Non-Gaussian fermionic ansatzes from many-body correlation measures


Herasymenko, Y. (2023). Non-Gaussian fermionic ansatzes from many-body correlation measures. Perimeter Institute. https://pirsa.org/23080032


Herasymenko, Yaroslav. Non-Gaussian fermionic ansatzes from many-body correlation measures. Perimeter Institute, Aug. 08, 2023, https://pirsa.org/23080032


          @misc{ pirsa_PIRSA:23080032,
            doi = {10.48660/23080032},
            url = {https://pirsa.org/23080032},
            author = {Herasymenko, Yaroslav},
            keywords = {Condensed Matter},
            language = {en},
            title = {Non-Gaussian fermionic ansatzes from many-body correlation measures},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {aug},
            note = {PIRSA:23080032 see, \url{https://pirsa.org}}
Talk Type Scientific Series


The notorious exponential complexity of quantum problems can be avoided for systems with limited correlations. For example, states of one-dimensional systems with bounded entanglement are approximable by matrix product states. We consider fermionic systems, where correlations can be defined as deviations from Gaussian states. Heuristically, one expects a link between compact non-Gaussian ansatzes and bounded fermionic correlations. This connection, however, has not been rigorously demonstrated. Our work resolves this conceptual gap.

We focus on pure states with a fixed number of fermions. Generalizing the so-called Plücker relations, we introduce k-particle correlation measures ω_k. The vanishing of ω_k at a constant k defines a class H_k of states with limited correlations. These sets H_k are nested, ranging from Gaussian for k=1 to the full n-fermion Hilbert space H for k=n+1. States in H_{k=O(1)} can be represented using a non-Gaussian ansatz of polynomial size. Classes H_k have physical meaning, containing all truncated perturbation series around Gaussian states. We also identify non-perturbative examples of states in H_{k=O(1)}, by a numerical study of excited states in the 1D Hubbard model. Finally, we discuss the information-theoretic implications of our results for the widely used coupled-cluster ansatz.

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