Strong edge zero modes in interacting systems

Thesis

I will discuss how edge spins in certain one-dimensional spin chains retain memory of their initial state for very long times, even with interactions and at infinite temperature. These long coherence times do not require disorder or integrability. I will show how this is a consequence of an "almost" strong edge zero mode that almost commutes with the Hamiltonian, and explain how to compute this operator explicitly with computer-aided algebra. I will examine the effect of this almost strong zero mode on the behaviour of a wide variety of one-dimensional systems analytically, from the ground state to infinite temperature, and from finite size to the thermodynamic limit. I will also examine the effect of the almost strong zero mode on the eigenstate spectrum and the matrix elements of the edge spin, and show that despite the long coherence time of the edge spin, the almost strong zero mode does not induce degeneracies in the entire spectrum, unlike its counterpart exact strong zero mode in non-interacting systems. At special values of the couplings, resonances dramatically limit the coherence time. I will explain how these resonances are related to physical processes which flip the edge spin for no change in the energy of the system, and calculate the coupling strengths for which they appear. I will propose an experimental test of the almost strong zero mode and the long coherence time of the edge spin in a trapped ion chain which is feasible to implement with current technology. Lastly, I will explain how these almost strong edge zero modes in a system with symmetry-protected topological order can be used to form a boundary qubit with both long decoherence and dephasing times.

Authors: Kemp, J

• DOI: 10.5287/ora-koja4aeen
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Subjects: Condensed matter