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Frustration free Hamiltonians for Finitely Correlated States – ground space structure and spectral gap

Activity: Talks and presentations › Talk or oral contribution › Science to Science

Description

Finitely Correlated States (FCS), or Matrix Product States, form an efficiently representable class of states on infinite spin chains, with the AKLT model as a prominent example. I will present some new findings on FCS and their parent Hamiltonians – frustration free Hamiltonians constructed to have the FCS as an exact ground state. First, I will discuss how such Hamiltonians can have a remarkably rich ground space structure, ranging from unique ground states and critical systems all the way to systems with undecidable ground space structure. Second, I will explain how to use hierarchies of semidefinite relaxations to systematically obtain rigorous and precise lower bounds on the spectral gaps of such models, which provably improve on all known methods to bound such gaps.
Period17 Mar 2026
Event title89th Annual Conference of the DPG and DPG Spring Meeting of the Matter and Cosmos Section
Event typeConference
LocationErlangen, Germany, BavariaShow on map

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