search

SunnySuite / Sunny.jl

Spin dynamics and generalization to SU(N) coherent states
Other
86 stars 19 forks source link

Stable bogoliubov transform #143

Closed Lazersmoke closed 1 year ago

Lazersmoke commented 1 year ago

This modifies the algorithm used to compute the bogoliubov transform very minorly. It sets the sign of the real part of the first entry of each eigenvector to be positive so that calling bogoliubov! on nearby hamiltonians results in nearby (or at least near-er than before) bogoliubov transform matrices. Is this allowed @Hao-Phys ? Can the eigenvectors be rotated by arbitrary phases, or just multiplied by -1? It may be even more stable to rotate them to have first entry real rather than simply positive real part.

This is in preparation for differentiating through bogoliubov! in some clever way.

Hao-Phys commented 1 year ago

Hi @Lazersmoke. If I understand correctly, you are trying to fix the U(1) gauge for the eigenvectors. Yes, in principle, the phase should be arbitrary. However, I am not sure about your criterion for fixing the gauge.

kbarros commented 1 year ago

Let's postpone this until we reach a conclusion about the strategies for gradient calculation.