2025-10-02 –, Jean-Baptiste Say Amphitheater
Language: English
Quantum many-body problems famously scale very badly and sometimes it cannot be avoided to work with a Hilbert space of infinite dimension. Rimu.jl can represent a Hamiltonian as a sparse matrix and implements a projector Monte Carlo method that can sample the ground and low-lying eigenstates, even when the matrix size is huge. This talk will introduce the Rimu.jl package and focus on updates since the JuliaCon24 talk. The highlights will include a new link to the quantum chemistry package ElemCo.jl and a bias-free taming of the Monte Carlo sign problem in the Fröhlich polaron model with a formally and practically infinite Hilbert space.
Rimu.jl aims to be an extensible platform for quantum many-body calculations. The problem of finding the energy and properties of the ground and low-lying excited quantum states is central to many important questions in quantum chemistry and condensed-matter physics. Formally these problems map into the linear algebra problem of finding the eigenvectors and eigenvalues of a large matrix. The size of the matrix scales very badly, typically exponentially, with the size of the physical system. Rimu.jl implements matrix-based and matrix-free exact diagonalisation, which has seen a significant upgrade and improved speed since last year's JuliaCon24 talk. When the matrix dimension is so large that eigenvectors can no longer be stored in memory, Rimu.jl can still help and sample the eigenstate with projector Monte Carlo, which is implemented in the flavour of full configuration interaction quantum Monte Carlo (FCIQMC). Rimu.jl is written in pure Julia and highly extensible. Computations are fully parallelised using native threading and MPI on HPC clusters.
In this talk I will highlight a recent application where the Monte Carlo sign problem for calculating excited states could be overcome by walker annihilation in the Fröhlich polaron model with a formally infinite linear dimension. I will further report on recent progress with linking Rimu.jl with the quantum chemistry package ElemCo.jl and the JuliaMolSim ecosystem and implementing a molecular Hamiltonian.
Joachim is a theoretical and computational physicist interested in quantum many-body physics, quantum simulation, and quantum technology.