Efficient Simulation of Strong System-Environment Interactions

Multicomponent quantum systems in strong interaction with their environment are receiving increasing attention due to their importance in a variety of contexts, ranging from solid state quantum information processing to the quantum dynamics of biomolecular aggregates. Unfortunately, these systems are difficult to simulate as the system-bath interactions cannot be treated perturbatively and standard approaches are invalid or inefficient. Here we combine the time-dependent density matrix renormalization group with techniques from the theory of orthogonal polynomials to provide an efficient method for simulating open quantum systems, including spin-boson models and their generalizations to multicomponent systems.

Figure 1

(a) The standard Hamiltonian has each site of the dimer interacting with its surrounding bath in a starlike configuration. (b) After a unitary transformation of the bosonic modes only, an infinite harmonic 1D chain Hamiltonian is generated with frequencies ${ϵ}_n$ and nearest-neighbor couplings $t_n$.

Figure 2

Evolutions of the population on site 1 for the overdamped Brownian oscillator at $T=0\mathrm{K}$ and various reorganization energies $\lambda$. Simulation parameters are $J=100{\mathrm{cm}}^{-1}$, ${ϵ}_1-{ϵ}_2=100{\mathrm{cm}}^{-1}$, and $\gamma =53{\mathrm{cm}}^{-1}$.

Figure 3

Evolutions of the population on site 1 for the spectral function of Eq. (6) at various reorganization energies $\lambda$ and $T=0\mathrm{K}$. Dimer parameters are $J=100{\mathrm{cm}}^{-1}$ and ${ϵ}_1-{ϵ}_2=100{\mathrm{cm}}^{-1}$. The dashed line shows how the dynamics when the high-energy mode is decoupled.