I will discuss recent work proving that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system spectral gaps uniform in the system size. To obtain this result, we extend the Bravyi-Hastings-Michalakis strategy so it can be applied to perturbations of the GNS Hamiltonian of the infinite-system ground state.

Stability of the bulk gap for quantum lattice systems Sponsored by the Meyer Fund

Thu, Apr. 20 3:35pm (MATH 3…

Probability

Bojan Basrak (University of Zagreb)

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Using the example of stationary subcritical branching processes with immigration, we discuss two essentially different ways in which power law tails can arise. For instance, if the immigrant distribution is regularly varying, then the same property holds for the stationary distribution. In this talk, we explain how the assumption that the branching takes place in a random environment also induces power law tail behavior of the stationary distribution. We explore probabilistic properties of the resulting stationary process. The original motivation comes from the seminal 1975 paper by Kesten, Kozlov, and Spitzer, which relates random walks in random environment models to a special Galton-Watson process with immigration in random environment. We show how our approach leads to new results even in this well-studied setting.

This talk is based on joint work with P. Kevei (University of Szeged).

On stationary branching models and random walks in random environment