Contributor info: Dr Paolo Molignini

Paolo Molignini, Bastien Lapierre, Ramasubramanian Chitra, Wei Chen

SciPost Phys. Core 6, 059 (2023) · published 29 August 2023 | Toggle abstract · pdf

In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials to circularly polarized light over a wide range of frequencies, measured in units of the fine structure constant, can be used to extract a spectral function that frequency-integrates to the Chern number, offering a simple optical experiment to measure it. This method is subsequently generalized to finite temperature and locally on every lattice site by a linear response theory, which helps to extract the Chern marker that maps the Chern number to lattice sites. The long range response in our theory corresponds to a Chern correlator that acts like the internal fluctuation of the Chern marker, and is found to be enhanced in the topologically nontrivial phase. Finally, from the Fourier transform of the valence band Berry curvature, a nonlocal Chern marker is further introduced, whose decay length diverges at topological phase transitions and therefore serves as a faithful indicator of the transitions, and moreover can be interpreted as a Wannier state correlation function. The concepts discussed in this work explore multi-faceted aspects of topology and should help address the impact of system inhomogeneities.

Jiabing Xiang, Paolo Molignini, Miriam Büttner, Axel U. J. Lode

SciPost Phys. 14, 003 (2023) · published 13 January 2023 | Toggle abstract · pdf

Pauli crystals are ordered geometric structures that emerge in trapped noninteracting fermionic systems due to their underlying Pauli repulsion. The deformation of Pauli crystals - often called melting - has been recently observed in experiments, but the mechanism that leads to it remains unclear. We address this question by studying the melting dynamics of $N=6$ fermions as a function of periodic driving and experimental imperfections in the trap (anisotropy and anharmonicity) by employing a combination of numerical simulations and Floquet theory. Surprisingly, we reveal that the melting of Pauli crystals is not simply a direct consequence of an increase in system energy, but is instead related to the trap geometry and the population of the Floquet modes. We show that the melting is absent in traps without imperfections and triggered only by a sufficiently large shaking amplitude in traps with imperfections.

Paolo Molignini, Antonio Zegarra, Evert van Nieuwenburg, R. Chitra, Wei Chen

SciPost Phys. 11, 073 (2021) · published 28 September 2021 | Toggle abstract · pdf

Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the curvature function diverges and changes sign at certain high symmetry points in the Brillouin zone. These generic properties suggest the introduction of a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. We apply this scheme to a variety of interacting topological insulators in different dimensions and symmetry classes. We demonstrate that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases with very little numerical effort. Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality in the examples studied.

Rui Lin, Christoph Georges, Jens Klinder, Paolo Molignini, Miriam Büttner, Axel U. J. Lode, R. Chitra, Andreas Hemmerich, Hans Keßler

SciPost Phys. 11, 030 (2021) · published 17 August 2021 | Toggle abstract · pdf

The competition between short-range and cavity-mediated infinite-range interactions in a cavity-boson system leads to the existence of a superfluid phase and a Mott-insulator phase within the self-organized regime. In this work, we quantitatively compare the steady-state phase boundaries of this transition measured in experiments and simulated using the Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles. To make the problem computationally feasible, we represent the full system by the exact many-body wave function of a two-dimensional four-well potential. We argue that the validity of this representation comes from the nature of both the cavity-atomic system and the Bose-Hubbard physics. Additionally we show that the chosen representation only induces small systematic errors, and that the experimentally measured and theoretically predicted phase boundaries agree reasonably. We thus demonstrate a new approach for the quantitative numerical determination of the superfluid--Mott-insulator phase boundary.