Spin-Peierls transition in an anisotropic two-dimensional XY model

TL;DR

This paper investigates the zero-temperature spin-Peierls transition in an anisotropic 2D XY model using Jordan-Wigner transformation, revealing phase boundaries and critical couplings in the parameter space.

Contribution

It provides a detailed phase diagram for the spin-Peierls transition in an anisotropic 2D XY model, including the critical spin-lattice coupling dependence on interchain coupling.

Findings

Spin-lattice coupling must exceed a critical value to induce dimerization.

The critical coupling depends on interchain coupling as -1/ln h.

The transition is first-order for h > 10^{-3}.

Abstract

The two-dimensional Jordan-Wigner transformation is used to investigate the zero temperature spin-Peierls transition for an anisotropic two-dimensional XY model in adiabatic limit. The phase diagram between the dimerized (D) state and uniform (U) state is shown in the parameter space of dimensionless interchain coupling $h$ $(=J_{\perp}/J)$ and spin-lattice coupling $\eta$. It is found that the spin-lattice coupling $\eta$ must exceed some critical value $\eta_c$ in order to reach the D phase for any finite $h$. The dependence of $\eta_c$ on $h$ is given by $-1/\ln h$ for $h\to 0$ and the transition between U and D phase is of first-order for at least $h>10^{-3}$.