TensorTrain Split Operator KSL (TTSOKSL) Method for Quantum Dynamics Simulations
Abstract
Numerically exact simulations of quantum reaction dynamics, including nonadiabatic 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 tensortrain splitoperator KSL (TTSOKSL) method for quantum simulations in tensortrain (TT)/matrix product state (MPS) representations. TTSOKSL propagates the quantum state as a tensor train using the Trotter expansion of the timeevolution operator, as in the tensortrain splitoperator Fourier transform (TTSOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank adaptive TTKSL scheme instead of using the scaling and squaring approach as in TTSOFT. We demonstrate the accuracy and efficiency of TTSOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including nonadiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a timedependent wavepacket evolving according to a twostate 25dimensional model Hamiltonian. We find that TTSOKSL converges faster than TTSOFT with respect to the maximally allowed memory requirement of the tensortrain representation and better preserves the norm of the timeevolving state. When compared to the corresponding simulations based on the TTKSL method, TTSOKSL 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 arXiv:
 arXiv:2203.00527
 Bibcode:
 2022arXiv220300527L
 Keywords:

 Physics  Chemical Physics;
 Quantum Physics
 EPrint:
 doi:10.1021/acs.jctc.2c00209