# A quantum magnetic analogue to the critical point of water

**By Frédéric Mila, EPFL
**Based on article published in Nature

In 1822, almost two centuries ago, a French engineer Charles Cagniard de la Tour discovered that above a pressure of 221 bar water does not boil anymore, but forms a single phase that evolves smoothly from densities typical of water at low temperature to densities typical of the gas phase at high temperature. In the pressure-temperature phase diagram, boiling stops at a critical point P=221 bar and T=374^{o} C. Later investigations revealed that at this point the system is scale invariant (density-density correlations decay algebraically), and that several quantities, in particular the specific heat, diverge.

In the present paper [1], we report on a similar behavior discovered in SrCu_{2}(BO_{3})_{2}, a spin-1/2 frustrated quantum antiferromagnet that is an almost perfect realization of the Shastry-Sutherland model (see Fig. 1). As in water, the specific heat diverges at an isolated point in the pressure-temperature phase diagram, and we have shown, thanks to an investigation of the finite-temperature properties of the Shastry-Sutherland model with tensor-network algorithms, that this is a critical point terminating a line of first-order transitions (the equivalent of the boiling line in water). This line starts at zero temperature when the exact dimer-singlet phase is abruptly replaced by a plaquette phase, and it continues up to a critical point whose location agrees quantitatively with experiments.

*Fig.1: Specific heat C/T of SrCu2(BO3)2 as a function of temperature and pressure. The critical point is around 20 kbar and 3.3 K. Inset: the orthogonal dimer lattice of SrCu2(BO3)2 (topologically equivalent to the Shastry-Sutherland model) with intradimer coupling JD and interdimer coupling J.*

After three decades of intensive investigation of quantum critical points at which systems undergo a continuous phase transition at zero temperature, the present work opens a new avenue in quantum magnetism by demonstrating that discontinuous phase transitions can also lead to critical points, but at finite temperature, with applications in several fields including spin-orbit dominated magnets with topological properties that are potentially useful for spintronic applications.

[1] //doi.org/10.1038/s41586-021-03411-8