arXiv subjects

Pierpaolo Fontana

Publications and source records attributed to Pierpaolo Fontana.

14 recordsLinked to original sources

arXiv2026

Surface lone-pair polarization probed by quantum-geometric transport in tellurium

Stereochemically active lone pairs are ubiquitous microscopic sources of polarity in molecules and solids, but their collective behavior in crystals is often hidden by symmetry or confined to surfaces. Here we show that quantum-geometry transport provides a sensitive probe of surface lone-pair polarization in trigonal tellurium. This surface polarization appears microscopically as an inversion-odd dipolar component of the crystal potential, which shifts the center of mass of Bloch wavepackets and produces quantum-geometric corrections to their velocity. We describe this lone-pair polar texture through a minimal three-component lattice model, and we show that the resulting linear and nonlinear transport coefficients probe, respectively, the second and first moments of the net polarization field. Because rectified voltages in tellurium flakes are directly proportional to the surface lone-pair polarization, our results provide a microscopic route to understanding and engineering polarization-driven, quantum-geometric electronic devices based on tellurium allotropes.

cond-mat.mes-hall↗

arXiv2026

Superconducting properties of the three-dimensional Hofstadter-Hubbard model below the critical flux for Weyl points

The three-dimensional Hofstadter model exhibits a critical rational flux at which Weyl points emerge in the single-particle spectrum. We study the superconducting regime of the model in the presence of a Hubbard attractive interaction by tuning the magnetic flux across its critical value. We determine the phase diagram in the plane of the coprime pairs parametrizing the magnetic flux. We show that the system exhibits two distinct regimes separated by a critical flux $Φ_c$: for $Φ>Φ_c$, a semimetal-to-superconductor quantum phase transition occurs at a finite interaction strength ($U_c\neq0$), while for $Φ<Φ_c$ superconductivity arises for arbitrarily weak attraction, with a BCS-like exponential scaling of the gap due to the finiteness of the density of states. Close to the transition, we study the scaling behavior and identify the critical exponents. Our results highlight the interplay between magnetic band topology and attractive pairing in three-dimensional Hofstadter systems.

cond-mat.str-el↗

arXiv2026

Polar unidirectional magnetotransport in $p-$type tellurene from quantum geometry

Unidirectional magnetoresistance, or electric magnetochiral anisotropy (eMChA), is a nonlinear magnetotransport phenomenon that arises in noncentrosymmetric conductors , where changes in resistance $R(B)$ are: (i) chiral, $ΔR(B)/R(0)=2\,χ\, {\bf I}\cdot{\bf B}$, or (ii) polar, $ΔR(B)/R(0)=2\,γ\, {\bf I}\cdot({\bf P}\times{\bf B})$, with eMChA coefficients $χ$ and $γ$. In [Phys. Rev. Lett. 135, 106602 (2025)], we showed that the eMChA in the conduction band of tellurene is polar ($χ=0$, $γ\neq 0$) and emerges from the quantum metric dipole due to its Weyl node and from the lone pair polarization ${\bf P}$. Here, we extend our work to the valence band of tellurene, where the eMChA is usually said to be chiral ($χ\neq 0, γ= 0$). We show that also a polar coefficient $γ\neq 0$ emerges naturally through a downfolding procedure, in which remote Weyl-node containing bands induce momentum-space gradients of the quantum metric in the low-energy levels, activating finite metric dipoles. Combining semiclassical Boltzmann transport with a ${\bf k}\cdot{\bf p}$ description of tellurene, our numerical calculations agree quantitatively with doping ($μ$) dependent second-harmonic measurements of the longitudinal voltage $V^{2ω}_\parallel(μ)$ in perpendicular field. The combined chiral and polar characters ($χ\neq0, γ\neq 0)$ of the eMChA in tellurene also explains the shift in the angular ($ϕ$) dependence of $V^{2ω}_\parallel(ϕ)$ for in plane fields. Our results demonstrate that the polar eMChA can arise in topologically trivial bands through multiband effects and establishes tellurene as a platform for quantum-geometric rectification in both electron and hole regimes.

cond-mat.mes-hall↗

arXiv2025

Gate-Tunable Giant Negative Magnetoresistance in Tellurene Driven by Quantum Geometry

Negative magnetoresistance in conventional two-dimensional electron gases is a well-known phenomenon, but its origin in complex and topological materials, especially those endowed with quantum geometry, remains largely elusive. Here, we report the discovery of a giant negative magnetoresistance, reaching a remarkable $- 90\%$ of the resistance at zero magnetic field, $R_0$, in $n$-type tellurene films. This record-breaking effect persists over a wide magnetic field range (measured up to $35$ T) at cryogenic temperatures and is suppressed when the chemical potential shifts away from the Weyl node in the conduction band, strongly suggesting a quantum geometric origin. We propose two novel mechanisms for this phenomenon: a quantum geometric enhancement of diffusion and a magnetoelectric spin interaction that locks the spin of a Weyl fermion, in cyclotron motion under crossed electric $\boldsymbol{\cal E}$ and magnetic ${\bf B}$ fields, to its guiding-center drift, $(\boldsymbol{\cal E}\times{\bf B})\cdotσ$. We show that the time integral of the velocity auto-correlations promoted by the quantum metric between the spin-split conduction bands enhance diffusion, thereby reducing the resistance. This mechanism is experimentally confirmed by its unique magnetoelectric dependence, $ΔR_{zz}(\boldsymbol{\cal E},{\bf B})/R_0=-β_{g}(\boldsymbol{\cal E}\times{\bf B})^2$, with $β_{g}$ determined by the quantum metric. Our findings establish a new, quantum geometric and non-Markovian memory effect in magnetotransport, paving the way for controlling electronic transport in complex and topological matter.

cond-mat.mes-hall↗

arXiv2025

The Lattice Schwinger Model and Its Quantum Simulation

In this chapter we review results on the lattice Schwinger model. In par-ticular, we show how the effect of the anomaly is reproduced on the lattice. We connect these results to recent developments in the field of quantum simulation of interacting field theories. Schemes for the quantum simulation of (approximations of) Schwinger models are discussed.

quant-ph↗

arXiv2025

An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension

Non-Abelian gauge theories provide the most accurate description of fundamental interactions, showing remarkable agreement with experimental data in cosmology and particle physics. Highly precise predictions can be made using standard techniques, both in the continuum and in the lattice frameworks. However, classical methods have limitations, particularly when attempting to extrapolate the continuum limit from the study of lattice gauge theories. Complementing classical computations or combining them with quantum computational methods, to improve the predictions towards the continuum limit with current quantum resources, is a formidable open challenge. In this paper, we propose a resource-efficient method to compute the running of the coupling in non-Abelian gauge theories beyond one spatial dimension. We first represent the Hamiltonian on periodic lattices in terms of loop variables and conjugate loop electric fields, exploiting the Gauss law to retain the gauge-independent ones. Then, we identify a local basis for small and large loops variationally to minimize the truncation error while computing the running of the coupling on small tori. Our method enables computations at arbitrary values of the bare coupling and lattice spacing with current quantum computers, simulators and tensor-network calculations, in regimes otherwise inaccessible.

quant-ph↗

arXiv2025

Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics

The classical and quantum simulation of lattice gauge theories (LGTs) with Lie groups is hindered by the infinite-dimensional Hilbert space of gauge degrees of freedom. In a recent work [Phys. Rev. X 15, 031065 (2025)], we introduced a new truncation scheme -- here renamed as Renormalized Dual Basis (RDB) -- based on the resolution of the single-plaquette problem, and demonstrated its performance for SU(2) LGTs. In this paper, we apply the RDB to compact quantum electrodynamics (cQED) in three spacetime dimensions (2+1D). We variationally determine the ground state of the theory for small lattices with periodic (for pure gauge) and open (in presence of fermionic matter) boundary conditions, achieving improved precision for the plaquette operator compared to previous approaches. By leveraging tensor networks, we extend the study to larger lattices and demonstrate the scalability of the method. Overall, we show that the RDB provides an efficient description across all coupling regimes.

quant-ph↗

arXiv2025

Mean Field Approaches to Lattice Gauge Theories: A Review

Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many other methods, with tools coming from statistical mechanics lattice models, such as mean field methods, which are often used to provide approximate results. Applying these methods to LGTs requires particular attention due to the intrinsic local nature of gauge symmetry, how it is reflected in the variables used to formulate the theory, and the breaking of gauge invariance when approximations are introduced. This issue has been addressed over the decades in the literature, yielding different conclusions depending on the formulation of the theory under consideration. In this article, we focus on the mean field theoretical approach to the analysis of GTs and LGTs, connecting both older and more recent results that, to the best of our knowledge, have not been compared in a pedagogical manner. After a brief overview of mean field theory in statistical mechanics and many-body systems, we examine its application to pure LGTs with a generic compact gauge group. Finally, we review the existing literature on the subject, discussing the results obtained so far and their dependence on the formulation of the theory.

hep-lat↗

arXiv2025

Quantum geometry and the electric magnetochiral anisotropy in noncentrosymmetric polar media

The electric magnetochiral anisotropy is a nonreciprocal phenomenon accessible via second harmonic transport in noncentrosymmetric, time-reversal invariant materials, in which the rectification of current, ${\bf I}$, can be controlled by an external magnetic field, ${\bf B}$. Quantum geometry, which characterizes the topology of Bloch electrons in a Hilbert space, provides a powerful description of the nonlinear dynamics in topological materials. Here, we demonstrate that the electric magnetochiral anisotropy in noncentrosymmetric polar media owes its existence to the quantum metric, arising from the spin-orbit coupling, and to large Born effective charges. In this context, the reciprocal magnetoresistance $β{\bf B}^2$ is modified to $R( I,P,B)=R_0[1+βB^2 + γ^{\pm}{\bf I}\cdot({\bf P}\times{\bf B})]$, where the chirality dependent $γ^{\pm}$ is determined by the quantum metric dipole and the polarization ${\bf P}$. We predict a universal scaling $γ^{\pm}(V)\sim V^{-5/2}$ which we verified by phase sensitive, second harmonic transport measurements on hydrothermally grown 2D tellurium films under applied gate voltage, $V$. The control of rectification by varying ${\bf I}$, ${\bf P}$, ${\bf B}$, and $V$, demonstrated in this work, opens up new avenues for the building of ultra-scaled CMOS circuits.

cond-mat.mes-hall↗

arXiv2024

Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model

We investigate the band structure of the three-dimensional Hofstadter model on cubic lattices, with an isotropic magnetic field oriented along the diagonal of the cube with flux $Φ=2 π\cdot m /n$, where $m,n$ are co-prime integers. Using reduced exact diagonalization in momentum space, we show that, at fixed $m$, there exists an integer $n(m)$ associated with a specific value of the magnetic flux, that we denote by $Φ_c(m) \equiv 2 π\cdot m/n(m)$, separating two different regimes. The first one, for fluxes $Φ<Φ_c(m)$, is characterized by complete band overlaps, while the second one, for $Φ>Φ_c(m)$, features isolated band touching points in the density of states and Weyl points between the $m$- and the $(m+1)$-th bands. In the Hasegawa gauge, the minimum of the $(m+1)$-th band abruptly moves at the critical flux $Φ_c(m)$ from $k_z=0$ to $k_z=π$. We then argue that the limit for large $m$ of $Φ_c(m)$ exists and it is finite: $\lim_{m\to \infty} Φ_c(m) \equiv Φ_c$. Our estimate is $Φ_c/2π=0.1296(1)$. Based on the values of $n(m)$ determined for integers $m\leq60$, we propose a mathematical conjecture for the form of $Φ_c(m)$ to be used in the large-$m$ limit. The asymptotic critical flux obtained using this conjecture is $Φ_c^{\rm (conj)}/2π=7/54$.

cond-mat.mes-hall↗

arXiv2023

Quantum simulator of link models using spinor dipolar ultracold atoms

We propose a scheme for the quantum simulation of quantum link models in two-dimensional lattices. Our approach considers spinor dipolar gases on a suitably shaped lattice, where the dynamics of particles in the different hyperfine levels of the gas takes place in one-dimensional chains coupled by the dipolar interactions. We show that at least four levels are needed. The present scheme does not require any particular fine-tuning of the parameters. We perform the derivation of the parameters of the quantum link models by means of two different approaches, a non-perturbative one tied to angular momentum conservation, and a perturbative one. A comparison with other schemes for $(2+1)$-dimensional quantum link models present in literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.

cond-mat.quant-gas↗

arXiv2021

Reformulation of gauge theories in terms of gauge invariant fields

We present a reformulation of gauge theories in terms of gauge invariant fields. Focusing on Abelian theories, we show that the gauge and matter covariant fields can be recombined to introduce new gauge invariant degrees of freedom. Starting from the $(1+1)$ dimensional case on the lattice, with both periodic and open boundary conditions, we then generalize to higher dimensions and to the continuum limit. To show explicit and physically relevant examples of the reformulation, we apply it to the Hamiltonian of a single particle in a (static) magnetic field, to pure abelian lattice gauge theories, to the Lagrangian of quantum electrodynamics in $(3+1)$ dimensions and to the Hamiltonian of the $2d$ and $3d$ Hofstadter model. In the latter, we show that the particular construction used to eliminate the the gauge covariant fields enters the definition of the magnetic Brillouin zone. Finally, we briefly comment on relevance of the presented reformulation to the study of interacting gauge theories.

quant-ph↗

arXiv2021

Topological van Hove singularities at phase transitions in Weyl metals

We show that in three-dimensional (3D) topological metals, a subset of the van Hove singularities of the density of states sits exactly at the transitions between topological and trivial gapless phases. We may refer to these as topological van Hove singularities. By investigating two minimal models, we show that they originate from energy saddle points located between Weyl points with opposite chiralities, and we illustrate their topological nature through their magnetotransport properties in the ballistic regime. We exemplify the relation between van Hove singularities and topological phase transitions in Weyl systems by analyzing the 3D Hofstadter model, which offers a simple and interesting playground to consider different kinds of Weyl metals and to understand the features of their density of states. In this model, as a function of the magnetic flux, the occurrence of topological van Hove singularities can be explicitly checked.

cond-mat.mes-hall↗

arXiv2019

Scaling behavior of Ising systems at first-order transitions

We investigate how the scaling behavior of finite systems at magnetic first-order transitions (FOTs) with relaxational dynamics changes in correspondence of various boundary conditions. As a theoretical laboratory we consider the two-dimensional Ising model in the low-temperature phase. When the boundary conditions do not favor any specific phase of the system, we show that a dynamic finite-size scaling (DFSS) theory can be developed to describe the dynamic behavior in the coexistence region, where different phases coexist. When the boundary conditions at two opposite sides of the system generate a planar interface separating the phases, we show that the autocorrelation times are characterized by a power-law behavior, related to the dynamics enforced by the interface. Numerical results for a purely relaxational dynamics confirm the general picture.

cond-mat.stat-mech↗