arXiv subjects

Riccardo Piombo

Publications and source records attributed to Riccardo Piombo.

7 recordsLinked to original sources

arXiv2026

An exact and fast solution of the inverse Regularized Optimal Transport problem

Optimal transport describes the most efficient way to move mass between two distributions, given a cost matrix for moving mass between each pair of locations. Entropic optimal transport, solved via the Sinkhorn algorithm, is a widely used regularized version of this problem. Its inverse problem asks the opposite question: given an observed transport plan, what cost matrix produced it? This is difficult because the cost is identifiable only up to an additive gauge freedom. Here we show that this freedom can be fixed exactly by a single double-centering operation applied to the observed plan, yielding the true cost matrix in closed form, with no iterative optimization required. When a modest number of true cost entries are known, the same approach lets us jointly estimate the temperature parameter controlling the entropic regularization, together with a diagnostic for the reliability of this estimate. We further show that the method is not specific to the entropic optimal transport, but extends to a broader class of transport models defined by an invertible relation between cost and plan.

cond-mat.stat-mech↗

arXiv2026

Information-theoretic formulation of the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) asks for the shortest route to visit a set of cities exactly once. It combines a simple local rule - each city must be visited once - with a hard, global constraint- all cities must be traversed within a single cycle. We cast the problem within a probabilistic, information-theoretic framework. The coexistence of local and global constraints is precisely what makes the problem difficult to address in this framework: the local rule can be enforced through vertex-level constraints, whereas the global constraint cannot be captured by independent edge probabilities. We show that this obstacle can be overcome by defining a maximum-entropy probability distribution over graphs, in which edge costs and degree constraints generate an assignment-like ensemble, and a global term, describing the hard constraint, tilts this ensemble toward Hamiltonian cycles. To make the construction tractable, we derive a mean-field approximation in terms of edge occupancies and implement a differentiable cycle penalty that suppresses sub-tours. This leads to a self-consistent numerical procedure whose output is not only a candidate tour but also a probability matrix encoding competing edges and degenerate solutions. We test the method on synthetic ensembles and on TSPLIB instances. The algorithm converges to connected tours in polynomial time, matching the best-known solution in the majority of instances and remaining within a small relative gap otherwise. Beyond its competitive performance, the proposed framework offers a general approach for handling hard constraints while reducing hard combinatorial optimization problems to simpler ones.

cond-mat.stat-mech↗

arXiv2026

Statistical Mechanics of the Sub-Optimal Transport

Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit, where systems collapse onto optimal configurations, a.k.a. the ground states. Real-world systems often occupy intermediate regimes where entropy and cost minimization genuinely compete, producing configurations that are structured yet sub-optimal. The Sub-Optimal Transport (SOT) model captures this competition through an ensemble of weighted bipartite graphs: a coupling parameter interpolates between entropy-dominated dense configurations and cost-dominated sparse structures. This crossover has been observed numerically but lacked analytical understanding. Here we develop a mean-field theory that characterizes this transition. We show that local fluctuations in Lagrange multipliers become sub-extensive in the thermodynamic limit, reducing the full model with strength constraints to an effective single-constraint problem admitting an exact solution in some intermediate regime. The resulting free energy is analytic in the coupling parameter, confirming a smooth crossover rather than a phase transition. We derive closed-form expressions for thermodynamic observables and weight distributions, validated against numerical simulations. These results establish the first analytical description of the SOT model, extending statistical mechanics methods beyond the zero-temperature regime.

cond-mat.stat-mech↗

arXiv2025

Maximum entropy modeling of Optimal Transport: the sub-optimality regime and the transition from dense to sparse networks

We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply or receive, while an external cost field favors a minimal set of links, driving the system toward a sparse, tree-like structure. By tuning the control parameter, one transitions from uniformly distributed weights to an optimal transport regime in which weights condense onto cost-favorable edges. We quantify this dense-to-sparse transition, showing with numerical analyses that the process does not hinge on specific assumptions about the node-strength or cost distributions. Finite-size analysis confirms that the results persist in the thermodynamic limit. Because the model offers explicit control over the degree of sub-optimality, this approach lends to practical applications in link prediction, network reconstruction, and statistical validation, particularly in systems where partial optimization coexists with other noise-like factors.

cond-mat.stat-mech↗

arXiv2022

Strength of Correlations in a Silver Based Cuprate Analogue

AgF2 has been proposed as a cuprate analogue which requires strong correlation and marked covalence. On the other hand, fluorides are usually quite ionic and 4d transition metals tend to be less correlated than their 3d counterparts, which calls for further scrutiny. We combine valence band photoemission and Auger-Meitner spectroscopy of AgF and AgF2 together with computations in small clusters to estimate values of the Ag 4d Coulomb interaction U 4d and charge-transfer energy. Based on these values, AgF2 can be classified as a charge-transfer correlated insulator according to the Zaanen-Sawatzky-Allen classification scheme. Thus, we confirm that the material is a cuprate analogue from the point of view of correlations, suggesting that it should become a high-temperature superconductor if metallization is achieved by doping. We present also a computation of the Hubbard U in density functional "+U" methods and discuss its relation to the Hubbard U in spectroscopies.

cond-mat.str-el↗

arXiv2022

Charge Transfer and $dd$ excitations in AgF$_{2}$

Charge transfer (CT) insulators are the parent phase of a large group of today's unconventional high-temperature superconductors. Here we study experimentally and theoretically the interband excitations of the CT insulator silver fluoride AgF$_2$, which has been proposed as an excellent analogue of oxocuprates. Optical conductivity and resonant inelastic X-ray scattering (RIXS) on AgF$_2$ polycrystalline sample show a close similarity with that measured on undoped La$_2$CuO$_4$. While the former shows a CT gap $\sim$3.4 eV, larger than in the cuprate, $dd$ excitations are nearly at the same energy in the two materials. DFT and exact diagonalization cluster computations of the multiplet spectra show that AgF$_2$ is more covalent than the cuprate, in spite of the larger fundamental gap. Furthermore, we show that AgF$_2$ is at the verge of a charge transfer instability. The overall resemblance of our data on AgF$_2$ to those published previously on La$_2$CuO$_4$ suggests that the underlying CT insulator physics is the same, while AgF$_2$ could also benefit from a proximity to a charge density wave phase as in BaBiO$_3$. Therefore, our work provides a compelling support to the future use of fluoroargentates for materials' engineering of novel high-temperature superconductors.

cond-mat.supr-con↗

arXiv2021

Multiple-magnon excitations shape the spin spectrum of cuprate parent compounds

Thanks to high resolution and polarization analysis, resonant inelastic x-ray scattering (RIXS) magnetic spectra of La2CuO4, Sr2CuO2Cl2 and CaCuO2 reveal a rich set of properties of the spin 1/2 antiferromagnetic square lattice of cuprates. The leading single-magnon peak energy dispersion is in excellent agreement with the corresponding inelastic neutron scattering measurements. However, the RIXS data unveil an asymmetric lineshape possibly due to odd higher order terms. Moreover, a sharp bimagnon feature emerges from the continuum at (1/2,0), coincident in energy with the bimagnon peak detected in optical spectroscopy. These findings show that the inherently complex spin spectra of cuprates, an exquisite manifestation of quantum magnetism, can be effectively explored by exploiting the richness of RIXS cross sections.

cond-mat.supr-con↗