Acceleration of the Stochastic Analytic Continuation Method via an Orthogonal Polynomial Representation of the Spectral Function

【摘要】 Stochastic analytic continuation is an excellent numerical method for analytically continuing Green’s functions from imaginary frequencies to real frequencies,although it requires significantly more computational time than the traditional MaxEnt method.We develop an alternate implementation of stochastic analytic continuation which expands the dimensionless field n(x)introduced by Beach using orthogonal polynomials.We use the kernel polynomial method(KPM)to control the Gibbs oscillations associated with truncation of the expansion in orthogonal polynomials.Our KPM variant of stochastic analytic continuation delivers improved precision at a significantly reduced computational cost.更多还原

【Abstract】 Stochastic analytic continuation is an excellent numerical method for analytically continuing Green’s functions from imaginary frequencies to real frequencies,although it requires significantly more computational time than the traditional MaxEnt method.We develop an alternate implementation of stochastic analytic continuation which expands the dimensionless field n(x) introduced by Beach using orthogonal polynomials.We use the kernel polynomial method(KPM) to control the Gibbs oscillations associated with truncation of the expansion in orthogonal polynomials.Our KPM variant of stochastic analytic continuation delivers improved precision at a significantly reduced computational cost.更多还原