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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 2: Correlated States

MP 2.1: Hauptvortrag

Dienstag, 17. März 2026, 11:00–11:30, KH 02.013

Frustration free Hamiltonians for Finitely Correlated States – ground space structure and spectral gap — •Norbert Schuch — Universität Wien, Wien, Austria

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.

Keywords: finitely correlated states; tensor networks; spin chains; ground states; spectral gaps