Publications

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Many-body quantum dynamics with MCTDH-X

Paolo Molignini, Sunayana Dutta, Elke Fasshauer

SciPost Phys. Lect. Notes 94 (2025) · published 26 March 2025 | · pdf

The lecture notes on "Many-body Quantum Dynamics with MCTDH-X", adapted from the 2023 Heidelberg MCTDH Summer School, provide an in-depth exploration of the Multiconfigurational Time-Dependent Hartree approach for indistinguishable particles. They serve as a comprehensive guide for understanding and utilizing the MCTDH-X software for both bosonic and fermionic systems. The tutorial begins with an introduction to the MCTDH-X software, highlighting its capability to handle various quantum systems, including those with internal degrees of freedom and long-range interactions. The theoretical foundation is then laid out on how to solve the time-dependent and time-independent Schrödinger equations for many-body systems. The workflow section provides practical instructions on setting up and executing simulations using MCTDH-X. Detailed benchmarks against exact solutions are presented, showcasing the accuracy and reliability of the software in ground-state and dynamic simulations. The notes then delve into the dynamics of quantum systems, covering relaxation processes, time evolution, and the analysis of propagation for both bosonic and fermionic particles. The discussion includes the interpretation of various physical quantities such as energy, density distributions, and orbital occupations. Advanced features of MCTDH-X are also explored in the last section, including the calculation of correlation functions and the creation of visualizations through video tutorials. The notes conclude with a Linux/UNIX command cheat sheet, facilitating ease of use for users operating the software on different systems. Overall, these lecture notes provide a valuable resource for researchers and students in the field of quantum dynamics, offering both theoretical insights and practical guidance on the use of MCTDH-X for studying complex many-body systems.

5 citations
Characterizing far from equilibrium states of the one-dimensional nonlinear Schrödinger equation

Abhik Kumar Saha, Romain Dubessy

SciPost Phys. Core 8, 028 (2025) · published 6 March 2025 | · pdf

We use the mathematical toolbox of the inverse scattering transform to study quantita- tively the number of solitons in far from equilibrium one-dimensional systems described by the defocusing nonlinear Schrödinger equation. We present a simple method to iden- tify the discrete eigenvalues in the Lax spectrum and provide a extensive benchmark of its efficiency. Our method can be applied in principle to all physical systems described by the defocusing nonlinear Schrödinger equation and allows to identify the solitons velocity distribution in numerical simulations and possibly experiments.
Boson-fermion pairing and condensation in two-dimensional Bose-Fermi mixtures

Leonardo Pisani, Pietro Bovini, Fabrizio Pavan, Pierbiagio Pieri

SciPost Phys. 18, 076 (2025) · published 3 March 2025 | · pdf

We consider a mixture of bosons and spin-polarized fermions in two dimensions at zero temperature with a tunable Bose-Fermi attraction. By adopting a diagrammatic $T$-matrix approach, we analyze the behavior of several thermodynamic quantities for the two species as a function of the density ratio and coupling strength, including the chemical potentials, the momentum distribution functions, the boson condensate density, and the Tan's contact parameter. By increasing the Bose-Fermi attraction, we find that the condensate is progressively depleted and Bose-Fermi pairs form, with a small fraction of condensed bosons surviving even for strong Bose-Fermi attraction. This small condensate proves sufficient to hybridize molecular and atomic states, producing quasi-particles with unusual Fermi liquid features. A nearly universal behavior of the condensate fraction, the bosonic momentum distribution, and Tan's contact parameter with respect to the density ratio is also found.

1 citation
Systematic analysis of relative phase extraction in one-dimensional Bose gases interferometry

Taufiq Murtadho, Marek Gluza, Khatee Zathul Arifa, Sebastian Erne, Jörg Schmiedmayer, Nelly Huei Ying Ng

SciPost Phys. 18, 065 (2025) · published 24 February 2025 | · pdf

Interference upon free expansion gives access to the relative phase between two interfering matter waves. Such measurements can be used to reconstruct the spatially-resolved relative phase, which is a key observable in many quantum simulations of quantum field theory and non-equilibrium experiments. However, in 1D systems, longitudinal dynamics is typically ignored in the analysis of experimental data. In our work, we give a detailed account of various effects and corrections that occur in finite temperatures due to longitudinal expansion. We provide an analytical formula showing a correction to the readout of the relative phase due to longitudinal expansion and mixing with the common phase. Furthermore, we numerically assess the error propagation to the estimation of the gases' physical quantities such as correlation functions and temperature. We also incorporate systematic errors arising from experimental imaging devices. Our work characterizes the reliability and robustness of interferometric measurements, directing us to the improvement of existing phase extraction methods necessary to observe new physical phenomena in cold-atomic quantum simulators.

1 citation
SOLAX: A Python solver for fermionic quantum systems with neural network support

Louis Thirion, Philipp Hansmann, Pavlo Bilous

SciPost Phys. Codebases 51 (2025) · published 20 February 2025 | · pdf

Numerical modeling of fermionic many-body quantum systems presents similar challenges across various research domains, necessitating universal tools, including state-of-the-art machine learning techniques. Here, we introduce SOLAX, a Python library designed to compute and analyze fermionic quantum systems using the formalism of second quantization. SOLAX provides a modular framework for constructing and manipulating basis sets, quantum states, and operators, facilitating the simulation of electronic structures and determining many-body quantum states in finite-size Hilbert spaces. The library integrates machine learning capabilities to mitigate the exponential growth of Hilbert space dimensions in large quantum clusters. The core low-level functionalities are implemented using the recently developed Python library JAX. Demonstrated through its application to the Single Impurity Anderson Model, SOLAX offers a flexible and powerful tool for researchers addressing the challenges of many-body quantum systems across a broad spectrum of fields, including atomic physics, quantum chemistry, and condensed matter physics.

2 citations
Codebase release 1.0 for SOLAX

Louis Thirion, Philipp Hansmann, Pavlo Bilous

SciPost Phys. Codebases 51-r1.0 (2025) · published 20 February 2025 | · src

Numerical modeling of fermionic many-body quantum systems presents similar challenges across various research domains, necessitating universal tools, including state-of-the-art machine learning techniques. Here, we introduce SOLAX, a Python library designed to compute and analyze fermionic quantum systems using the formalism of second quantization. SOLAX provides a modular framework for constructing and manipulating basis sets, quantum states, and operators, facilitating the simulation of electronic structures and determining many-body quantum states in finite-size Hilbert spaces. The library integrates machine learning capabilities to mitigate the exponential growth of Hilbert space dimensions in large quantum clusters. The core low-level functionalities are implemented using the recently developed Python library JAX. Demonstrated through its application to the Single Impurity Anderson Model, SOLAX offers a flexible and powerful tool for researchers addressing the challenges of many-body quantum systems across a broad spectrum of fields, including atomic physics, quantum chemistry, and condensed matter physics.

1 citation
Quantum rotor in a two-dimensional mesoscopic Bose gas

Michał Suchorowski, Alina Badamshina, Mikhail Lemeshko, Michał Tomza, Artem G. Volosniev

SciPost Phys. 18, 059 (2025) · published 19 February 2025 | · pdf

We investigate a molecular quantum rotor in a two-dimensional Bose-Einstein condensate. The focus is on studying the angulon quasiparticle concept in the crossover from few- to many-body physics. To this end, we formulate the problem in real space and solve it with a mean-field approach in the frame co-rotating with the impurity. We show that the system starts to feature angulon characteristics when the size of the bosonic cloud is large enough to screen the rotor. More importantly, we demonstrate the departure from the angulon picture for large system sizes or large angular momenta where the properties of the system are determined by collective excitations of the Bose gas.

1 citation
Necklace Ansatz for strongly repulsive spin mixtures on a ring

Gianni Aupetit-Diallo, Giovanni Pecci, Artem Volosniev, Mathias Albert, Anna Minguzzi, Patrizia Vignolo

SciPost Phys. Core 8, 022 (2025) · published 14 February 2025 | · pdf

We propose an alternative to the Bethe Ansatz method for repulsive strongly-interacting fermionic (or bosonic) mixtures on a ring. Starting from the knowledge of the solution for single-component non-interacting fermions (or strongly-interacting bosons), we explicitly impose periodic condition on the amplitudes of the spin configurations. This reduces drastically the number of independent complex amplitudes that we determine by constrained diagonalization of an effective Hamiltonian. This procedure allows us to obtain a complete basis for the exact low-energy many-body solutions for mixtures with a large number of particles, both for $SU(\kappa)$ and symmetry-breaking systems.
Kinetics of quantum reaction-diffusion systems

Federico Gerbino, Igor Lesanovsky, Gabriele Perfetto

SciPost Phys. Core 8, 014 (2025) · published 4 February 2025 | · pdf

We discuss many-body fermionic and bosonic systems subject to dissipative particle losses in arbitrary spatial dimensions $d$, within the Keldysh path-integral formulation of the quantum master equation. This open quantum dynamics represents a generalisation of classical reaction-diffusion dynamics to the quantum realm. We first show how initial conditions can be introduced in the Keldysh path integral via boundary terms. We then study binary annihilation reactions $A+A\to \emptyset$, for which we derive a Boltzmann-like kinetic equation. The ensuing algebraic decay in time for the particle density depends on the particle statistics. In order to model possible experimental implementations with cold atoms, for fermions in $d=1$ we further discuss inhomogeneous cases involving the presence of a trapping potential. In this context, we quantify the irreversibility of the dynamics studying the time evolution of the system entropy for different quenches of the trapping potential. We find that the system entropy features algebraic decay for confining quenches, while it saturates in deconfined scenarios.

2 citations
Insulator phases of Bose-Fermi mixtures induced by intraspecies next-neighbor interactions

Felipe Gómez-Lozada, Roberto Franco, Jereson Silva-Valencia

SciPost Phys. Core 8, 007 (2025) · published 21 January 2025 | · pdf

We study a one-dimensional mixture of two-color fermions and scalar bosons at the hardcore limit, focusing on the effect that the intraspecies next-neighbor interactions have on the zero-temperature ground state of the system for different fillings of each carrier. Exploring the problem's parameters, we observed that the nearest-neighbor interaction could favor or harm the well-known mixed Mott and spin-selective Mott insulators. We also found the emergence of three unusual insulating states with charge density wave (CDW) structures in which the orders of the carriers are out of phase between each other. For instance, the immiscible CDW appears only at half-filling bosonic density, whereas the mixed CDW state is characterized by equal densities of bosons and fermions. Finally, the spin-selective CDW couples the bosons and only one kind of fermions. Appropriate order parameters were proposed for each phase to obtain the critical parameters for the corresponding superfluid-insulator transition. Our results can inspire or contribute to understanding experiments in cold-atom setups with long-range interactions or recent reports involving quasiparticles in semiconductor heterostructures.

2 citations

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