Cross Validation in Stochastic Analytic Continuation

Abstract

Stochastic Analytic Continuation (SAC) of Quantum Monte Carlo (QMC) imaginary-time correlation function data is a valuable tool in connecting many-body models to experimentally measurable dynamic response functions. Recent developments of the SAC method have allowed for spectral functions with sharp features, e.g. narrow peaks and divergent edges, to be resolved with unprecedented fidelity. Often times, it is not known what exact sharp features, if any, are present \textit{a priori}, and, due to the ill-posed nature of the analytic continuation problem, multiple spectral representations may be acceptable. In this work, we borrow from the machine learning and statistics literature and implement a cross validation technique to provide an unbiased method to identify the most likely spectrum amongst a set obtained with different spectral parameterizations and imposed constraints. We demonstrate the power of this method with examples using imaginary-time data generated by QMC simulations and synthetic data generated from artificial spectra. Our procedure, which can be considered a form of model selection, can be applied to a variety of numerical analytic continuation methods, beyond just SAC.

18 pages, 17 figures

References in corpus (19)

• A high-bias, low-variance introduction to Machine Learning for physicists
• Computational Studies of Quantum Spin Systems
• Computation of dynamical correlation functions of Heisenberg chains in a field
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
• Constrained sampling method for analytic continuation
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
• The amplitude mode in three-dimensional dimerized antiferromagnets
• Spin Waves in Antiferromagnetic Spin Chains with Long Range Interactions
• Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions
• The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid
• Extending the average spectrum method: Grid points sampling and density averaging
• Analytic continuation average spectrum method for quantum liquids
• Time correlation functions for quantum systems: validating Bayesian approaches for harmonic oscillators and beyond

Cited by in corpus (3)

• Single-Particle Dispersion and Density of States of the Half-Filled 2D Hubbard Model
• Dynamic structure factor of a spin-1/2 Heisenberg chain with long-range interactions
• Single-hole spectral functions in one-dimensional quantum magnets with different ground states