Free probability approach to the energy gap problem

Finding a quantum phase transition between two even well-studied phases of matter can be a hard problem. Free probability theory suggests a new method which can give an answer if the Hamiltonians of two phases satisfy certain conditions. In the latter case, the spectral gap behavior can be calculated without solving the full Hamiltonian but using probabilistic estimation instead. As an example, I will consider generic artificial topological systems created by a periodic drive, including Floquet Majorana modes, and show how FPT can be used to predict and characterize disorder-driven phase transitions.

See also: Phys. Rev. Lett. 121, 126803

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Friday, November 30, 2018 - 11:00 to 12:30
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