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Researcher profile

Bruno Juliá-Díaz

Bruno Juliá-Díaz contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
cond-mat.quant-gasquant-phcond-mat.stat-mechhep-thMachine Learningnucl-thphysics.ed-ph

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Published work

9 published item(s)

preprint2026arXiv

Quantum Monte Carlo study of systems interacting via long-range interactions mediated by a cavity

We study one-dimensional quantum gases in continuous space with cavity-mediated infinite-range interactions using variational and diffusion Monte Carlo methods. Starting from the exact two-body solution, we construct a non-translationally invariant Jastrow wavefunction that accurately captures the spatial structure induced by the cavity field and provides an efficient many-body ansatz for both bosonic and fermionic systems. We analize properties of three characteristic quantum systems, subject to long-range interactions: (i) ideal Bose gas (ii) interacting Bose gas (iii) ideal Fermi gas. In the absence of short-range interactions, we identify a crossover from a stable, weakly modulated phase realized for repulsive interactions to a delocalized bound state for attractive interactions, marked by clustering, loss of superfluidity, and the absence of a thermodynamic limit. Introducing short-range repulsion, either through contact interactions or fermionic statistics, leads to the formation of a mesoscopic gas-like regime that disappears in the thermodynamic limit. A qualitative phase diagram is proposed to illustrate the combined effects of short- and long-range interactions, highlighting the emergence of distinct regimes with characteristic structural properties.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Towards interpretable AI with quantum annealing feature selection

Deep learning models are used in critical applications, in which mistakes can have serious consequences. Therefore, it is crucial to understand how and why models generate predictions. This understanding provides useful information to check whether the model is learning the right patterns, detect biases in the data, improve model design, and build systems that can be trusted. This work proposes a new method for interpreting Convolutional Neural Networks in image classification tasks. The approach works by selecting the most important feature maps that contribute to each prediction. To solve this combinatorial problem, we encode it into a quantum constrained optimization problem and propose to solve it using quantum annealing. We evaluate our method against the state-of-the-art explainable AI techniques, specifically GradCAM and GradCAM++, and observe an improved class disentanglement, i.e. the model's decision boundaries become more distinct and its reasoning more transparent. This demonstrates that our approach enhances the quality of explanations, making it easier to understand which features the model relies on for specific predictions. In addition, we study the computational behavior of the quantum annealing algorithm. Specifically, we analyze the minimum energy gap of the system during computation and the probability that the algorithm finds the correct solution. These analyses provide theoretical insight into why the method works effectively in practice.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On the direct diagonalization method for a few particles trapped in harmonic potentials

We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a renormalization method for the interparticle interactions. The procedure is benchmarked with state-of-the-art numerical results for three and four symmetric fermions.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Entanglement entropy in low-energy field theories at finite chemical potential

We investigate the leading area-law contribution to entanglement entropy in a system described by a general Lagrangian with O(2) symmetry containing first- and second-order time derivatives, namely breaking the Lorentz-invariance. We establish a connection between the Higgs gap present in a symmetry-broken phase and the area-law term for the entanglement entropy in the general, non-relativistic case. Our predictions for the entanglement entropy and correlation length are successfully compared to numerical results in two paradigmatic systems: the Mott insulator to superfluid transition for ultracold lattice bosons, and the ground state of ferrimagnetic systems.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Functional renormalization for repulsive Bose-Bose mixtures at zero temperature

We study weakly-repulsive Bose-Bose mixtures in two and three dimensions at zero temperature using the functional renormalization group (FRG). We examine the RG flows and the role of density and spin fluctuations. We study the condition for phase separation and find that this occurs at the mean-field point within the range of parameters explored. Finally, we examine the energy per particle and condensation depletion. We obtain that our FRG calculations compare favorably with known results from perturbative approaches for macroscopic properties.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Quantum droplets of bosonic mixtures in a one-dimensional optical lattice

We demonstrate the existence of quantum droplets in two-component one-dimensional Bose-Hubbard chains. The droplets exist for any strength of repulsive intra-species interactions provided they are balanced by comparable attractive inter-species interactions. The ground-state phase diagram is presented and the different phases are characterized by examining the density profile and off-diagonal one- and two-body correlation functions. A rich variety of phases is found, including atomic superfluid gases, atomic superfluid droplets, pair superfluid droplets, pair superfluid gases and a Mott-insulator phase. A parameter region prone to be experimentally explored is identified, where the average population per site is lower than three atoms, thus avoiding three-body losses. Finally, the bipartite entanglement of the droplets is found to have a non-trivial dependence on the number of particles.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Spin-orbit coupled bosons interacting in a two-dimensional harmonic trap

A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value of $\hatσ_z \hat{L}_z$ for the eigenstates of the system, regardless of the trapping potential. The low-energy states of the repulsively interacting two-boson system are characterized. With the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is a direct energy-level crossing in the ground state of the system between states of different $J_z$, the third component of the total angular momentum, that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The Hellmann-Feynman theorem at finite temperature

We present a simple derivation of the Hellmann-Feynman theorem at finite temperature. We illustrate its validity by considering three relevant examples which can be used in quantum mechanics lectures: the one-dimensional harmonic oscillator, the one-dimensional Ising model and the Lipkin model. We show that the Hellmann-Feynman theorem allows one to calculate expectation values of operators that appear in the Hamiltonian. This is particularly useful when the total free-energy is available, but there is not direct access to the thermal average of the operators themselves.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Universal dimerized quantum droplets in a one-dimensional lattice

The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive inter-component and repulsive intra-component interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by DMRG method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state. Finally, we identify conditions for the formation of a solitonic solution.

0 citations0 reviewsNo code linkedOpen access