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Parent Hamiltonians of ergodic matrix product states
Mathematical Physics| Speaker: | Owen Ekblad, MSU |
| Location: | 3024 PDSB |
| Start time: | Wed, May 20 2026, 4:10PM |
Description
Matrix product states (MPS) are an important class of states on quantum spin chains. Under a translation-invariance assumption, thermodynamic limits of MPS have been well-studied, but without this assumption, MPS are less well-understood. In this talk, I will discuss ongoing collaborative work with E. Moreno-Nadales, E. Roon, and J. Schenker on thermodynamic limits of ergodic matrix product states (EMPS), which are matrix product states defined by local tensors that are not translation-invariant but rather statistically translation-invariant. We establish general conditions for the uniqueness of thermodynamic limits of EMPS, construct an interaction on the spin chain whose unique frustration-free ground state is the EMPS, and discuss the quantitative properties of this interaction, giving a description of its physical properties in terms of the statistics of the EMPS. Notably, unlike their translation-invariant counterparts, EMPS are typically not gapped, and our work points to explicit quantities that explain why this is the case, which I will also discuss.