Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions

Abstract

We have performed a numerical investigation of the ground state properties of the frustrated quantum Heisenberg antiferromagnet on the square lattice ("J 1 − J 2 model"), using exact diagonalization of finite clusters with 16, 20, 32, and 36 sites. Using a finite-size scaling analysis we obtain results for a number of physical properties: magnetic order parameters, ground state energy, and magnetic susceptibility (at q = 0). For the unfrustrated case these results agree with series expansions and quantum Monte Carlo calculations to within a percent or better. In order to assess the reliability of our calculations, we also investigate regions of parameter space with well-established magnetic order, in particular the non-frustrated case J 2 < 0. We find that in many cases, in particular for the intermediate region 0.3 < J 2 /J 1 < 0.7, the 16 site cluster shows anomalous finite size effects. Omitting this cluster from the analysis, our principal result is that there is Néel type order for J 2 /J 1 < 0.34 and collinear magnetic order (wavevector Q = (0, π)) for J 2 /J 1 > 0.68. There thus is a region in parameter space without any form of magnetic order. Including the 16 site cluster, or analyzing the independently calculated magnetic susceptibility we arrive at the same conclusion, but with modified values for the range of existence of the nonmagnetic region. We also find numerical values for the spin-wave velocity and the spin stiffness. The spin-wave velocity remains finite at the magnetic-nonmagnetic transition, as expected from the nonlinear sigma model analogy. 75.10.Jm, 75.40.Mg

Phase diagram of the frustrated spatially-anisotropicS=1antiferromagnet on a square lattice

“…This region is considerably smaller than in the S = 1 2 case, where a paramagnetic regime 0.4Շ J 2 / J 1 Շ 0.6 presumably with columnar valence-bond order has been established by various numerical methods. [18][19][20][21][22][23][24][25][26][27][28] Interestingly, the stabilization of the Néel phase above the classical transition point is in agreement with the SBMFT. Furthermore, we also calculate the lowest spin singlet excitation gap for the system N =4ϫ 4 by 9.…”

“…In fact, in the case S = 1 2 various numerical studies including exact diagonalization, [18][19][20][21] variational Monte Carlo 22,23 series expansion [24][25][26][27][28] as well as the coupled cluster approach 29 give the consistent picture that in the regime 0.4Շ J 2 / J 1 Շ 0.6 no magnetic order is present clearly indicating that the aforementioned semiclassical treatments overestimate the stability of the ordered states. Another key observation of the series expansion and in particular of the unbiased exact diagonalization studies is that in the paramagnetic phase the lattice symmetry is spontaneously broken due to the formation of columnar valence-bond solid order.…”

Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure

“…In the classical version of this model (S → ∞), two magnetic phases meet at exactly g = 0.5, separated by a first-order transition. [39][40][41][42] In the S = 1/2 problem, the two magnetically ordered ground states obtain for values g 0.4 and g 0.6, [43][44][45][46][47][48] and a magnetically disordered phase intervenes. (There is, however, a good deal of disagreement over the exact positions of the critical points; cf.…”

Magnon dispersion and anisotropies inSrCu2(BO3)2

“…It has appeared before ͑but for the simple square lattice͒ that the 16-site cluster can be quite special compared with larger clusters. 35 Comparison of the bandwidths of the 20-site and 32-site clusters is also difficult because the reciprocal points are not identical. In particular, the bandwidth of the 20-site cluster is inherently smaller because of the absence of the ͑ , ͒ reciprocal point: the only nonzero point in reciprocal space is at ͑ 2 5 , 4 5 ͒ .…”