A closer look at symmetry breaking in the collinear phase of the $J_1-J_2$ Heisenberg Model

Abstract

The large $J_2$ limit of the square-lattice $J_1-J_2$ Heisenberg antiferromagnet is a classic example of order by disorder where quantum fluctuations select a collinear ground state. Here, we use series expansion methods and a meanfield spin-wave theory to study the excitation spectra in this phase and look for a finite temperature Ising-like transition, corresponding to a broken symmetry of the square-lattice, as first proposed by Chandra et al. (Phys. Rev. Lett. 64, 88 (1990)). We find that the spectra reveal the symmetries of the ordered phase. However, we do not find any evidence for a finite temperature phase transition. Based on an effective field theory we argue that the Ising-like transition occurs only at zero temperature.

arXiv comment4 pages and 5 figures

References in corpus (4)

• Li${}_2$VO(Si,Ge)O${}_4$, a prototype of a two-dimensional frustrated quantum Heisenberg antiferromagnet
• Magnetic and thermodynamic properties of Li(2)VOSiO(4): a two-dimensional S=1/2 frustrated antiferromagnet on a square lattice
• Realization of a large J_2 quasi-2D spin-half Heisenberg system: Li2VOSiO4
• Quantum Phase Transition in the Frustrated Heisenberg Antiferromagnet

Cited by in corpus (41)

• Preemptive nematic order, pseudogap, and orbital order in the iron pnictides
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Gapless quantum spin liquid, stripe and antiferromagnetic phases in frustrated Hubbard models in two dimensions
• Ising transition driven by frustration in a 2D classical model with SU(2) symmetry
• Frustrated two dimensional quantum magnets
• Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• Phase diagram of the Ising square lattice with competing interactions
• The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
• Pnictides as frustrated quantum antiferromagnet close to a quantum phase transition
• Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model
• Self-consistent spin-wave theory for a frustrated Heisenberg model with biquadratic exchange in the columnar phase and its application to iron pnictides
• Thermodynamics of a two-dimensional frustrated spin-1/2 Heisenberg ferromagnet
• Spin liquid versus dimer phases in an anisotropic J1-J2 frustrated square antiferromagnet
• Spin-waves in the $J_{1a}-J_{1b}-J_2$ orthorombic square-lattice Heisenberg models: Application to the iron pnictide materials
• Classical spin-liquid on the maximally frustrated honeycomb lattice
• Ground-state phases of the frustrated spin-1/2 $J_1$--$J_2$--$J_3$ Heisenberg ferromagnet ($J_1<0$) on the honeycomb lattice with $J_3=J_2>0$
• Pseudo-Goldstone magnons in the frustrated S=3/2 Heisenberg helimagnet ZnCr2Se4 with a pyrochlore magnetic sublattice
• The quantum $J_1$-$J_1^{\prime }$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Three dimensional generalization of the $J_1$-$J_2$ Heisenberg model on a square lattice and role of the interlayer coupling $J_c$
• Finite-temperature properties of frustrated classical spins coupled to the lattice
• Double stage nematic bond-ordering above double stripe magnetism: application to BaTi${}_2$Sb${}_2$O
• The Ising phase in the J1-J2 Heisenberg Model
• Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• Magnetic order in a spin-1/2 interpolating kagome-square Heisenberg antiferromagnet
• Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Ground state selection by magnon interactions in the fcc antiferromagnet
• Role of Frustration and Dimensionality in the Hubbard Model on the Stacked Square Lattice: Variational Cluster Approach
• Thermodynamic properties of the 2D frustrated Heisenberg model for the entire $J_1-J_2$ circle
• The ground-state magnetic ordering of the spin-1/2 frustrated J1-J2 XXZ model on the square lattice
• Weakly frustrated two-dimensional Heisenberg antiferromagnets: thermodynamic properties from a non-perturbative approach
• A Frustrated 3-Dimensional Antiferromagnet: Stacked $J_1-J_2$ Layers
• Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model
• Effective field theories and spin-wave excitations in helical magnets
• Spectroscopic fingerprints of the frustrated magnetic order in Li2VOSiO4: a t-J model study
• Quantum order by disorder in Frustrated Spin Nanotubes
• Superconductivity in model cuprate as an S=1 pseudomagnon condensation