POLFED - a new diagonalization approach to study non-equilibrium phenomena
Piotr Sierant (ICFO)
Abstract: I will describe polynomially filtered exact diagonalization (POLFED) method of computing eigenvectors of large sparse matrices at arbitrary energies - a task that often arises when studying non-equilibrium phenomena in quantum many-body systems. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a spectral transformation using a high order polynomial of the matrix. The memory requirements scale much better with system size than in the state-of-the-art shift-invert approach, while the total CPU time used by the two methods is similar. Also, the performance of POLFED is not severly impeded when the the number of non-zero elements in the matrix is increased allowing to efficiently study models with long-range interactions. A straightforward modification allows POLFED to investigate spectra of large Floquet unitary operators. I will demonstrate the potential of POLFED examining many-body localization transition in 1D interacting quantum spin-1/2 chains.
condensed matterHEP - theory
Audience: researchers in the topic
Numerical Methods in Theoretical Physics
Organizers: | Anosh Joseph, Byungmin Kang, Dario Rosa, Masaki Tezuka, Junggi Yoon* |
*contact for this listing |