Spin-Peierls Dimerization of a \(\mib{s}=\frac{{\bf 1}}{{\bf 2}}\) Heisenberg Antiferromagnet on a Square Lattice

Abstract

Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice is investigated by taking unexpanded exchange couplings. Several dimerized configurations are considered some of which are shown to have lower ground state energies than others. In particular, the lattice deformations resulting in alternate strong and weak couplings along both the principal axes of a square lattice are shown to result in a larger gain in energy. In addition, a 'columnar' configuration is shown to have a lower ground state energy and a faster increase in the energy gap parameter than a 'staggered' configuration. The inclusion of unexpanded exchange coupling leads to a power law behaviour for the magnetic energy gain and the spin-Peierls gap, which is qualitatively different from that reported earlier. Instead of varying as δ x , the two quantities are shown proportional to δ ν / |ln δ| . It is thus proposed that the logarithmic correction, that was regarded as an outcome of including umklapp processes for small distortions, can also be a direct consequence of using an un-truncated spin-spin exchange interaction. The calculations, which employ the coupled cluster method, lead to a conclusion result that the dimerization of a spin-half Heisenberg antiferromagnet on a sqaure lattice is unconditional.

Frustration-Induced Valence-Bond Ordering in a New Quantum Triangular Antiferromagnet Based on [Pd(dmit)2]

“…Although such explicit relevance does not generally exist in the 2D cases, VB ordering with lattice-symmetry breaking is often referred to as a spin-Peierls state in the literature, with respect to similar real-space physics. The VB order (or VB solid, VBS) ground state in 2D systems has been studied theoretically, [30][31][32][33][34][35][36][37][38][39][40] as well as the on-bond charge-densitywave states, 30,31,[41][42][43] particularly on the square lattice (with frustrated interactions). Unlike the 1D cases, the stability of the 2D VB order is not trivial.…”

Néel to spin-Peierls transition in a quasi-one-dimensional Heisenberg model coupled to bond phonons

“…The spatially isotropic 2D spin- 1 2 Heisenberg model with static dimerization patterns has been studied by several authors. [8][9][10][11][12][13] In these previous works, the energetically most favored dimerization pattern was predicted by comparing the ground state energies for different patterns. Using this same method, the 2D tight binding model with bond-distortions 14 and the 2D Peierls-Hubbard model [15][16][17] have also been studied.…”

Thermodynamic properties of the two-dimensionalS=12Heisenberg antiferromagnet coupled to bond phonons

“…15,16 In the case of the 2D S = 1/2 Heisenberg antiferromagnet with spin phonon coupling discussions of statically dimerized models are found in the literature. 17,18,19,20,21 As in one dimension, these models are thought to de-scribe the dimerized phase of dynamical models in the adiabatic limit. In contrast to the 1D case though it is not clear how to place alternating magnetic couplings in both spatial directions on a square lattice.…”