The J1-J2 Heisenberg model at and close to its z=4 quantum critical point

TL;DR

This paper investigates the quantum critical behavior of the frustrated J1-J2 Heisenberg model near its z=4 quantum critical point, revealing a divergence in susceptibility with temperature that differs from classical predictions.

Contribution

It provides a comprehensive analysis combining field theory, spin-wave theory, and numerical methods to characterize quantum criticality in the J1-J2 model near the z=4 QCP.

Findings

Susceptibility diverges as T^{-1.2} at the QCP in the quantum model

Classical model shows susceptibility diverging as T^{-4/3}

Numerical and analytical methods confirm the quantum critical behavior

Abstract

We study the frustrated J1-J2 Heisenberg model with ferromagnetic nearest neighbor coupling J1<0 and antiferromagnetic next-nearest neighbor coupling J2>0 at and close to the z=4 quantum critical point (QCP) at J1/J2=-4. The J1-J2 model plays an important role for recently synthesized chain cuprates as well as in supersymmetric Yang Mills theories. We study the thermodynamic properties using field theory, a modified spin-wave theory as well as numerical density-matrix renormalization group calculations. Furthermore, we compare with results for the classical model obtained by analytical methods and Monte-Carlo simulations. As one of our main results we present numerical evidence that the susceptibility at the QCP seems to diverge with temperature T as chi ~ T^{-1.2} in the quantum case in contrast to the classical model where chi ~ T^{-4/3}.