Exact boson expansion for spin- systems

P. Wróbel, H. Barentzen

Martin Lohmann

Isaac Goldhirsch

An exact Bose expansion for general spin S is presented. It is a generalisation of a previously derived expansion for S= 1 / 2 . The analysis of the resulting Bose-Hilbert space yields a new understanding of existing Bose expansions and of the meaning of the spin-boson transformations in general. Bose expansions and of the meaning of the spin-boson transformations in general. The Bloch sum rule for spin systems is proven rigorously for any value of S and every temperature. It is argued that phase transitions in quantum spin systems can be regarded as generalised Bose condensation processes. Possible applications to quantum spin systems are mentioned.

J. Dobaczewski

Yanying Liu, Yaming Yan, Meng Xu +2 more

The time-convolutionless (TCL) quantum master equation provides a powerful tool to simulate reduced dynamics of a quantum system coupled to a bath. The key quantity in the TCL master equation is the so-called kernel or generator, which describes effects of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion (HEOM) and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with different sets of parameters, to investigate the convergence of the high order expansions of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.

Meng Xu, Yaming Yan, Yanying Liu +1 more

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.