Tensor-Train Split Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations

TL;DR

The paper introduces TT-SOKSL, a tensor-train split-operator method for quantum dynamics simulations that improves efficiency and accuracy over previous methods, especially in modeling non-adiabatic effects in complex molecular systems.

Contribution

It develops the TT-SOKSL method, combining tensor-train split-operator techniques with a rank adaptive TT-KSL scheme for improved quantum dynamics simulations.

Findings

Faster convergence than TT-SOFT in tensor-train memory usage

Better preservation of quantum state norm during evolution

Efficient simulation of non-adiabatic dynamics in high-dimensional systems

Abstract

Numerically exact simulations of quantum reaction dynamics, including non-adiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of molecular spectroscopy. Here, we introduce the tensor-train split-operator KSL (TT-SOKSL) method for quantum simulations in tensor-train (TT)/matrix product state (MPS) representations. TT-SOKSL propagates the quantum state as a tensor train using the Trotter expansion of the time-evolution operator, as in the tensor-train split-operator Fourier transform (TT-SOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank adaptive TT-KSL scheme instead of using the scaling and squaring approach as in TT-SOFT. We demonstrate the accuracy and efficiency of TT-SOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including non-adiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a time-dependent wavepacket evolving according to a two-state 25-dimensional model Hamiltonian. We find that TT-SOKSL converges faster than TT-SOFT with respect to the maximally allowed memory requirement of the tensor-train representation and better preserves the norm of the time-evolving state. When compared to the corresponding simulations based on the TT-KSL method, TT-SOKSL has the advantage of avoiding the need of constructing the matrix product state Laplacian by exploiting the linear scaling of multidimensional tensor train Fourier transforms.