Improving the efficiency of open-quantum-system simulations using matrix product states in the interaction picture

Abstract

Modeling open quantum systems-quantum systems coupled to a bath-is of value in condensed matter theory, cavity quantum electrodynamics, nanosciences and biophysics. The real-time simulation of open quantum systems was advanced significantly by the recent development of chain mapping techniques and the use of matrix product states that exploit the intrinsic entanglement structure in open quantum systems. The computational cost of simulating open quantum systems, however, remains high when the bath is excited to high-lying quantum states. We develop an approach to reduce the computational costs in such cases. The interaction representation for the open quantum system is used to distribute excitations among the bath degrees of freedom so that the occupation of each bath oscillator is ensured to be low. The interaction picture also causes the matrix dimensions to be much smaller in a matrix product state of a chain-mapped open quantum system than in the Schrödinger picture. Using the interaction-representation accelerates the calculations by one to two orders of magnitude over existing matrix-product-state method. In the regime of strong system-bath coupling and high temperatures, the speedup can be as large as three orders of magnitude. The approach developed here is especially promising to simulate the dynamics of open quantum systems in the high-temperature and strong-coupling regimes [1].

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

“…As mentioned in Sec , HM is feasible for those models which contain a large number of phonon modes and few exciton states. Therefore, to test the validity of the HM method, we first apply HM to two model systems: a singlet fission , model with 183 discrete modes , and a spin-boson model with an infinite number of phonon modes in finite temperature . Subsequently, we simulate the singlet fission process in the realistic rubrene crystals .…”

“…Actually, the spin-boson model is just a special case of the general exciton–phonon coupling model. And we choose the “adiabatic regime” in ref . Because different spin states share the same spectral density function we have N dir = 1.…”

“…The temperature effect here just enlarges the exciton−phonon coupling because for T > 0, cosh θ K > 1. Moreover, the so-called "thermalized spectral density" 38,40,60 is theoretically equal to the TFD treatment. Unlike Fermionic systems, the exciton−phonon model does not conserve the phonon number.…”

“…We perform the 2TDVP for the first half of the time followed by the stochastic adaptive one-site TDVP (SA-1TDVP) 53 to accelerate the computation. Other parameters are the same as in ref 40.…”

“…Consequently, the HEM computational costs increase quickly when N ex is relatively large. A similar approach is the time-evolving density operator with orthogonal polynomials (t-TEDOPA), − which is the simplified version of HEM when N ex = 1.…”