arXiv subjects

V. V. França

Publications and source records attributed to V. V. França.

At least 19 recordsLinked to original sources

arXiv2026

BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains: entanglement and correlation signatures from DMRG and effective-pairing theory

Confined ultracold atoms in optical lattices provide a versatile platform for simulating lattice models of strongly correlated quantum systems, where pairing phenomena and superfluid phases can be explored under controlled conditions. While the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and the Bose-Einstein condensation (BEC) is well understood in homogeneous systems, spatial confinement breaks translational symmetry and reshapes correlation patterns, making the BCS-BEC identification in trapped geometries challenging and allowing unconventional phases to emerge with no direct analog in homogeneous systems. Here we present a characterization of the BCS-BEC crossover in harmonically confined one-dimensional Fermi-Hubbard chains. Our analysis combines Density Matrix Renormalization Group (DMRG) simulations and entanglement-based diagnostics with effective models describing the formation of tightly bound fermion pairs. This combined approach enables a detailed understanding of how the interplay between interactions and confinement reshapes the crossover, leading to insulating regions coexisting with persistent superfluid correlations. Within this framework, we further introduce conditioned correlation functions whose power-law decay allows a clear distinction between BCS-like and BEC-like regimes. The consistency between the effective descriptions and the numerical DMRG results yields a unified picture of the crossover in harmonically confined geometries.

cond-mat.quant-gas↗

arXiv2025

Single-site diagonal quantities capture off-diagonal long-range order

Quantum phase transitions are typically marked by changes in quantum correlations across various spatial scales within the system. A key challenge lies in the fact that experimental probes are generally restricted to diagonal quantities at the single-site scale, which are widely believed to be insufficient for detecting phases with off-diagonal long-range order, such as superconducting states. In a striking departure from conventional expectations, we show that single-site diagonal descriptors -- charge and spin fluctuations, occupation probabilities, and entanglement -- can capture the emergence of off-diagonal long-range order in the one-dimensional extended Hubbard model at half-filling. These single-site quantities display clear critical signatures of the superconducting transition, preceded by a continuous breaking of particle-hole symmetry, consistent with a second-order phase transition. While this symmetry breaking has a negligible effect on single-site descriptors, it allows a direct connection between local fluctuations and nonlocal correlations.

cond-mat.str-el↗

arXiv2025

Ant Colony Optimization for Density Functionals in Strongly Correlated Systems

The Ant Colony Optimization (ACO) algorithm is a nature-inspired metaheuristic method used for optimization problems. Although not a machine learning method per se, ACO is often employed alongside machine learning models to enhance performance through optimization. We adapt an ACO algorithm to optimize the so-called FVC density functional for the ground-state energy of strongly correlated systems. We find the parameter configurations that maximize optimization efficiency, while reducing the mean relative error ($MRE$) of the ACO functional. We then analyze the algorithm's performance across different dimensionalities ($1D-5D$), which are related to the number of parameters to be optimized within the FVC functional. Our results indicate that $15$ ants with a pheromone evaporation rate superior to $0.2$ are sufficient to minimize the $MRE$ for a vast regime of parameters of the strongly-correlated system -- interaction, particle density and spin magnetization. While the optimizations $1D$, $2D$, and $4D$ yield $1.5\%< MRE< 2.7\%$, the $3D$ and $5D$ optimizations lower the $MRE$ to $\sim0.8\%$, reflecting a $67\%$ error reduction compared to the original FVC functional ($MRE = 2.4\%$). As simulation time grows almost linearly with dimension, our results highlight the potential of ant colony algorithms for density-functional problems, combining effectiveness with low computational cost.

cond-mat.str-el↗

arXiv2024

Quantum phase transitions in one-dimensional nanostructures: a comparison between DFT and DMRG methodologies

In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density Functional Theory (DFT) and Density Matrix Renormalization Group (DMRG) have emerged as two powerful computational methods for addressing electronic correlation effects in diverse molecular systems. We compare ground-state energies ($e_0$), density profiles ($n$) and average entanglement entropies ($\bar S$) in metals, insulators and at the transition from metal to insulator, in homogeneous, superlattices and harmonically confined chains described by the fermionic one-dimensional Hubbard model. While for the homogeneous systems there is a clear hierarchy between the deviations, $D\%(\bar S)<D\%(e_0)< \bar D\%(n)$, and all the deviations decrease with the chain size; for superlattices and harmonical confinement the relation among the deviations is less trivial and strongly dependent on the superlattice structure and the confinement strength considered. For the superlattices, in general increasing the number of impurities in the unit cell represents less precision on the DFT calculations. For the confined chains, DFT performs better for metallic phases, while the highest deviations appear for the Mott and band-insulator phases. This work provides a comprehensive comparative analysis of these methodologies, shedding light on their respective strengths, limitations, and applications.

cond-mat.str-el↗

arXiv2023

Linear entropy fails to predict entanglement behavior in low-density fermionic systems

Entanglement is considered a fundamental ingredient for quantum technologies and condensed matter systems are among the good candidates for quantum devices. For bipartite pure states the von Neumann entropy is a proper measure of entanglement, while the linear entropy, associated to the mixedness of the reduced density matrices, is a simpler quantity to be obtained and is considered to be qualitatively equivalent to the von Neumann. Here we investigate both linear and von Neumann entropies for quantifying entanglement in homogeneous, superlattice and disordered Hubbard chains. We find regimes of parameters for which the linear entropy fails in reproducing the qualitative behavior of the von Neumann entropy. This then may lead to incorrect predictions i) of maximum and minimum entanglement states and ii) of quantum phase transitions.

quant-ph↗

arXiv2022

Effects of Temperature and Magnetization on the Mott-Anderson Physics in one-dimensional Disordered Systems

We investigate the Mott-Anderson physics in interacting disordered one-dimensional chains through the average single-site entanglement quantified by the linear entropy, which is obtained via density-functional theory calculations. We show that the minimum disorder strength required to the so-called full Anderson localization $-$ characterized by the real-space localization of pairs $-$ is strongly dependent on the interaction regime. The degree of localization is found to be intrinsically related to the interplay between the correlations and the disorder potential. In magnetized systems, the minimum entanglement characteristic of the full Anderson localization is split into two, one for each of the spin species. We show that although all types of localization eventually disappear with increasing temperature, the full Anderson localization persists for higher temperatures than the Mott-like localization.

cond-mat.str-el↗

arXiv2021

Mott-Anderson Metal-Insulator Transitions from Entanglement

A metal can be driven to an insulating phase through distinct mechanisms. A possible way is via the Coulomb interaction, which then defines the Mott metal-insulator transition (MIT). Another possibility is the MIT driven by disorder, the so-called Anderson MIT. Here we analyze interacting particles in disordered Hubbard chains $-$ thus comprising the Mott-Anderson physics $-$ by investigating the ground-state entanglement with density functional theory. The localization signature on entanglement is found to be a local minimum at a certain critical density. Individually, the Mott (Anderson) MIT has a single critical density whose minimum entanglement decreases as the interaction (disorder) enhances. While in the Mott MIT entanglement saturates at finite values, characterizing partial localization, in the Anderson MIT the system reaches full localization, with zero entanglement, for sufficiently strong disorder. In the combined Mott-Anderson MIT, we find three critical densities referring to local minima on entanglement. One of them is the same as for the Anderson MIT, but now the presence of interaction requires a stronger disorder potential to induce localization. A second critical density is related to the Mott MIT, but due to disorder it is displaced by a factor proportional to the concentration of impurities. The third local minimum on entanglement is unique to the concomitant presence of disorder and interaction, found to be related to an effective density phenomenon, thus referred to as a Mott-like MIT. Since entanglement has been intrinsically connected to the magnetic susceptibility $-$ a quantity promptly available in cold atoms experiments $-$ our detailed numerical description might be useful for the experimental investigation of Mott-Anderson MIT.

cond-mat.str-el↗

arXiv2020

Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids

We investigate the mapping between magnetic susceptibility and entanglement in the metallic, insulating, conventional and exotic polarized superfluid phases of one-dimensional fermionic lattice systems as described by the Hubbard model. Motivated by recent proposals for determining and quantifying entanglement via magnetic susceptibility measurements, we numerically study the intrinsic relationship between the two quantities at zero temperature. We find signatures of the metal-insulator transition and of the BCS-BEC crossover, but the most relevant result is that for conventional and exotic superfluids the mapping between magnetic susceptibility and entanglement is surprisingly simple: inversely proportional. This linear behavior could be exploited to quantify entanglement in current cold-atoms and condensed-matter experiments.

cond-mat.quant-gas↗

arXiv2019

Entanglement in disordered superfluids: the impact of density, interaction and harmonic confinement on the Superconductor-Insulator transition

We investigate the influence of density, interaction and harmonic confinement on the superfluid to insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. We quantify the ground-state single-site entanglement via density-functional theory calculations of the linear entropy. We analyze the critical concentration $C_C$ at which the fully-localized state $-$ a special type of localization, with null entanglement $-$ emerges. We find that $C_C$ is independent on the interaction, but demands a minimum disorder strength to occur. We then derive analytical relations for $C_C$ as a function of the average particle density for attractive and repulsive disorder. Our results reveal that weak harmonic confinement does not impact the properties of the fully-localized state, which occurs at the same $C_C$, but stronger confinements may lead the system from the fully-localized state to the ordinary localization.

cond-mat.supr-con↗

arXiv2019

Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

We use entanglement to track the superfluid-insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. Entanglement is found to have remarkable signatures of the SIT driven by i) the disorder strength $V$, ii) the concentration of impurities $C$ and iii) the particle density $n$. Our results reveal the absence of a critical potential intensity on the SIT driven by $V$, i.e. any small $V$ suffices to decrease considerably the degree of entanglement: it drops $\sim 50\%$ for $V=-0.25t$. We also find that entanglement is non-monotonic with the concentration $C$, approaching to zero for a certain critical value $C_C$. This critical concentration is found to be related to a special type of localization, here named as fully-localized state, which can be also reached for a particular density $n_C$. Our results show that the SIT driven by $n$ or $C$ has distinct nature whether it leads to the full localization or to the ordinary one: it is a first-order quantum phase transition when leading to full localization, and a smoother transition when reaching ordinary localization. In contrast, the SIT driven by $V$ is always a smoother transition independently on the type of localization reached.

cond-mat.supr-con↗

arXiv2018

Artificial neural networks for density-functional optimizations in fermionic systems

In this work we propose an artificial neural network functional to the ground-state energy of fermionic interacting particles in homogeneous chains described by the Hubbard model. Our neural network functional was proven to has an excellent performance: it deviates from numerically exact calculations by less than $0.15\%$ for all the regimes of filling factors and magnetizations, and for a vast regime of interactions. When compared to analytical functionals, the neural functional was found to be more precise for all the regimes of parameters, being particularly superior at the weakly interacting regime: where the analytical parametrization fails the most, $\sim7\%$, against only $\sim0.1\%$ for the neural functional. We have also applied our homogeneous functional to finite, localized impurities and harmonically confined systems within density-functional theory (DFT) methods. The results show that while our artificial neural network approach is substantially more accurate than other equivalently simple and fast DFT treatments, it has similar performance than more costly DFT calculations and other independent many-body calculations, at a fraction of the computational cost.

physics.comp-ph↗

arXiv2018

Metric-space approach for distinguishing quantum phase transitions in spin-imbalanced systems

Metric spaces are characterized by distances between pairs of elements. Systems that are physically similar are expected to present smaller distances (between their densities, wave functions and potentials) than systems that present different physical behaviors. For this reason metric spaces are good candidates for probing quantum phase transitions, since they could identify regimes of distinct phases. Here we apply metric space analysis to explore the transitions between the several phases in spin imbalanced systems. In particular we investigate the so-called FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) phase, which is an intriguing phenomenon in which superconductivity and magnetism coexist in the same material. This is expected to appear for example in attractive fermionic systems with spin-imbalanced populations, due to the internal polarization produced by the imbalance. The transition between FFLO phase (superconducting phase) and the normal phase (non-superconducting) and their boundaries have been subject of discussion in recent years. We consider the Hubbard model in the attractive regime for which Density Matrix Renormalization Group calculations allow us to obtain the exact density function of the system. We then analyze the exact density distances as a function of the polarization. We find that our distances display signatures of the distinct quantum phases in spin-imbalanced fermionic systems: with respect to a central reference polarization, systems without FFLO present a very symmetric behavior, while systems with phase transitions are asymmetric.

quant-ph↗

arXiv2017

Testing density-functional approximations on a lattice and the limits of the related Hohenberg-Kohn-type theorem

We present a metric-space approach to quantify the performance of density-functional approximations for interacting many-body systems and to explore the validity of the Hohenberg-Kohn-type theorem on fermionic lattices. This theorem demonstrates the existence of one-to-one mappings between particle densities, wave functions and external potentials. We then focus on these quantities, and quantify how far apart in metric space the approximated and exact ones are. We apply our method to the one-dimensional Hubbard model for different types of external potentials, and assess its validity on one of the most used approximations in density-functional theory, the local density approximation (LDA). We find that the potential distance may have a very different behaviour from the density and wave function distances, in some cases even providing the wrong assessments of the LDA performance trends. We attribute this to the systems reaching behaviours which are borderline for the applicability of the one-to-one correspondence between density and external potential. On the contrary the wave function and density distances behave similarly and are always sensitive to system variations. Our metric-based method correctly predicts the regimes where the LDA performs fairly well and the regimes where it fails. This suggests that our method could be a practical tool for testing the efficiency of density-functional approximations.

quant-ph↗

arXiv2016

Uniqueness of density-to-potential mapping for fermionic lattice systems

We demonstrate that, for a fermionic lattice system, the ground-state particle density uniquely determines the external potential except for the sites corresponding to nodes of the wave function, and the limiting case where the Pauli exclusion principle completely determines the occupation of all sites. Our fundamental finding completes, for this general class of systems, the one-to-one correspondence between ground states, their densities, and the external potential at the base of the Hohenberg-Kohn theorem. Moreover we demonstrate that the mapping from wave function to potential is unique not just for the ground state, but also for excited states. To illustrate our findings, we develop a practical inversion scheme to determine the external potential from a given density. Our results hold for a general class of lattice models, which includes the Hubbard model.

cond-mat.str-el↗

arXiv2011

Feasibility of approximating spatial and local entanglement in long-range interacting systems using the extended Hubbard model

We investigate the extended Hubbard model as an approximation to the local and spatial entanglement of a one-dimensional chain of nanostructures where the particles interact via a long range interaction represented by a `soft' Coulomb potential. In the process we design a protocol to calculate the particle-particle spatial entanglement for the Hubbard model and show that, in striking contrast with the loss of spatial degrees of freedom, the predictions are reasonably accurate. We also compare results for the local entanglement with previous results found using a contact interaction (PRA, 81 (2010) 052321) and show that while the extended Hubbard model recovers a better agreement with the entanglement of a long-range interacting system, there remain realistic parameter regions where it fails to predict the quantitative and qualitative behaviour of the entanglement in the nanostructure system.

cond-mat.str-el↗

arXiv2010

The Hubbard model as an approximation to the entanglement in nanostructures

We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in M wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally we calculate the spatial entanglement for the quantum well system and compare it to its average single-site entanglement.

cond-mat.str-el↗

arXiv2008

Entanglement in spatially inhomogeneous many-fermion systems

We investigate entanglement of strongly interacting fermions in spatially inhomogeneous environments. To quantify entanglement in the presence of spatial inhomogeneity, we propose a local-density approximation (LDA) to the entanglement entropy, and a nested LDA scheme to evaluate the entanglement entropy on inhomogeneous density profiles. These ideas are applied to models of electrons in superlattice structures with different modulation patterns, electrons in a metallic wire in the presence of impurities, and phase-separated states in harmonically confined many-fermion systems, such as electrons in quantum dots and atoms in optical traps. We find that the entanglement entropy of inhomogeneous systems is strikingly different from that of homogeneous systems.

cond-mat.str-el↗

arXiv2007

Stability and entanglement in optical-atomic amplification of trapped atoms: the role of atomic collisions

Atomic collisions are included in an interacting system of optical fields and trapped atoms allowing field amplification. We study the effects of collisions on the system stability. Also a study of the degree of entanglement between atomic and optical fields is made. We found that, for an atomic field initially in a vacuum state and optical field in a coherent state, the degree of entanglement does not depend on the optical field intensity or phase. We show that in conditions of exponential instability the system presents at long times two distinct stationary degree of entanglement with collisions affecting only one of them.

quant-ph↗