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Title: Clock quantum Monte Carlo technique: An imaginary-time method for real-time quantum dynamics

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 91; Journal Issue: 1; Related Information: CHORUS Timestamp: 2017-06-22 23:24:56; Journal ID: ISSN 1050-2947
American Physical Society
Country of Publication:
United States

Citation Formats

McClean, Jarrod R., and Aspuru-Guzik, Alán. Clock quantum Monte Carlo technique: An imaginary-time method for real-time quantum dynamics. United States: N. p., 2015. Web. doi:10.1103/PhysRevA.91.012311.
McClean, Jarrod R., & Aspuru-Guzik, Alán. Clock quantum Monte Carlo technique: An imaginary-time method for real-time quantum dynamics. United States. doi:10.1103/PhysRevA.91.012311.
McClean, Jarrod R., and Aspuru-Guzik, Alán. 2015. "Clock quantum Monte Carlo technique: An imaginary-time method for real-time quantum dynamics". United States. doi:10.1103/PhysRevA.91.012311.
title = {Clock quantum Monte Carlo technique: An imaginary-time method for real-time quantum dynamics},
author = {McClean, Jarrod R. and Aspuru-Guzik, Alán},
abstractNote = {},
doi = {10.1103/PhysRevA.91.012311},
journal = {Physical Review A},
number = 1,
volume = 91,
place = {United States},
year = 2015,
month = 1

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Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevA.91.012311

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Cited by: 1work
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  • We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green{close_quote}s functions generated in quantum Monte Carlo simulations to obtain the real-time Green{close_quote}s functions. For test problems, we considered chains of harmonic and anharmonic oscillators whose properties we simulated by a hybrid path-integral quantum Monte Carlo method. From the imaginary-time displacement-displacement Green{close_quote}s function, we first obtained its spectral density. For harmonic oscillators, we demonstrated the peaks of this function were in the correct position and their areas satisfied a sum rule. Additionally, as a function of wave number, the peak positions followed themore » correct dispersion relation. For a double-well oscillator, we demonstrated that the peak location correctly predicted the tunnel splitting. Transforming the spectral densities to real-time Green{close_quote}s functions, we conclude that we can predict the real-time dynamics for length of times corresponding to five to ten times the natural period of the model. The length of time was limited by an overbroadening of the peaks in the spectral density caused by the simulation algorithm. {copyright} {ital 1996 The American Physical Society.}« less
  • We report the details of an application of the method of maximum entropy to the extraction of spectral and transport properties from the imaginary-time correlation functions generated from quantum Monte Carlo simulations of the nondegenerate, symmetric, single-impurity Anderson model. We find that these physical properties are approximately universal functions of temperature and frequency when these parameters are scaled by the Kondo temperature. We also found that important details for successful extractions included the generation of statistically independent, Gaussian-distributed data, and a good choice of a default model to represent the state of our prior knowledge about the result in themore » absence of data. We suggest that our techniques are not restricted to the Hamiltonian and quantum Monte Carlo algorithm used here, but that maximum entropy and these techniques lay the general groundwork for the extraction of dynamical information from imaginary-time data generated by other quantum Monte Carlo simulations.« less
  • The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the 'weight', and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The Monte-Carlo algorithmsmore » are applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.« less
  • We present a Monte Carlo algorithm suitable for the calculation of excited state energies of multidimensional quantum systems. Energies are extracted from a maximum entropy analysis of the imaginary time evolution of a state prepared by application of a projection operator on an initial wave function. The imaginary time evolution is computed with a pure diffusion Monte Carlo algorithm. The method is demonstrated on a harmonic oscillator and several Morse oscillator test problems. {copyright} {ital 1997} {ital The American Physical Society}
  • The phaseless Auxiliary Field Quantum Monte Carlo (AFQMC) method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we address the possibility of calculating imaginary time correlation functions with the phaseless AFQMC. We give a detailed description of the technique and test the quality of the results for static properties and imaginary time correlation functions against exact values for small systems.