Quantum Lunch: PEPS: Boundaries and spectral gap – University of Copenhagen

Forward this page to a friend Resize Print kalender-ikon Bookmark and Share

QMath > Events > Quantum Lunch > w17 Angelo Lucia

Quantum Lunch: PEPS: Boundaries and spectral gap

Speaker: Angelo Lucia from QMATH

Title: PEPS: Boundaries and spectral gap

Abstract:
In quantum spin models, one of the crucial characteristic of
Hamiltonians is whether the spectral gap - the difference between the two
lowest eigenvalues - is lower bounded by a non-zero constant independent of the
system size. For the specific case of parents Hamiltonians of PEPS, we have the
advantage of having a complete description of the groundstate space, which
provides us a path for bounding the gap. I will introduce the notion of
boundary (unnormalized) states for 1D and 2D systems and show how to prove a
lower bound to the spectral gap if these are thermal states of local
Hamiltonians.

This will be a follow-up to Michael Kastoryano's Quantum Lunch of March 15th. I
will try to get into the details of the proof and present some of the technical
problems.