Speaker: Dr. Flavio Baccari (Università di Padova, Italy)

December 5, 2024 at 16:00 in Room 0M04 - Department of Physics - Federico II

Abstract

Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad applicability, ranging from many-body physics to quantum computing and classical sampling techniques. In this talk I will present a general method for obtaining lower bounds on the spectral gap of frustration-free quantum Hamiltonians in the thermodynamic limit. We formulate the gap certification problem as a hierarchy of optimization problems (semidefinite programs) in which the certificate -- a proof of a lower bound on the gap -- is improved with increasing levels. The approach encompasses existing finite-size methods, such as Knabe's bound and its subsequent improvements, as those appear as particular possible solutions in our optimization, which is thus guaranteed to either match or surpass them. I will demonstrate the power of the method on one-dimensional spin-chain models where we observe an improvement by several orders of magnitude over existing finite size criteria in both the accuracy of the lower bound on the gap, as well as the range of parameters in which a gap is detected.

Online: Online participation via MS Teams link . IMPORTANT: In case your access is denied, log out from your institutional account and open MS Teams in your web browser.

A complete list of the past and upcoming seminars can be found here: https://www.qst.unina.it/?page_id=54.

The QST Seminars Group