Using Quantum Fluctuations to Regularize an Analytic Continuation Problem from Many-Body Physics
Date of Award
Ph.D. in Physics
University of Mississippi
Extracting spectral information via inversion from Quantum Monte Carlo sampled data isa difficult task. There is a need to analytically continue noisy and often incomplete imaginary-time data into the full complex domain. A new approach is proposed that uses the quantum fluctuations of spin momenta to regularize the inversion. A one-dimensional Heisenberg chain in the presence of a transverse field is first encoded with synthetic data representing several classes of spectral functions and then run through a Density Matrix Renormalization Group algorithm to find its ground state. This solution corresponds to a probable, high quality solution to the inversion. Using optimization constraints and sampling techniques, forward model spectra are replicated by inversion that capture distinguishing characteristics that are often washed out in methods that favor smoothed out solutions.
Coleman, Lucretius, "Using Quantum Fluctuations to Regularize an Analytic Continuation Problem from Many-Body Physics" (2022). Electronic Theses and Dissertations. 2362.