Mi-Song Dupuy - Sparse and symmetry-preserving compression of matrix product operators

Recorded 04 May 2022. Mi-Song Dupuy of Sorbonne Université, Mathematics, presents "Sparse and symmetry-preserving compression of matrix product operators" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop.
Abstract: Efficient representations of the Hamiltonian in the tensor train format, also known as matrix product operators (MPO), is central in QC-DMRG. Although exact representations can be achieved with ranks scaling as O(L²), where L is the number of sites, this can be lowered using the TT-SVD algorithm. It is however well-known that the resulting MPO generically breaks the symmetries of the original Hamiltonian, namely the Hermitian symmetry and the particle number conservation. In this talk, we show that MPO of Hamiltonians in QC-DMRG have a particular structure that can be exploited to design a symmetry-preserving compression scheme. This is a joint work with Siwar Badreddine, Matthias Beaupere, Eric Cances and Laura Grigori.
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