We exhibit a new method for calculating high-and low-temperature series expansions for diagonal spin-spin correlation functions in the $d=2$ Ising model. The method makes use of a differential equation obeyed by these functions.We exhibit a new method for calculating high-and low-temperature series expansions for diagonal spin-spin correlation functions in the $d=2$ Ising model. The method makes use of a differential equation obeyed by these functions.

Physical review. B, Condensed matterJul 1, 19846 citations

On correlation functions of the XY model

Anatoli G. Izergin, N. A. Kitanin, N. A. Slavnov

Journal of Mathematical SciencesJan 1, 199825 citations

Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach

Linze Song, Qiang Shi

Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes.Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes.

The Journal of Chemical PhysicsNov 20, 201538 citations

New method of computing correlation functions. I

Raoul Rashidovich Nigmatullin

Russian Physics JournalOct 1, 19770 citations

Application of the imaginary time hierarchical equations of motion method to calculate real time correlation functions

Tao Xing, Tianchu Li, Yaming Yan +2 more

We investigate the application of the imaginary time hierarchical equations of motion method to calculate real time quantum correlation functions. By starting from the path integral expression for the correlated system-bath equilibrium state, we first derive a new set of equations that decouple the imaginary time propagation and the calculation of auxiliary density operators. The new equations, thus, greatly simplify the calculation of the equilibrium correlated initial state that is subsequently used in the real time propagation to obtain the quantum correlation functions. It is also shown that a periodic decomposition of the bath imaginary time correlation function is no longer necessary in the new equations such that different decomposition schemes can be explored. The applicability of the new method is demonstrated in several numerical examples, including the spin-Boson model, the Holstein model, and the double-well model for proton transfer reaction.We investigate the application of the imaginary time hierarchical equations of motion method to calculate real time quantum correlation functions. By starting from the path integral expression for the correlated system-bath equilibrium state, we first derive a new set of equations that decouple the imaginary time propagation and the calculation of auxiliary density operators. The new equations, thus, greatly simplify the calculation of the equilibrium correlated initial state that is subsequently used in the real time propagation to obtain the quantum correlation functions. It is also shown that a periodic decomposition of the bath imaginary time correlation function is no longer necessary in the new equations such that different decomposition schemes can be explored. The applicability of the new method is demonstrated in several numerical examples, including the spin-Boson model, the Holstein model, and the double-well model for proton transfer reaction.

The Journal of Chemical PhysicsMay 31, 202212 citations

We exhibit a new method for calculating high-and low-temperature series expansions for diagonal spin-spin correlation functions in the

d=2

Ising model. The method makes use of a differential equation obeyed by these functions.