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Events
A Quantum Afternoon

MPI for Mathematics in the Sciences

G3 10 (Lecture hall)

seminar

02.09.25

A Quantum Afternoon

seminar

02.09.25

A Quantum Afternoon

- Previous Events

Previous Events


02.09.25	Otto Schmidt (Università die Trento + MPI MiS, Leipzig) : Beyond Gutzwiller: Exploring correlated excitations with perturbative tensor networks The Mott insulator–superfluid transition in the one-dimensional Bose–Hubbard model is a paradigmatic example of a second-order quantum phase transition. While mean-field approaches capture the transition itself, they fail to accurately describe correlated excitations in the Mott phase. We introduce a perturbative tensor network ansatz based on the Bogoliubov–de Gennes (BdG) equations that overcomes this limitation. Our results demonstrate that BdG excitations provide both conceptual insight and quantitative accuracy for correlated excitations in the Mott phase. Moreover, we establish a connection between these excitations and tangent vectors on the tensor network variety.
02.09.25	Claire de Korte (MPI MiS, Leipzig) : Charge Conservation Equations as a Test of the Validity of Field Theories in de Sitter Space In order for a field theory in de Sitter space to be physically consistent, it must satisfy a series of equations called charge conservation relations. These relations are generated iteratively, and can be expressed in the form of polynomial equations. The process for generating these equations is long and complicated, and it is unclear for which theories the process will converge on a single solution set. The purpose of our research is to study these systems of equations and their solutions to see if we can determine for which theories there is convergence.
02.09.25	Svala Sverrisdottir (MPI MiS, Leipzig) : Algebraic varieties in second quantization We develop algebraic geometry for coupled cluster theory in second quantization. In quantum chemistry, electronic systems are represented by binary tensors. The creation and annihilation operators of particles generate a Clifford algebra known as the Fermi-Dirac algebra. We present a non-commutative Gröbner basis giving an alternative proof of Wick's theorem, a foundational result in quantum chemistry. In coupled cluster theory, the Schrödinger equation is approximated through a hierarchy of polynomial equations at various levels of truncation. The exponential parameterization gives rise to truncation varieties. This reveals well-known varieties, such as the Grassmannian, flag varieties and spinor varieties. We offer a detailed study of the truncation varieties and their CC degrees.