Andrea Baldanza | Searcharxiv

arXiv2026

Spin Response of a Magnetic Monopole and Quantum Hall Response in Topological Lattice Models through Local Invariants and Light

Here, we elaborate on and develop the geometrical approach introduced in K. Le Hur, Physics Reports 1104 1-42 (2025) between the magnetic monopole created from a radial field, quantum physics and topological lattice models through quantum phase transitions. We introduce an effective magnetic moment for a monopole when applying an additional source field along z-direction which also mediates the quantum phase transition. We present its relation with the transverse pumped quantum Hall current. The magnetic susceptibility can be introduced as a measure of the topological invariant i.e. it remains quantized within the topological phase until the transition. We show the relation with two-dimensional topological lattice models such as a honeycomb Haldane model in real space. We develop the theory and present a numerical analysis between local invariants in momentum space introduced from Dirac points, correlation functions and the responses to circularly polarized light. We develop the formalism for coupled-planes materials including the possibility of quantum spin Hall effect and address a relation between the Ramanujan infinite alternating series and an interface in real space with a topological number one-half.

cond-mat.mes-hall↗

arXiv2026

Efficient simulation of second-order phase transitions in quantum anharmonic materials

When a crystal undergoes a second-order structural phase transition, such as in ferroelectrics, Peierls, and charge-density waves, the diverging fluctuations of the order parameter lead to the break- down of the standard phonon quasiparticle picture. Simulating these highly anharmonic regimes is notoriously challenging, as methods such as molecular dynamics suffer from a critical slowdown near the transition point, while the harmonic approximation fails dramatically at saddle points of the energy landscape stabilized by quantum or thermal ionic fluctuations. This work introduces a new approach, based on the variational free-energy principle, to predict critical long-range behavior and dynamical spectra in strongly anharmonic systems, even when quantum ionic fluctuations dominate. The proposed framework builds upon the stochastic self- consistent harmonic approximation but reduces its computational scaling with the number of atoms, N, from O(N^6) to O(N^2) and the memory requirement from O(N^4) to O(N). We benchmark the method on the prototypical lead-free metal-halide perovskite CsSnI3, a promising candidate for photovoltaic engineering, simulating its phase stability and Raman spectrum near the phase transition, where the breakdown of the quasiparticle picture becomes evident. We demonstrate the effectiveness of the method by computing the full free-energy Hessian and the critical temperature in a supercell with 1080 atoms. Such simulations would have required tens of thousands of years with the legacy approach; it is now feasible in a few hours on consumer hardware.

cond-mat.mtrl-sci↗