Constrained sampling method for analytic continuation

Abstract

A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large number of delta-functions, treated as a statistical-mechanics problem, it avoids distortions caused by (as demonstrated here) configurational entropy in previous sampling methods. The key development is the suppression of entropy by constraining the spectral weight to within identifiable optimal bounds and imposing a set number of peaks. As a test case, the dynamic structure factor of the S=1/2 Heisenberg chain is computed. Very good agreement is found with Bethe Ansatz results in the ground state (including a sharp edge) and with exact diagonalization of small systems at elevated temperatures.

5 pages, 4 figures

References in corpus (5)

• Spectral functions in one-dimensional quantum systems at T>0
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Dynamical Signatures of Edge-State Magnetism on Graphene Nanoribbons
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Asymmetric spin-1/2 two-leg ladders

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