Finite-temperature critical points and quantum critical end point in a 2D magnet

The Mermin–Wagner theorem has long told us that in two dimensions a continuous symmetry can be broken, allowing a finite order parameter, only at zero temperature. Now PSI theorist Bruce Normand, working with colleagues in Aachen, Amsterdam, Lausanne and Paris, has circumvented this rule.

The team was considering the thermodynamics

of a two-dimensional quantum magnet, the spin-½ frustrated Heisenberg bilayer. This is a model in which, by working in a basis of the dimer bonds connecting the two layers, the infamous quantum Monte Carlo (QMC) sign problem can be reduced, and even eliminated when the frustration is perfect. In this limit, the ground state is based on pure dimer singlets or dimer triplets, the two separated by a first-order transition. As they report in a paper published today in Physical Review Letters [1], the researchers showed by QMC that this transition persists to finite temperatures, but then the first-order line terminates at a critical point, just like the critical point in the liquid–gas phase diagram. They found that this critical point is in the Ising universality class, the additional binary variable arising from the two-site unit cell of the lattice (and not in fact violating Mermin–Wagner).

The first-order transition in the ground state runs across the entire phase diagram from full frustration to no frustration, and the team showed that a line of finite-temperature critical points should follow it all the way. However, at low frustration the system has an additional line of second-order quantum phase transitions between an ordered magnetic bilayer and the dimer-singlet state. This line terminates on the first-order line, providing a rare example of a `quantum critical end point' (QCEP, meaning the end of a second-order line). The authors used tensor-network calculations to follow the first-order discontinuities in the vicinity of the QCEP, which is a phenomenon yet to be investigated in detail.