Found 2 result(s)
Regular Seminar Paul Fendley (Oxford)
Traditionally, most studies of quantum many-body systems have been mainly concerned with properties of the states of low-lying energy. Recently, however, fascinating features of the full energy spectrum have been uncovered. Among these are eigenstate phase transitions, where sharp transitions occur not only in the ground state, but in all the states. I describe a simple example of such, a transition for a strong zero mode in the XYZ spin chain. The strong zero mode is an operator that pairs states in different symmetry sectors, resulting in identical spectra up to exponentially small finite-size corrections. Such pairing occurs in the Ising/Majorana fermion chain and possibly in parafermionic systems and strongly disordered many-body localized phases. My proof here shows that the strong zero mode occurs in a clean interacting system, and that it possesses some remarkable structure – despite being a rather elaborate operator, it squares to the identity.
Regular Seminar Paul Fendley (University of Virginia, USA)
I discuss how systems with non-abelian anyons can be used to build a topological quantum computer. Operations are performed by braiding the anyons, because the outcome of braiding is a purely topological property, such quantum computers should be robust against local errors. I will give several examples of how such anyons arise in fractional quantum Hall systems and in quantum loop models. Mathematical byproducts of this work are algebraic proofs and extensions of Tutte's identities for the chromatic polynomial (the zero-temperature Potts-model partition function).