Maxime Debertolis

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Quantum impurity problems are known to exhibit a compact representation of their ground state or for quench protocols when an optimized single-particle basis is chosen. This work extends the study of single-particle rotations taylored to operators in the Heisenberg picture. We present the concept of natural super-orbitals for many-body operators, defined as the eigenvectors of the one-body super-density matrix associated with a vectorized operator. These objects are related to measures of non-Gaussianity of operators associated to the occupations of the natural super-orbitals. We perform a numerical investigation of the natural super-orbitals corresponding to both the time-evolution operator and a time-evolved local operator in the t-V model and in a quantum impurity model using tensor network simulations. In the quantum impurity model, occupations of the natural orbitals for both operators decay exponentially at all times. More surprisingly, the non-Gaussianity of the local operator saturates in time. This indicates that only a small number of orbitals contribute significantly “many-body-ness” of the operator, enabling a compact matrix-product-operator representation. This framework opens the door to future research that leverages the compressed structure of operators in their natural super-orbital basis to perform efficient time evolution of operators whose non-Gaussianity is low and structured.

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Universität Bonn
0.03
Contact: Neil Dowling