TY - JOUR
T1 - Simulating vibronic spectra via Matsubara-like dynamics
T2 - Coping with the sign problem
AU - Karsten, Sven
AU - Ivanov, Sergei D.
AU - Bokarev, Sergey I.
AU - Kühn, Oliver
N1 - Publisher Copyright:
© 2018 Author(s).
PY - 2018/11/21
Y1 - 2018/11/21
N2 - Measuring vibronic spectra probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body problems, such an approach usually requires the formulation of proper classical-like approximations, which is particularly challenging if multiple electronic states are involved. In this work, we express the imaginary-time shifted time correlation function and, thus, the vibronic spectrum in terms of the so-called Matsubara dynamics, which combines quantum statistics and classical-like dynamics. By applying the Matsubara approximation in the adiabatic limit, we derive a formal generalization of the existing Matsubara dynamics formalism to multiple potential energy surfaces (PESs), which, however, does not feature all the defining properties of its single-PES counterpart though suffering equally from the sign problem. The mathematical analysis for two shifted harmonic oscillators suggests a new modified method to practically simulate the standard correlation function via Matsubara-like dynamics. Importantly, this modified method samples the thermal Wigner function without suffering from the sign problem and yields an accurate approximation to the vibronic absorption spectrum, not only for the harmonic system but also for the anharmonic one.
AB - Measuring vibronic spectra probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body problems, such an approach usually requires the formulation of proper classical-like approximations, which is particularly challenging if multiple electronic states are involved. In this work, we express the imaginary-time shifted time correlation function and, thus, the vibronic spectrum in terms of the so-called Matsubara dynamics, which combines quantum statistics and classical-like dynamics. By applying the Matsubara approximation in the adiabatic limit, we derive a formal generalization of the existing Matsubara dynamics formalism to multiple potential energy surfaces (PESs), which, however, does not feature all the defining properties of its single-PES counterpart though suffering equally from the sign problem. The mathematical analysis for two shifted harmonic oscillators suggests a new modified method to practically simulate the standard correlation function via Matsubara-like dynamics. Importantly, this modified method samples the thermal Wigner function without suffering from the sign problem and yields an accurate approximation to the vibronic absorption spectrum, not only for the harmonic system but also for the anharmonic one.
UR - http://www.scopus.com/inward/record.url?scp=85057138903&partnerID=8YFLogxK
U2 - 10.1063/1.5046874
DO - 10.1063/1.5046874
M3 - Article
C2 - 30466277
AN - SCOPUS:85057138903
SN - 0021-9606
VL - 149
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 19
M1 - 194103
ER -