Monte Carlo studies of diamagnetism and charge density wave order in the cuprate pseudogap regime

The pseudogap regime of the hole-doped cuprate superconductors is often characterized experimentally in terms of a substantial diamagnetic response and, from another point of view, in terms of strong charge density wave (CDW) order. We introduce a dimensionless ratio, $R$, that incorporates both diamagnetic susceptibility and the correlation length of CDW order, and therefore reconciles these two fundamental characteristics of the pseudogap [PRB 90, 094515 (2014)]. We perform Monte Carlo simulations on a classical model that considers angular fluctuations of a six-dimensional order parameter [Science 343, 1336 (2014)], and compare our Monte Carlo results for $R$ with existing data from torque magnetometry and x-ray scattering experiments on YBa$_2$Cu$_3$O$_{6+x}$. We achieve qualitative agreement, and also propose future experiments to further investigate the behaviour of this dimensionless ratio.