Spectral Gaps in Quantum Spin Systems
Spectral Gaps in Quantum Spin Systems
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Marius Lemm, Harvard University
Quantum spin systems are many-body models which are of wide interest in modern physics and at the same time amenable to rigorous mathematical analysis. A central question about a quantum spin system is whether its Hamiltonian exhibits a听spectral听gap above the ground state. The existence of such a听spectral听gap has far-reaching consequences, e.g., for the ground state complexity. In this talk, we survey recent progress on deriving听spectral听gaps听for frustration-free quantum spin systems in dimensions greater than 1, in particular, in the antiferromagnetic models of Affleck-Kennedy-Lieb-Tasaki (AKLT).