arXiv subjects

Paolo Fachin

Publications and source records attributed to Paolo Fachin.

5 recordsLinked to original sources

arXiv2026

Frequency-dependent electron-phonon coupling and vibrational responses in tight-binding and continuous Dirac models with nuclear velocity correction

The nuclear motion induces in the electronic atomic orbitals a nuclear-velocity-dependent phase (also known as electron-translation factor), which modifies the effective Hamiltonians constructed from localised atomic orbitals. In this work, using an Ehrenfest Lagrangian approach for the localised atomic orbitals (LCAO) and tight-binding methods, we determine, at any order in the nuclear velocity, the equations of motion and the vibrational responses within a linear response formalism, focusing on the tight-binding assessment of the Born effective charges and the force-constant matrix. The appearance of nuclear-velocity-dependent Peierls-like phases in the non-local part of the interactions restores the all-electron sum rules for frequency-dependent vibrational responses. In tight-binding models these corrections crucially modify the vibrational response from a qualitative point of view, also yielding contributions required to capture phenomena such as vibrational circular dichroism. We test these corrections in the tight-binding model for metallic gapped graphene - finding excellent agreement with \textit{ab initio} calculations - and for the topological time-reversal symmetry breaking Haldane model.

cond-mat.mes-hall↗

arXiv2026

Non-adiabatic Ehrenfest dynamics with norm-conserving and ultra-soft pseudo-potentials with nuclear velocity corrections on the atomic orbitals within the Projector Augmented Wave Method framework

We derive the first-principles Ehrenfest molecular dynamics describing non-adiabatic processes with the inclusion of the nuclear-velocity-dependent phases (also known as electron-translation factors) on the atomic-orbital basis. These phases, appearing when nuclei are treated dynamically, affect effective Hamiltonians constructed from localised orbitals. In this work, we focus on the effects in the first-principles pseudo-potential Hamiltonian, both for the norm-conserving and ultra-soft cases, derived within the Projector-Augmented-Wave (PAW) method framework. Peierls-like phases depending on the nuclear velocities appear in the non-local part of the potential, while additional nuclear velocity and acceleration-dependent corrections appear in the ultra-soft pseudo-potential case. The use of velocity-including atomic orbital basis enables a Galilean-invariant description of the non-adiabatic Ehrenfest molecular dynamics, removing spurious non-adiabatic couplings that arise from neglecting the nuclear velocity phases in the atomic orbitals.

cond-mat.mes-hall↗

arXiv2025

Quantized Born Effective charges as probes for the topological phase transition in the Haldane and Kane-Mele models

We propose a new approach to study the transition between different topological states, based on the assessment of the vibrational resonances in infrared spectra. We consider the Haldane and Kane-Mele models finding that Born effective charges are nearly quantized, with a discontinuous jump concomitant with the topological phase transition. In particular, Born effective charges display a finite value in the trivial phase and a null one in the nontrivial one. This is rooted in the connection between Born effective charges and electronic Berry curvature at the band edges. Finally, at the topological phase transition of the Haldane model, we also observe a nearly quantized jump of the chiral splitting of the zone-center phonon frequencies, induced by time-reversal symmetry breaking.

cond-mat.mtrl-sci↗

arXiv2025

Infrared markers of topological phase transitions in quantum spin Hall insulators

Using first principles techniques, we show that infrared optical response can be used to discriminate between the topological and the trivial phases of two-dimensional quantum spin Hall insulators (QSHI). We showcase germanene and jacutingaite, of recent experimental realization, as prototypical systems where the infrared spectrum is discontinuous across the transition, due to sudden and large discretized jumps of the value of Born effective charges (up to 2). For these materials, the topological transition can be induced via the application of an external electrostatic potential in the field-effect setup. Our results are rationalized in the framework of a low-energy Kane-Mele model and are robust with respect to dynamical effects which come into play when the energy gap of the material is of the same order of the infrared active phonon frequency. In the small gap QSHI germanene, due to dynamical effects, the in-plane phonon resonance in the optical conductivity shows a Fano profile with remarkable differences in the intensity and the shape between the two phases. Instead, the large gap QSHI jacutingaite presents several IR-active phonon modes whose spectral intensities drastically change between the two phases.

cond-mat.mes-hall↗

arXiv2021

Mismatching as a tool to enhance algorithmic performances of Monte Carlo methods for the planted clique model

Over-parametrization was a crucial ingredient for recent developments in inference and machine-learning fields. However a good theory explaining this success is still lacking. In this paper we study a very simple case of mismatched over-parametrized algorithm applied to one of the most studied inference problem: the planted clique problem. We analyze a Monte Carlo (MC) algorithm in the same class of the famous Jerrum algorithm. We show how this MC algorithm is in general suboptimal for the recovery of the planted clique. We show however how to enhance its performances by adding a (mismatched) parameter: the temperature; we numerically find that this over-parametrized version of the algorithm can reach the supposed algorithmic threshold for the planted clique problem.

cond-mat.stat-mech↗