MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software
We introduce and describe the multiconfigurational time-depenent Hartree for indistinguishable particles (MCTDH-X) software. This powerful tool allows the investigation of ground state properties 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, 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 many-body basis states. The time-dependence of the basis set enables MCTDH-X to deal with quantum dynamics at a superior accuracy as compared to, for instance, exact diagonalization approaches. Herein, we give an introduction to the MCTDH-X software via an easy-to-follow tutorial with a focus on accessibility. 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 quantum phase transitions. Our tutorial guides the potential user to apply the MCTDH-X software also to more complex systems.