Extraction of Spectra in the Shell Model Monte Carlo Method Using Imaginary-Time Correlation Matrices

Area of Science:

• Nuclear physics
• Computational physics
• Quantum many-body systems

Background:

• Conventional configuration-interaction (CI) shell model methods struggle with large nuclear model spaces.
• Shell Model Monte Carlo (SMMC) is effective for nuclear observables but extracting spectra is difficult.

Purpose of the Study:

• To develop a novel method for extracting low-lying nuclear energy levels within the SMMC framework.
• To enable spectral calculations for nuclei in very large model spaces.

Main Methods:

• Utilizing imaginary-time correlation matrices (ITCMs) of one-body densities.
• Employing a generalized eigenvalue problem for spectral extraction.
• Validating the method on a light nucleus against exact CI diagonalization.

Main Results:

• Successfully extracted low-lying energy levels with specified quantum numbers (spin, parity).
• Demonstrated method's accuracy by comparing with established CI shell-model results.
• Showcased the broad applicability of the SMMC-based spectral extraction technique.

Conclusions:

• The novel ITCM-based method effectively extracts nuclear spectra within SMMC.
• This technique expands the applicability of SMMC to detailed nuclear structure studies.
• The method holds potential for quantum many-body systems beyond nuclear physics.