Understand
The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the underlying quantum critical point.
- Here, we employ quantum Monte Carlo simulations to examine these relations in detail for two-dimensional quantum systems that exhibit a finite-temperature Ising-transition line in the vicinity of a quantum critical point that belongs to the universality class of either (i) the three-dimensional Ising model for the case of the quantum Ising model in a transverse magnetic field on the square lattice or (ii) the ${\it chiral}$ Ising transition for the case of a half-filled system of spinless fermions on the honeycomb lattice with nearest-neighbor repulsion.
- While the first case allows large-scale simulations to assess the scaling predictions to a high precision in terms of the known values for the critical exponents at the quantum critical point, for the later case we extract values of the critical exponents $\nu$ and $\eta$, related to the order parameter fluctuations, which we discuss in relation to other recent estimates from ground state quantum Monte Carlo calculations as well as analytical approaches.