Magnetization Plateaus in One Dimensional $\v{S}=1/2$ Heisenberg Model with Dimerization and Quadrumerization

TL;DR

This study investigates magnetization plateaus in a one-dimensional $S=1/2$ Heisenberg model with dimerization and quadrumerization, revealing the existence of a plateau at half saturation and analyzing its critical properties using numerical and conformal field theory methods.

Contribution

It demonstrates the existence of a magnetization plateau at half saturation for non-zero quadrumerization and provides a detailed analysis of the critical exponents and effective theories involved.

Findings

Magnetization plateau exists for $ eq 0$ quadrumerization.

Critical exponent $ u$ varies non-monotonically with $j$.

Conformal field theory describes the system at $oxed{0}$.

Abstract

The one dimensional $S=1/2$ Heisenberg model with dimerization ($1-j$) and quadrumerization ($\delta$) in the magnetic field is studied by means of the numerical exact diagonalization of finite size systems and the conformal field theory. It is found that the magnetization plateau at half of the saturation value exists for $\delta \neq 0$. For $\delta = 0$, this model is described by the conformal field theory with central charge $c=1$ at this value of magnetization. The critical exponent $\nu$ which characterizes the $\delta$-dependence of the width of the plateau is calculated using the level spectroscopy method. The $j$-dependence of the critical exponent $\nu$ is found to be non-monotonic and discontinuous at $j = 0$. The effective theory of the magnetization plateau is also presented for various limiting cases.