CMSA Strongly Correlated Quantum Materials and High-Temperature Superconductors Seminar: Order Fractionalization*

I will discuss the interplay of spin fractionalization with broken symmetry.   When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter.   The concept of "order fractionalization" enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial

order[1].

A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2].  This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an

order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed.

* Work done with Yashar Komijani, Anna Toth, Premi Chandra and Alexei Tsvelik.

[1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018).

[2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).