arXiv subjects
Publications and source records attributed to J. Richter.
We consider a class of one-dimensional Heisenberg spin models (plaquette chains) related to the recently found 1/5-depleted square-lattice Heisenberg system $CaV_4O_9$. A number of exact and exact-numerical results concerning the properties of the competing dimer and resonating plaquette phases are presented.
The paper presents exact calculations of thermodynamic quantities for the spin-1/2 isotropic XY chain with random lorentzian intersite interaction and transverse field that depends linearly on the surrounding intersite interactions.
We examine the influence of an anisotropic interaction term of Dzyaloshinskii-Moriya (DM) type on the groundstate ordering of the J_1-J_2 spin-1/2-Heisenberg antiferromagnet on the square lattice. For the DM term we consider several symmetries corresponding to different crystal structures. For the pure J_1-J_2 model there are strong indications for a quantum spin liquid in the region of 0.4 < J_2/J_1 < 0.65. We find that a DM interaction influences the breakdown of the conventional antiferromagnetic order by i) shifting the spin liquid region, ii) changing the isotropic character of the groundstate towards anisotropic correlations and iii) creating for certain symmetries a net ferromagnetic moment.
We present a spin-1/2 bilayer model for the quantum order-disorder transition which (i) can be solved by mean-field theory for bulk quantities, (ii) becomes critical at the transition, and (iii) allows to include intralayer frustration. We present numerical data (for systems with up to 240 sites) and analytical results for the critical coupling strength, ground-state energy, order parameter and for the gap. We show that the critical coupling decreases linearly with frustration.
We study the zero-temperature phase diagram of a square-lattice $S=1/2$ Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbor exchange constants, $J_1>0$ (antiferromagnetic) and $-\infty < J_2 < \infty $, using spin-wave series based on appropriate mean-field Hamiltonian and exact-diagonalization data for small clusters. At a quasiclassical level, the model displays two critical points separating the Néel state from (i) a helicoidal magnetic phase for relatively small frustrating ferromagnetic couplings $J_2<0$ ($J_2/J_1<-1/3$ for classical spins), and (ii) a finite-gap quantum paramagnetic phase for large enough antiferromagnetic exchange constants $J_2>0$. The quantum order-disorder transition (ii) is similar to the one recently studied in two-layer Heisenberg antiferromagnets and is a pure result of the zero-point spin fluctuations. On the other hand, the melting of the Néel state in the ferromagnetic region, $J_2<0$, is a combined effect of the frustration and quantum spin fluctuations. The second-order spin-wave calculations of the ground-state energy and on-site magnetization are in accord with our exact diagonalization data in a range away from the quantum paramagnetic phase. In approaching the phase boundary, the theory fails due to the enhanced longitudinal spin fluctuations, as it has recently been argued by Chubukov and Morr.
We reconsider the results cocerning the extreme-quantum $S=1/2$ square-lattice Heisenberg antiferromagnet with frustrating diagonal couplings ($J_1-J_2$ model) drawn from a comparison with exact-diagonalization data. A combined approach using also some intrinsic features of the self-consistent spin-wave theory leads to the conclusion that the theory strongly overestimates the stabilizing role of quantum flutcuations in respect to the Néel phase in the extreme-quantum case $S=1/2$. On the other hand, the analysis implies that the Néel phase remains stable at least up to the limit $J_{2}/J_{1} = 0.49$ which is pretty larger than some previous estimates. In addition, it is argued that the spin-wave ansatz predicts the existence of a finite range ($J_{2}/J_{1}<0.323$ in the linear spin-wave theory) where the Marshall-Peierls sigh rule survives the frustrations.
We present a number of arguments in favor of the suggestion that the Marshall-Peierls sign rule survives the frustration in the square-lattice Heisenberg antiferromagnet with frustrating next-nearest-neighbor (diagonal) bonds ($J_{1}-J_{2}$ model) for relatively large values of the parameter $J_{2}/J_{1}$. Both the spin-wave analysis and the exact-diagonalization data concerning the weight of Marshall states support the above suggestion.