Certified spectral gaps for frustration free spin chains

Speaker: Norbert Schuch (University of Vienna)
Series: Isaac Newton Institute Seminar Series
Note: MMBW03 - Structure of entanglement

I will discuss some recent results on how to obtain rigorous and accurate computer-assisted lower bounds on the spectral gap of any frustration free spin chain. I will present two methods: The first builds on the martingale method of Fannes, Nachtergaele, and Werner, and the second on semidefinite programming. As a cherry on the cake, the first method also yields a much simplified proof - free of computer assistance - for the existence of a spectral gap of any parent Hamiltonian of Matrix Product States.