Article

Antiferromagnetic order in systems with doublet Stot=1/2 ground states

Department of Theoretical Physics, Tata Institute of Fundamental Research, 400005, Mumbai, India; Department of Physics, Boston University, 02215, Boston, Massachussetts, USA
Physical review. B, Condensed matter (Impact Factor: 3.77). 08/2012; 86(6). DOI: 10.1103/PhysRevB.86.064418
Source: arXiv

ABSTRACT We use projector quantum Monte Carlo methods to study the doublet ground states of two-dimensional S=1/2 antiferromagnets on L×L square lattices with L odd. We compute the ground-state spin texture Φz(r⃗)=〈Sz(r⃗)〉↑ in the ground state |G〉↑ with Stotz=1/2, and relate nz, the thermodynamic limit of the staggered component of Φz(r⃗), to m, the thermodynamic limit of the magnitude of the staggered magnetization vector in the singlet ground state of the same system with L even. If the direction of the staggered magnetization in |G〉↑ were fully pinned along the ẑ axis in the thermodynamic limit, then we would expect nz/m=1. By studying several different deformations of the square lattice Heisenberg antiferromagnet, we find instead that nz/m is a universal function of m, independent of the microscopic details of the Hamiltonian, and well approximated by nz/m≈0.266+0.288m−0.306m2 for S=1/2 antiferromagnets. We define nz and m analogously for spin-S antiferromagnets, and explore this universal relationship using spin-wave theory, a simple mean-field theory written in terms of the total spin of each sublattice, and a rotor model for the dynamics of the staggered magnetization vector. We find that spin-wave theory predicts nz/m≈(0.987−1.003/S)+0.013m/S to leading order in 1/S, while the sublattice-spin mean-field theory and the rotor model both give nz/m=S/(S+1) for spin-S antiferromagnets. We argue that this latter relationship becomes asymptotically exact in the limit of infinitely long-range unfrustrated exchange interactions.

0 Bookmarks
 · 
52 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The study of impurities in antiferromagnets is of considerable interest in condensed matter physics. In this Letter we address the elementary question of the effect of vacancies on the orientation of the surrounding magnetic moments in an antiferromagnet. In the presence of a magnetic field, alternating magnetic moments are induced, which can be described by a universal expression that is valid in any ordered antiferromagnet and turns out to be independent of temperature over a large range. The universality is not destroyed by quantum fluctuations, which is demonstrated by quantum Monte Carlo simulations of the two-dimensional Heisenberg antiferromagnet. Physical predictions for finite doping are made, which are relevant for experiments probing Knight shifts and the order parameter.
    Physical Review Letters 09/2007; 99(9):097204. · 7.73 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The correlation length of the square-lattice spin-1/2 Heisenberg antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime. Our novel approach combines a very efficient loop cluster algorithm -- operating directly in the Euclidean time continuum -- with finite-size scaling. This enables us to probe correlation lengths up to $\xi \approx 350,000$ lattice spacings -- more than three orders of magnitude larger than any previous study. We resolve a conundrum concerning the applicability of asymptotic-scaling formulae to experimentally- and numerically-determined correlation lengths, and arrive at a very precise determination of the low-energy observables. Our results have direct implications for the zero-temperature behavior of spin-1/2 ladders. Comment: 12 pages, RevTeX, plus two Postscript figures. Some minor modifications for final submission to Physical Review Letters. (accepted by PRL)
    Physical Review Letters 09/1997; · 7.73 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We develop a generalization of the singlet sector valence bond basis projection algorithm of Sandvik, Beach, and Evertz (A. W. Sandvik, Phys. Rev. Lett. 95, 207203 (2005); K. S. D. Beach and A. W. Sandvik, Nucl. Phys. B750, 142 (2006); A. W. Sandvik and H. G. Evertz, arXiv:0807.0682, unpublished.) to cases in which the ground state of an antiferromagnetic Hamiltonian has total spin $S_{tot} = 1/2$ in a finite size system. We explain how various ground state expectation values may be calculated by generalizations of the estimators developed in the singlet case, and illustrate the power of the method by calculating the ground state spin texture and bond energies in a $L \times L$ Heisenberg antiferromagnet with $L$ odd and free boundaries. Comment: 6 pages, 6 figures
    Journal of Statistical Mechanics Theory and Experiment 06/2010; · 1.87 Impact Factor

Full-text (2 Sources)

Download
24 Downloads
Available from
May 26, 2014