by Dr. Abhishodh Prakash, Harishchandra Research Institute, Allahabad

Abstract: 

Striking examples of phase transitions in everyday life are the boiling and freezing of water. However, only one of these (freezing) is considered a genuine transition separating distinct phases. The transition separating liquids and gases abruptly terminates and thus, the two are nominally the same phase. This liquid-gas transition, which seemingly has no business existing, is nevertheless ubiquitous and seen in many phase diagrams. There has been no explanation for this although this information is often repurposed as a warning not to take first-order transitions seriously for they are fickle and might abruptly terminate. Interest in such terminating transitions was recently reinvigorated by the discovery that even continuous second order transitions can abruptly terminate — a phenomenon dubbed 'unnecessary criticality’ [1,2]. In this talk, I will argue that such terminating transitions, both first and second order, arise due to the non-trivial topology of the family of states surrounding them [3]. This manifests itself in the form of non-contractible loops, spheres etc in parameter space and terminating transitions are obstructions to their contraction, much like the core of a superfluid vortex. Examples of topologically non-trivial families of states have been known in the past, eg: Berry’s quantum spin in magnetic field and Thouless’s charge pump. I hope to convey that their presence in phase diagrams can lead to new and interesting physical consequences. 

 

[1] https://journals.aps.org/prx/abstract/10.1103/PhysRevX.9.021034

[2] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.256401

[3] https://arxiv.org/abs/2408.15351