Comparison of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) for ground state properties of linear rotor chains

Abstract

We demonstrate the applicability of the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method to the problem of computing ground states of one-dimensional chains of linear rotors with dipolar interactions. Specifically, we successfully obtain energies, entanglement entropies, and orientational correlations that are in agreement with the Density Matrix Renormalization Group (DMRG), which has been previously used for this system. We find that the entropies calculated by ML-MCTDH for the larger system sizes contain a nonmonotonicity, as expected in the vicinity of a second-order quantum phase transition between ordered and disordered rotor states. We observe that this effect remains when all couplings besides nearest-neighbor are omitted from the Hamiltonian, which suggests that it is not sensitive to the rate of decay of the interactions. In contrast to DMRG, which is tailored to the one-dimensional case, ML-MCTDH (as implemented in the Heidelberg MCTDH package) requires more computational time and memory, although the requirements are still within reach of commodity hardware. The numerical convergence and computational demand of two practical implementations of ML-MCTDH and DMRG are presented in detail for various combinations of system parameters.

Time‐dependent density matrix renormalization group method for quantum dynamics in complex systems

“…For comparison, we also use ML‐MCTDH to do the same calculations. The comparison of the efficiency of these two methods previously focused on the eigenvalue problems 153 . Here, we focus on the time evolution problems.…”

Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue

“…Peaks can be resolved in J 01 , and are mostly assigned to in-plane symmetric stretches (A 1 symmetry). For example, 250(#14), 520 (27), 800 (37), 880 (43), 990 (45), 1200 (58), 1360 (66), 1460 (70), and 1710(90) cm −1 . The small peak at 470 cm −1 is reasonably further (30 cm −1 ) from any A 1 mode that it is possible to be coupled to a mode of alternate symmetry in relation to the electronic symmetry of S 1 being B 2 .…”

“…Indeed, a recent comparison of ML-MCTDH and MPS methods for 1D dipolar chains found that the MPS approach was both faster and required less computational memory to obtain accurate ground states for this class of models. [45] TEDOPA is in principle numerically exact, can be combined with machine learning and entanglement renormalization methods, and also gives full access to observable bath dynamics, as recently verified through time-resolved excited-state vibrational spectroscopy in bipentacenes [40,46]. However, until recently, accessing finite temperatures required time-consuming sampling over bath configurations.…”

Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space

“…55, MPS has also been applied to open quantum system dynamics, in particular in connection with other approaches based on a reduced system dynamics description, such as quasi-adiabatic path-integral approach, [66][67][68] and hierarchy of pure state. 69,70 The MPS representation, as a wave function approach, can be considered as a special case of the multi-layer multiconfigurational time-dependent Hartree (ML-MCTDH) method, 33,[71][72][73][74][75] which has also been applied to a variety of prototype open quantum systems. [76][77][78][79] While it has been demonstrated that the combination of the HEOM approach and tensor train decomposition is a promising way forward, Borrelli 53,54 further pointed out that it is instrumental to reformulate the reduced system in twin space, which renders the method more flexible as it allows for the tensor train decomposition in the central system DoFs.…”