Finite-Size Scaling for the Two-Dimensional Frustrated Quantum Heisenberg Antiferromagnet

Abstract

Using results for the 4 x 4 and 6 x 6 lattice, we produce the first finite-size scaling analysis of the frustrated Heisenberg model in two dimensions. The results indicate a continuous phase transition from the ordered phase into an intermediate phase without long-range magnetic order, as for the (2 + 1)-dimensional nonlinear sigma-model. The intermediate phase is stable for 0.4 < J 2 / J I < 0.65 and exhibits either dimerization or broken chiral symmetry. The transition to the collinear phase at J z / J 1 = 0.65 is apparently of first order.

Quantum phase transitions of a square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor bonds: A high-order coupled-cluster treatment

“…By using the extrapolation scheme of Ref. 42, we find a critical value J ′ s ≈ 2.45 for the magnetization. Note however that better accuracy requires larger systems because of the exact diagonalization (ED) extrapolation ansatz for M (i.e., M = M ∞ + const × N −1/2 ).…”

“…We use periodic boundary conditions with N = 16, 18, 20, 26 and 32 spins, and we extrapolate to the infinite system using standard finite-size scaling laws. 41,42 We present results for the ground-state energy, the order parameter and the excitation gap. We examine the formation of local singlets (for J ′ > 1), the effects of frustration (for J ′ < 0), and the special case of the honeycomb lattice (J ′ = 0).…”

J1-J2quantum Heisenberg antiferromagnet: improved spin-wave theories versus exact-diagonalization data

“…In addition, the same analysis predicts a lowest limit α * = 0.49 where the Néel state is destroyed which is quite larger than the previous estimate α ≈ 0.4 based on the linear spin-wave theory [1,14] and on the N = 36 exact-diagonalization results [10].…”

“…The magnetically disordered spin-Peierls dimer state is preferable in a number of studies: 1) series expansions around dimer states [5], 2) 1/N-expansion technique [6], 3) bond-operator techniques [7], 4) effectiveaction approaches leading to quantum nonlinear σ-models [8], 5) numerical exactdiagonalization data [9,10]. However, each of the mentioned methods has its own defects, so that some other states (e.g., the chiral states [10,11,12]) seem to be possible candidates, as well.…”

Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1–J2 circle

“…Frustrated two-dimensional (2D) and quasi-2D magnets are of particular interest, as they demonstrate strong quantum fluctuations effects. The 2D spin-1/2 J 1 -J 2 quantum Heisenberg model is a conventional tool for the investigation of frustration effects and quantum phase transitions (see, e.g., [2][3][4][5][6][7]). …”