2}spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice. Journal of Statistical Mechanics: Theory and Experiment. 2010 Jul 6;2010(6). P06022. https://doi.org/10.1088/1742-5468/2010/06/P06022

}

TY - JOUR

T1 - The ground state phase diagram of the quantum J1-J2 spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice

AU - Mendonça, Griffith

AU - Lapa, Rodrigo

AU - Ricardo De Sousa, J.

AU - Neto, Minos A.

AU - Majumdar, Kingshuk

AU - Datta, Trinanjan

PY - 2010/7/6

Y1 - 2010/7/6

N2 - 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 .

AB - 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 .

KW - phase diagrams (theory)

KW - quantum phase transitions (theory)

UR - http://www.scopus.com/inward/record.url?scp=77954170443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954170443&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2010/06/P06022

DO - 10.1088/1742-5468/2010/06/P06022

M3 - Article

AN - SCOPUS:77954170443

VL - 2010

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 6

M1 - P06022

ER -