MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software

Abstract

We introduce and describe the multiconfigurational time-depenent Hartree for indistinguishable particles (MCTDH-X) software, which is hosted, documented, and distributed at http://ultracold.org. This powerful tool allows the investigation of ground state properties with time-independent Hamiltonians, and dynamics of interacting quantum many-body systems in different spatial dimensions. The MCTDH-X software is a set of programs and scripts to compute, analyze, and visualize solutions for the time-dependent and time-independent many-body Schrödinger equation for indistinguishable quantum particles. As the MCTDH-X software represents a general solver for the Schrödinger equation, it is applicable to a wide range of problems in the fields of atomic, optical, molecular physics as well as condensed matter systems. In particular, it can be used to study light-matter interactions, correlated dynamics of electrons in solid states, as well as some aspects related to quantum information and computing. The MCTDH-X software solves a set of non-linear coupled working equations based on the application of the variational principle to the Schrödinger equation. These equations are obtained by using an ansatz for the many-body wavefunction that is a time-dependent expansion in a set of time-dependent, fully symmetrized bosonic (X=B) or fully anti-symmetrized fermionic (X=F) many-body basis states. It is the time-dependence of the basis set, that enables MCTDH-X to deal with quantum dynamics at a superior accuracy as compared to, for instance, exact diagonalization approaches with a static basis, where the number of basis states necessary to capture the dynamics of the wavefunction typically grows rapidly with time.Herein, we give an introduction to the MCTDH-X software via an easy-to-follow tutorial with a focus on accessibility.The illustrated exemplary problems are hosted at http://ultracold.org/tutorial and consider the physics of a few interacting bosons or fermions in a double-well potential. We explore computationally the position-space and momentum-space density, the one-body reduced density matrix, Glauber correlation functions, phases, (dynamical) phase transitions as well as the imaging of the quantum systems. Although a few particles in a double well potential represent a minimal model system, we are able to demonstrate a rich variety of phenomena with it. We use the double well to illustrate the fermionization of bosonic particles, the crystallization of fermionic particles, characteristics of the superfluid and Mott-insulator quantum phases in Hubbard models, and even dynamical phase transitions. We provide a complete set of input files and scripts to redo all computations in this paper at http://ultracold.org/data/tutorial_input_files.zip, accompanied by tutorial videos at https://www.youtube.com/playlist?list=PLJIFUqmSeGBKxmLcCuk6dpILnni_uIFGu. Our tutorial should guide the potential users to apply the MCTDH-X software also to more complex systems. arXiv:1911.00525v2 [cond-mat.quant-gas] 16 Jan 2020The time-dependen...

Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction

“…We solve the time-dependent many-boson Schrödinger equation presented in Eq. (1) using the MCTDHB method 36,39,40,49,57,58,61,[65][66][67][68][69][70][71][72][73][73][74][75][76][77][78][79][80][81][82] . The method is well documented and applied in the literature 59 .…”

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

“…MCTDH-X was successfully applied to demonstrate the importance of variances of observables [ 39 , 40 , 41 , 42 , 43 ] and of single-shot images [ 9 , 44 ] to the correlations of particles in the many-body state. Using MCTDH-X, intriguing correlation effects beyond the commonly employed Bose-Hubbard description were found to be present in lattices [ 45 , 46 , 47 , 48 , 49 , 50 ] and cavity-generated lattices [ 51 , 52 , 53 ] and the breakdown of commonly used mean-field approaches has been demonstrated in tunneling dynamics [ 54 , 55 , 56 ] and in harmonic traps [ 57 , 58 , 59 ]. A key focus of the applications of MCTDH-B has been the emergence of fragmentation [ 60 , 61 , 62 ], where the reduced one-body density matrix has multiple significant eigenvalues, see, for instance, Refs.…”

“…[ 54 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 ]. To obtain the results presented in this work, we used the MCTDH-X software hosted at (accessed on -day, 14 March 2021), see References [ 38 , 50 , 71 , 72 , 73 , 74 ].…”

Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

“…Therefore, the accuracy of MCTDH-X strongly depends on the choice of the number of orbitals M used in the simulations and the convergence of the MCTDH-X results can be improved by increasing the number of orbitals M [ 27 , 28 , 82 , 85 ]. We have used the freely available software implementation MCTDHB [ 14 ] within the MCTDH-X package [ 52 , 86 ] where the spatial discretization relies on a discrete variable representation (DVR) combined with a fast Fourier transformation [ 87 ]. In practice, we have used orbitals, and grid points.…”

“…We have used the freely available software implementation MCTDHB [ 14 ] within the MCTDH-X package [ 52 , 86 ] where the spatial discretization relies on a discrete variable representation (DVR) combined with a fast Fourier transformation [ 87 ]. In practice, we have used orbitals, and grid points.…”