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Undecidability of the Spectral Gap in 1D

Event Details

Event Dates: 

Monday, April 23, 2018 - 1:30pm

Seminar Location: 

  • JILA X317

Speaker Name(s): 

Johannes Bausch

Speaker Affiliation(s): 

University of Cambridge
Seminar Type/Subject

Scientific Seminar Type: 

  • JILA Public Seminar

Event Details & Abstract: 

In this work, we show that for local Hamiltonians in 1D with translationally invariant nearest neighbour interactions, deciding whether or not the system is gapped or gapless, is undecidable. In order to prove this, we need to go beyond the already-known 2D case, and replace a fractal Robinson tiling---only possible in more than one dimension---with a specific Hamiltonian that has a type of attractive force in its ground state. We further need to augment the quantum phase estimation algorithm to self-detect whether it succeded in its expansion.

Joint work with T. Cubitt, A. Lucia and D. Perez-Garcia