arXiv subjects

Andrea Trombettoni

Publications and source records attributed to Andrea Trombettoni.

At least 19 recordsLinked to original sources

arXiv2026

From Laplacian-to-Adjacency Matrix for Continuous Spins on Graphs

The study of spins and particles on graphs has broad applications, from the dynamics of interacting systems on networks to combinatorial problems. Here, we study the large-$n$ limit of the $O(n)$ model on graphs, which is considerably more challenging than on regular lattices, as the loss of translational invariance gives rise to an infinite set of saddle point constraints in the thermodynamic limit. We show that the free energy at low and high temperature $T$ is determined by the spectrum of two fundamental graph-theoretic objects: the Laplacian matrix at low $T$ and the Adjacency matrix at high $T$. Their interplay is studied across several classes of graphs. For regular lattices the two coincide. We obtain an exact solution on trees, where the Lagrange multipliers interestingly depend solely on the number of nearest neighbors. We further contrast these classical results with those for a quantum spin model on an exemplary tree. For decorated lattices, the singular part of the free energy is governed by the Laplacian spectrum, whereas this is true for the full free energy only in the zero temperature limit. Finally, we discuss a bipartite fully connected graph to highlight the importance of a finite coordination number in these results.

cond-mat.stat-mech↗

arXiv2026

Restoration of Ensemble Equivalence by Quantum Fluctuations

We study the thermodynamic phase diagram of a one-dimensional quantum spin chain subjected to both mean-field and nearest-neighbor interactions, and to a transverse magnetic field $h$. The purpose is to determine the effect of the quantum fluctuations, due to the transverse field, on the phase diagram, in particular with respect to the occurrence of ensemble inequivalence. We denote our model as a quantum Nagle-Kardar model. To perform the calculation of the canonical partition function, we show that, due to the presence of the mean-field term, in the thermodynamic limit one can use the Hubbard-Stratonovich transformation in spite of the non-commutativity of the different operators appearing in the Hamiltonian, and we adopt a procedure of successive approximations that lead to the determination of the phase diagram thanks to a scaling property of the phase transition lines. The results show that the ensemble inequivalence, present in the classical Nagle-Kardar model, is removed above a threshold value $h_c$ for the transverse field. For $h$ larger than $h_c$ the phase diagram exhibits only second-order phase transition lines, implying therefore restoration of ensemble equivalence.

cond-mat.stat-mech↗

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

Crossover and Critical Behavior in the Layered XY Model

Motivated by the interplay between 2D and 3D scaling signatures observed in unconventional layered superconductors, we present a systematic Monte Carlo study of the three-dimensional classical XY model with anisotropic in-plane $J_\parallel$ and inter-plane $J_\perp$ couplings. Our study includes very small values of the system anisotropy $Δ=J_\perp /J_\parallel$ not studied before, and focuses on characterizing the crossover from quasi-2D topological scaling to genuine 3D critical behavior. The numerical results for the critical temperature unambiguously reveal a logarithmic scaling with $Δ$, directly related to the topological scaling in the 2D limit. Despite the 3D nature of the layered XY criticality, topological scaling signatures survive up to system sizes comparable to the crossover length $\ell_J$, which diverges at small $Δ$ with a scaling behavior reminiscent of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This shows that genuine 3D symmetry-breaking behavior emerges only at exceedingly large system sizes when the anisotropy is very strong. Our results indicate that new experimental evidence is required to clarify the extent to which the critical signatures observed in layered strongly correlated materials are shaped by their pronounced anisotropy.

cond-mat.supr-con↗

arXiv2026

Phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction

We derive the phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction in the canonical ensemble. The free energy is obtained by mapping the model onto the spin-$1$ Blume-Emery-Griffiths model and solving it by using an Hubbard-Stratonovich transformation combined with the transfer matrix method. A complex structure with lines of first-order transitions, two triple points and a critical point appears at finite temperature. The phase diagram is two-dimensional, since there are two adjustable parameters, the nearest-neighbour coupling $K$ and the temperature $T$. We show that the phase diagram does not present second-order phase transition lines, due to the fact that the order parameter is not a symmetry-breaking one. Quite remarkably, we are able to determine analytically one of the first-order phase-transition lines. We also prove that, when the nearest-neighbour coupling $K$ is large and negative, the first-order transition temperature becomes asymptotically independent of $K$.

cond-mat.stat-mech↗

arXiv2026

The $O(n\to\infty)$ Rotor Model and the Quantum Spherical Model on Graphs

We show that the large $n$ limit of the $O(n)$ quantum rotor model defined on a general graph has the same critical behavior as the corresponding quantum spherical model and that the critical exponents depend solely on the spectral dimension $d_s$ of the graph. To this end, we employ a classical to quantum mapping and use known results for the large $n$ limit of the classical $O(n)$ model on graphs. Away from the critical point, we discuss the interplay between the Laplacian and the Adjacency matrix in the whole parameter plane of the quantum Hamiltonian. These results allow us to paint the full picture of the $O(n)$ quantum rotor model on graphs in the large $n$ limit.

cond-mat.stat-mech↗

arXiv2026

Ultracold Quantum Gravimeters: An Introduction for Geophysicists

This paper aims at providing an accessible introduction to ultracold quantum gravimeters tailored for geophysicists. We do not focus here on geophysical applications, as these are already well known to geophysicists, but rather provide a pedagogical exposition of the quantum-mechanical concepts needed to understand the operation of quantum gravimeters. We present a review of gravimeters based on two- and three-level atomic systems, focusing on the fundamental mechanisms of atomic interferometry. The functioning of Mach-Zehnder interferometers is discussed through the action of $π/2$ and $π$ pulses, showing how the resulting phase shift encodes gravitational acceleration. The effect of noise is briefly discussed.

quant-ph↗

arXiv2025

Insensitivity points and performance of open quantum interferometers under number-conserving & non-conserving Lindblad dynamics

We investigate the phase sensitivity of a linear two-mode atom interferometer subject to environmental noise, modeled within the framework of open quantum systems with both number-conserving and non-conserving Lindblad operators. Considering several input states, we first study the cases N=1,2 (N number of particles) and perform numerical simulations for N>2. The sensitivity as a function of the holding time can display divergence points where phase estimation becomes impossible, to which we refer as insensitivity points. We characterize their behavior as the input state, particle number, and noise operator are varied, and we find that their positions are independent of the noise intensity. Moreover, while our fixed measurement scheme may favor number-conserving noise at small N (i.e., having better sensitivity), the Cramér-Rao bound reveals that particle non-conserving noise yields strictly lower achievable sensitivity for all particle numbers.

quant-ph↗

arXiv2025

One-dimensional long-range Ising model: two (almost) equivalent approximations

We investigate the critical behavior of the one-dimensional Ising model with long-range interactions using the functional renormalization group in the local potential approximation (LPA), and compare our findings with Dyson's hierarchical model (DHM). While the DHM lacks translational invariance, it admits a field-theoretical description closely resembling the LPA, up to minor but nontrivial differences. After reviewing the real-space renormalization group approach to the DHM, we demonstrate a remarkable agreement in the critical exponent $ν$ between the two methods across the entire range of power-law decays $1/2 < σ< 1$. We further benchmark our results against Monte Carlo simulations and analytical expansions near the upper boundary of the nontrivial regime, $σ\lesssim 1$.

cond-mat.stat-mech↗

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

Effect of Energy Extensivity on the Performance of Open Quantum Interferometers

Studying the performance of a quantum interferometer coupled to an external environment is a problem of conceptual and practical importance. If we consider a quantum interferometer featuring Heisenberg-limited sensitivity, then a typical result is that introducing coupling with the environment degrades the sensitivity to the shot-noise limit. Here we argue that this result crucially depends on whether the interferometer-environment coupling term is subject (or not) to the so-called Kac rescaling that restores extensivity, i.e., whether the coupling Hamiltonian is extensive or not. We present results of the Lindblad equation in the presence and absence of Kac rescaling of the coupling constant. Our results show that for a linear coupling and a harmonic model of the environment, often used in modeling of a quantum interferometer coupled with an environment, the Heisenberg-limited sensitivity may be restored after the Kac rescaling. This result points out the need and the importance to characterize the (model of the) environment of the interferometer at hand.

quant-ph↗

arXiv2025

Thermal and Quantum Phase Transitions of the $ϕ^4$ Model

In this paper we discuss and revisit the finite temperature extension of the renormalization group (RG) treatment of $T=0$ field theories, focusing as a case study on the $ϕ^4$ model. We first discuss the extension of RG equations of the very same model from $T=0$ to finite $T$ in the usual way by resorting to sums on the Matsubara frequencies and fixing the physical temperature parameter $T$. We show that this approach, although useful for a variety of applications, may lead to the disappearance of the critical points as extracted from the RG flow. Since the identification of fixed points is key in the study of classical and quantum phase transitions, wepropose a modification of the usual finite-temperature RG approach by relating the temperature parameter to the running RG scale, $T \equiv k_T = τk$ where $k_T$ is the running cutoff for thermal, and $k$ is for the quantum fluctuations. Once introduced this dimensionless temperature $τ$, we investigate the consequences on the thermal RG approach for the $ϕ^4$ model and construct its phase diagram. Finally, we formulate requirements for the phase diagram of the $ϕ^4$ theory based on known properties of the quantum and classical phase diagrams of the Ising model.

hep-th↗

arXiv2025

Achieving quantum advantage in a search for a violations of the Goldbach conjecture, with driven atoms in tailored potentials

The famous Goldbach conjecture states that any even natural number $N$ greater than $2$ can be written as the sum of two prime numbers $p^{\text{(I)}}$ and $p^{\text{(II)}}$. In this article we propose a quantum analogue device that solves the following problem: given a small prime $p^{\text{(I)}}$, identify a member $N$ of a $\mathcal{N}$-strong set even numbers for which $N-p^{\text{(I)}}$ is also a prime. A table of suitable large primes $p^{\text{(II)}}$ is assumed to be known a priori. The device realizes the Grover quantum search protocol and as such ensures a $\sqrt{\mathcal{N}}$ quantum advantage. Our numerical example involves a set of 51 even numbers just above the highest even classical-numerically explored so far [T. O. e Silva, S. Herzog, and S. Pardi, Mathematics of Computation {\bf 83}, 2033 (2013)]. For a given small prime number $p^{\text{(I)}}=223$, it took our quantum algorithm 5 steps to identify the number $N=4\times 10^{18}+14$ as featuring a Goldbach partition involving $223$ and another prime, namely $p^{\text{(II)}}=4\times 10^{18}-239$. Currently, our algorithm limits the number of evens to be tested simultaneously to $\mathcal{N} \sim \ln(N)$: larger samples will typically contain more than one even that can be partitioned with the help of a given $p^{\text{(I)}}$, thus leading to a departure from the Grover paradigm.

quant-ph↗

arXiv2025

Criticality-amplified quantum probing of a spontaneous collapse model

Spontaneous collapse models, which are phenomenological mechanisms introduced and designed to account for dynamical wavepacket reduction, are attracting a growing interest from the community interested in the characterisation of the quantum-to-classical transition. Here, we introduce a quantum-probing approach to the quest of deriving metrological upper bounds on the free parameters of such empirical models. To illustrate our approach, we consider an extended quantum Ising chain whose elements are -- either individually or collectively -- affected by a mechanism responsible for spontaneous collapse. We explore configurations involving out-of-equilibrium states of the chain, which allows us to infer information about the collapse mechanism before it is completely scrambled from the state of the system. Moreover, we investigate potential amplification effects on the probing performance based on the exploitation of quantum criticality.

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

Transport of ultracold dipolar fermions in one-dimensional optical lattices

We investigate the transport properties in out-of-equilibrium dynamics of strongly correlated dipolar fermions initially localized in one-dimensional inhomogeneous optical lattice. The dynamics is studied by experimentally measurable dynamical variables such as one-body density, pair-correlation function and size of the expanding cloud. In the noninteracting limit, we trace the usual fingerprints of ballistic expansion in the short time dynamics. However, dynamics is strongly affected by system size due to Pauli principle. The dynamics also exhibits significant dependence on the sign of the interactions. We observe that strong repulsive dipolar interaction gives rise to many-body features in the dynamics, while strong attractive dipolar interaction leads to stabilized cluster states. Intermediate dipolar interaction are found to hinder expansion of correlations, while very strong dipolar interaction favors expansion of the cloud. Our work show the effect of dipolar interaction in the transport properties of interacting fermions, that can be studied in on-going experiments with ultracold dipolar fermions.

cond-mat.quant-gas↗

arXiv2025

Ensemble Inequivalence in Ising Chains with Competing Interactions

We study the effect of competing interactions on ensemble inequivalence. We consider a one-dimensional Ising model with ferromagnetic mean-field interactions and short-range nearest-neighbor and next-nearest-neighbor couplings which can be either ferromagnetic or antiferromagnetic. Despite the relative simplicity of the model, our calculations in the microcanonical ensemble reveal a rich phase diagram. The comparison with the corresponding phase diagram in the canonical ensemble shows the presence of phase transition points and lines which are different in the two ensembles. As an example, in a region of the phase diagram where the canonical ensemble shows a critical point and a critical end point, the microcanonical ensemble has an additional critical point and also a triple point. The regions of ensemble inequivalence typically occur at lower temperatures and at larger absolute values of the competing couplings. The presence of two free parameters in the model allows us to obtain a fourth-order critical point, which can be fully characterized by deriving its Landau normal form.

cond-mat.stat-mech↗

arXiv2024

Lagrangian Homotopy Analysis Method using the Least Action Principle

The Homotopy Analysis Method (HAM) is a powerful technique which allows to derive approximate solutions of both ordinary and partial differential equations. We propose to use a variational approach based on the Least Action Principle (LAP) in order to improve the efficiency of the HAM when applied to Lagrangian systems. The extremization of the action is achieved by varying the HAM parameter, therefore controlling the accuracy of the approximation. As case studies we consider the harmonic oscillator, the cubic and the quartic anharmonic oscillators, and the Korteweg-de Vries partial differential equation. We compare our results with those obtained using the standard approach, which is based on the residual error square method. We see that our method accelerates the convergence of the HAM parameter to the exact value in the cases in which the exact solution is known. When the exact solution is not analytically known, we find that our method performs better than the standard HAM for the cases we have analyzed. Moreover, our method shows better performance when the order of the approximation is increased and when the nonlinearity of the equations is stronger.

physics.comp-ph↗