arXiv subjects

Federico Becca

Publications and source records attributed to Federico Becca.

At least 19 recordsLinked to original sources

arXiv2026

Influence of the inter-orbital interaction and kinetic terms on superconductivity: a simple two-orbital Hubbard model

We investigate a minimal two-orbital Hubbard model with intra- and inter-orbital nearest-neighbor hopping $t$ and $\tilde{t}$, as well as intra- and inter-orbital density-density interactions $U$ and $U'$ by means of variational ans\"atze based on Jastrow-Slater wave functions within quantum Monte Carlo techniques. To focus on the electronic mechanisms of superconductivity, we restrict the variational ans\"atze to uniform nonmagnetic states with an explicit pairing amplitude and compute the pairing correlations as a function of filling and model parameters. At $U/t=10$, superconducting correlations are highly enhanced by the presence of inter-orbital terms, $U'$ and $\tilde{t}$. For $\tilde{t}=0$, a finite value of $U'$ effectively screens the intra-orbital repulsion $U$, producing a shift in the superconducting dome. Consequently, inter-orbital repulsion yields a sizable increase in electron pairing compared to the single-orbital baseline. Furthermore, introducing a finite $\tilde{t}$ provides an additional boost to superconducting correlations, an effect driven by the simultaneous presence of flat and broad bands in the electronic structure.

cond-mat.str-el↗

arXiv2026

Emergence of a monopole phase in the $J_1{-}J_2$ Heisenberg model on the triangular lattice for small magnetic fields

We investigate the ground-state phase diagram of the $J_1{-}J_2$ Heisenberg model on the triangular lattice under an external Zeeman field $H$ by using the variational Monte Carlo approach. We span a region with $0 \le J_2/J_1 \le 0.2$ and $0 \le H/J_1 \le 2$, to assess the fate of the (putative) spin-liquid phase that has been detected for $J_2/J_1=1/8$ at zero magnetic field. Simple variational ansatze are proposed for a few candidate states, and their energetics are compared on large clusters to obtain the phase diagram. For $J_2/J_1 \lesssim 1/6$, a continuous transition from a gapless "Y'' phase to a gapped "up-up-down'' phase is obtained, as predicted by spin-wave theory. Most importantly, around $J_2/J_1=1/8$, a condensate of monopoles (which are gapless gauge excitations of the spin liquid at $H=0$) is stabilized in a significant region of the phase diagram, for small Zeeman fields. Here, a finite scalar chirality is present, while no transverse magnetic order is detected. The stability of the monopole phase is confirmed by a field-theory approach that includes a self-consistent random-phase approximation of the low-lying spin fluctuations. The boundary between the monopole and "Y'' phases is also obtained with no free parameters.

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arXiv2025

Triangular $J_1$-$J_2$ Heisenberg Antiferromagnet in a Magnetic Field

The behavior of the paradigmatic $J_1-J_2$ triangular lattice Heisenberg antiferromagnet in a magnetic field remains unsettled despite decades of study. We map out the phase diagram using three complementary approaches, including self-consistent nonlinear spin-wave theory, density-matrix renormalization group, and variational Monte Carlo. This combined analysis resolves the competition among different field-induced magnetic orders and magnetization plateaux across the classically frustrated parameter range. In particular, there is a finite range in the parameter regime around $J_2/J_1=\frac{1}{8}$ in which i) upon the application of the external field, the gapless quantum spin liquid acquires a finite density of monopoles, and ii) by further increasing the field, two plateaux are clearly obtained at $m=\frac{1}{3}$ and $m=\frac{1}{2}$. We discuss the experimental importance of the consecutive magnetization plateaux transitions as a signature of an underlying quantum spin-liquid phase.

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arXiv2025

A many-body marker for three-dimensional topological insulators with inversion symmetry

We extend the previously defined many-body marker for two-dimensional $\mathbb{Z}_2$ topological insulators [I. Gilardoni {\it et al.}, Phys. Rev. B {\bf 106}, L161106 (2022)] to distinguish trivial, weak-, and strong-topological insulators in three dimensions, in presence of the inversion symmetry. The marker is written in term of ground-state expectation values of position operators and can be employed to detect topological phases of interacting systems beyond mean-field approximations, e.g., within quantum Monte Carlo techniques. Here, we show that the correct results of the non-interacting limit are reproduced by the many-body marker.

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arXiv2025

Foundation Neural-Networks Quantum States as a Unified Ansatz for Multiple Hamiltonians

Foundation models are highly versatile neural-network architectures capable of processing different data types, such as text and images, and generalizing across various tasks like classification and generation. Inspired by this success, we propose Foundation Neural-Network Quantum States (FNQS) as an integrated paradigm for studying quantum many-body systems. FNQS leverage key principles of foundation models to define variational wave functions based on a single, versatile architecture that processes multimodal inputs, including spin configurations and Hamiltonian physical couplings. Unlike specialized architectures tailored for individual Hamiltonians, FNQS can generalize to physical Hamiltonians beyond those encountered during training, offering a unified framework adaptable to various quantum systems and tasks. FNQS enable the efficient estimation of quantities that are traditionally challenging or computationally intensive to calculate using conventional methods, particularly disorder-averaged observables. Furthermore, the fidelity susceptibility can be easily obtained to uncover quantum phase transitions without prior knowledge of order parameters. These pretrained models can be efficiently fine-tuned for specific quantum systems. The architectures trained in this paper are publicly available at https://huggingface.co/nqs-models, along with examples for implementing these neural networks in NetKet.

quant-ph↗

arXiv2024

Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension

We explore the ground-state properties of a one-dimensional model with two orbitals per site, where, in addition to atomic energies $\pm M$, intra- and inter-orbital hoppings, the intra-orbital Hubbard ($U$) and nearest-neighbor density-density ($V$) repulsions are included. Our results are primarily based on a Jastrow-Slater wave function and variational Monte Carlo methods, but also corroborated by density-matrix renormalization group calculations. In the non-interacting limit, when varying $M>0$, a gapless point separates a trivial phase from a topological one. The inclusion of a finite Hubbard-$U$ repulsion does not give rise to any phase transition within the topological region, inducing a smooth crossover into a Haldane (spin gapped) insulator; notably, the string-order parameter, which characterizes the latter phase, is already finite in the non-interacting limit. Most importantly, at finite values of $U$, the transition between the trivial and topological states is not direct, since an emergent insulator, which shows evidence of sustaining gapless spin excitations, intrudes between them. A small $V$ interaction further stabilizes the intermediate insulator, while a sufficiently large value of this nearest-neighbor repulsion gives rise to two different charge-density wave insulators, one fully gapped and another still supporting gapless spin excitations. Our results demonstrate the richness of multi-orbital Hubbard models, in the presence of a topologically non-trivial band structure, and serve as a basis for future investigations on similar two-dimensional models.

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arXiv2024

Monopole excitations in the $U(1)$ Dirac spin liquid on the triangular lattice

The $U(1)$ Dirac spin liquid might realize an exotic phase of matter whose low-energy properties are described by quantum electrodynamics in $2+1$ dimensions, where gapless modes exists but spinons and gauge fields are strongly coupled. Its existence has been proposed in frustrated Heisenberg models in presence of frustrating super-exchange interactions, by the (Abrikosov) fermionic representation of the spin operators [X.-G. Wen, \href{https://doi.org/10.1103/PhysRevB.65.165113}{Phys. Rev. B {\bf 65}, 165113 (2002)}], supplemented by the Gutzwiller projection. Here, we construct charge-$Q$ monopole excitations in the Heisenberg model on the triangular lattice with nearest- ($J_1$) and next-neighbor ($J_2$) couplings. In the highly frustrated regime, singlet and triplet monopoles with $Q=1$ become gapless in the thermodynamic limit; in addition, the energies for generic $Q$ agree with field-theoretical predictions, obtained for a large number of gapless fermion modes. Finally, we consider localized gauge excitations, in which magnetic $\pi$-fluxes are concentrated in the triangular plaquettes (in analogy with $\mathbb{Z}_2$ visons), showing that these kind of states do not play a relevant role at low energies. All our findings lend support to a stable $U(1)$ Dirac spin liquid in the $J_1-J_2$ Heisenberg model on the triangular lattice.

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arXiv2024

Insulating and metallic phases in the one-dimensional Hubbard-Su-Schrieffer-Heeger model: Insights from a backflow-inspired variational wave function

The interplay between electron-electron and electron-phonon interactions is studied in a one-dimensional lattice model, by means of a variational Monte Carlo method based on generalized Jastrow-Slater wave functions. Here, the fermionic part is constructed by a pair-product state, which explicitly depends on the phonon configuration, thus including the electron-phonon coupling in a backflow-inspired way. We report the results for the Hubbard model in presence of the Su-Schrieffer-Heeger coupling to optical phonons, both at half-filling and upon hole doping. At half-filling, the ground state is either a translationally invariant Mott insulator, with gapless spin excitations, or a Peierls insulator, which breaks translations and has fully gapped excitations. Away from half-filling, the charge gap closes in both Mott and Peierls insulators, turning the former into a conventional Luttinger liquid (gapless in all excitation channels). The latter, instead, retains a finite spin gap that closes only above a threshold value of the doping. Even though consistent with the general theory of interacting electrons in one dimension, the existence of such a phase (with gapless charge but gapped spin excitations) has never been demonstrated in a model with repulsive interaction and with only two Fermi points. Since the spin-gapped metal represents the one-dimensional counterpart of a superconductor, our results furnish evidence that a true off-diagonal long-range order may exist in the two-dimensional case.

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arXiv2024

Intertwined superconductivity and orbital selectivity in a three-orbital Hubbard model for the iron pnictides

We study a three-orbital Hubbard-Kanamori model relevant for iron-based superconductors using variational wave functions explicitly including spatial correlations and electron pairing. We span the nonmagnetic sector from filling $n=4$, which is representative of undoped iron-based superconductors, to $n=3$, where a Mott insulating state with each orbital at half filling is found. In the strong-coupling regime, when the electron density is increased, we find a spontaneous differentiation between the occupation of $d_{xz}$ and $d_{yz}$ orbitals, leading to an orbital-selective state with a nematic character that becomes stronger at increasing density. One of these orbitals stays half-filled for all densities while the other one hosts (together with the $d_{xy}$ orbital) the excess of electron density. Most importantly, in this regime long-range pairing correlations appear in the orbital with the largest occupation. Our results highlight a strong link between orbital-selective correlations, nematicity, and superconductivity, which requires the presence of a significant Hund's coupling.

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arXiv2024

Fine-tuning Neural Network Quantum States

Recent progress in the design and optimization of neural-network quantum states (NQSs) has made them an effective method to investigate ground-state properties of quantum many-body systems. In contrast to the standard approach of training a separate NQS from scratch at every point of the phase diagram, we demonstrate that the optimization of a NQS at a highly expressive point of the phase diagram (i.e., close to a phase transition) yields features that can be reused to accurately describe a wide region across the transition. We demonstrate the feasibility of our approach on different systems in one and two dimensions by initially pretraining a NQS at a given point of the phase diagram, followed by fine-tuning only the output layer for all other points. Notably, the computational cost of the fine-tuning step is very low compared to the pretraining stage. We argue that the reduced cost of this paradigm has significant potential to advance the exploration of strongly-correlated systems using NQS, mirroring the success of fine-tuning in machine learning and natural language processing.

cond-mat.dis-nn↗

arXiv2023

Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model

Understanding quantum magnetism in two-dimensional systems represents a lively branch in modern condensed-matter physics. In the presence of competing super-exchange couplings, magnetic order is frustrated and can be suppressed down to zero temperature. Still, capturing the correct nature of the exact ground state is a highly complicated task, since energy gaps in the spectrum may be very small and states with different physical properties may have competing energies. Here, we introduce a variational Ansatz for two-dimensional frustrated magnets by leveraging the power of representation learning. The key idea is to use a particular deep neural network with real-valued parameters, a so-called Transformer, to map physical spin configurations into a high-dimensional feature space. Within this abstract space, the determination of the ground-state properties is simplified and requires only a shallow output layer with complex-valued parameters. We illustrate the efficacy of this variational Ansatz by studying the ground-state phase diagram of the Shastry-Sutherland model, which captures the low-temperature behavior of SrCu$_2$(BO$_3$)$_2$ with its intriguing properties. With highly accurate numerical simulations, we provide strong evidence for the stabilization of a spin-liquid between the plaquette and antiferromagnetic phases. In addition, a direct calculation of the triplet excitation at the $\Gamma$ point provides compelling evidence for a gapless spin liquid. Our findings underscore the potential of Neural-Network Quantum States as a valuable tool for probing uncharted phases of matter, and open up new possibilities for establishing the properties of many-body systems.

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arXiv2023

Spin-phonon interactions on the kagome lattice: Dirac spin liquid versus valence-bond solids

We investigate the impact of the spin-phonon coupling on the S=1/2 Heisenberg model on the kagome lattice. For the pure spin model, there is increasing evidence that the low-energy properties can be correctly described by a Dirac spin liquid, in which spinons with a conical dispersion are coupled to emergent gauge fields. Within this scenario, the ground-state wave function is well approximated by a Gutzwiller-projected fermionic state [Y. Ran, M. Hermele, P.A. Lee, and X.-G. Wen, Phys. Rev. Lett. 98, 117205 (2007)]. However, the existence of U(1) gauge fields may naturally lead to instabilities when small perturbations are included. Since phonons are ubiquitous in real materials, they may play a relevant role in the determination of the actual physical properties of the kagome antiferromagnet. We perform a step forward in this direction, including phonon degrees of freedom (at the quantum level) and applying a variational approach based upon Gutzwiller-projected fermionic Ans\"atze. Our results suggest that the Dirac spin liquid is stable for small spin-phonon couplings, while valence-bond solids are obtained at large couplings. Even though different distortions can be induced by the spin-phonon interaction, the general aspect is that the energy is lowered by maximizing the density of perfect hexagons in the dimerization pattern.

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arXiv2023

A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States

Neural-network architectures have been increasingly used to represent quantum many-body wave functions. These networks require a large number of variational parameters and are challenging to optimize using traditional methods, as gradient descent. Stochastic Reconfiguration (SR) has been effective with a limited number of parameters, but becomes impractical beyond a few thousand parameters. Here, we leverage a simple linear algebra identity to show that SR can be employed even in the deep learning scenario. We demonstrate the effectiveness of our method by optimizing a Deep Transformer architecture with $3 \times 10^5$ parameters, achieving state-of-the-art ground-state energy in the $J_1$-$J_2$ Heisenberg model at $J_2/J_1=0.5$ on the $10\times10$ square lattice, a challenging benchmark in highly-frustrated magnetism. This work marks a significant step forward in the scalability and efficiency of SR for Neural-Network Quantum States, making them a promising method to investigate unknown quantum phases of matter, where other methods struggle.

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arXiv2023

Piercing the Dirac spin liquid: From a single monopole to chiral states

The parton approach for quantum spin liquids gives a transparent description of low-energy elementary excitations, e.g., spinons and emergent gauge-field fluctuations. The latter ones are directly coupled to the hopping/pairing of spinons. By using the fermionic representation of the $U(1)$ Dirac state on the kagome lattice and variational Monte Carlo techniques to include the Gutzwiller projection, we analyse the effect of modifying the gauge fields in the spinon kinematics. In particular, we construct low-energy monopole excitations, which are shown to be gapless in the thermodynamic limit. States with a finite number of monopoles or with a finite density of them are also considered, with different patterns of the gauge fluxes. We show that these chiral states are not stabilized in the Heisenberg model with nearest-neighbor super-exchange couplings, and the Dirac state corresponds to the lowest-energy Ansatz within this family of variational wave functions. Our results support the idea that spinons with a gapless conical spectrum coexist with gapless monopole excitations, even for the spin-1/2 case.

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arXiv2023

A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas

We show that a two-body Jastrow wave function is able to capture the ground-state properties of the $S=1$ antiferromagnetic Heisenberg chain with the single-ion anisotropy term, in both the topological and trivial phases. Here, the optimized Jastrow pseudo potential assumes a very simple form in Fourier space, i.e., $v_{q} \approx 1/q^2$, which is able to give rise to a finite string-order parameter in the topological regime. The results are analysed by using an exact mapping from the quantum expectation values over the variational state to the classical partition function of the one-dimensional Coulomb gas of particles with charge $q=\pm 1$. Here, two phases are present at low temperatures: the first one is a diluted gas of dipoles (bound states of particles with opposite charges), which are randomly oriented (describing the trivial phase); the other one is a dense liquid of dipoles, which are aligned thanks to the residual dipole-dipole interactions (describing the topological phase, with the finite string order being related to the dipole alignment). Our results provide an insightful interpretation of the ground-state nature of the spin-1 antiferromagnetic Heisenberg model.

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arXiv2023

Variational Benchmarks for Quantum Many-Body Problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

quant-ph↗

arXiv2022

A real-space many-body marker for correlated ${\mathbb Z}_2$ topological insulators

Taking the clue from the modern theory of polarization [R. Resta, Rev. Mod. Phys. {\bf 66}, 899 (1994)], we identify an operator to distinguish between ${\mathbb Z}_2$-even (trivial) and ${\mathbb Z}_2$-odd (topological) insulators in two spatial dimensions. Its definition extends the position operator [R. Resta and S. Sorella, Phys. Rev. Lett. {\bf 82}, 370 (1999)], which was introduced in one-dimensional systems. We first show a few examples of non-interacting models, where single-particle wave functions are defined and allow for a direct comparison with standard techniques on large system sizes. Then, we illustrate its applicability for an interacting model on a small cluster, where exact diagonalizations are available. Its formulation in the Fock space allows a direct computation of expectation values over the ground-state wave function (or any approximation of it), thus allowing us to investigate generic interacting systems, such as strongly-correlated topological insulators.

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arXiv2022

Transformer variational wave functions for frustrated quantum spin systems

The Transformer architecture has become the state-of-art model for natural language processing tasks and, more recently, also for computer vision tasks, thus defining the Vision Transformer (ViT) architecture. The key feature is the ability to describe long-range correlations among the elements of the input sequences, through the so-called self-attention mechanism. Here, we propose an adaptation of the ViT architecture with complex parameters to define a new class of variational neural-network states for quantum many-body systems, the ViT wave function. We apply this idea to the one-dimensional $J_1$-$J_2$ Heisenberg model, demonstrating that a relatively simple parametrization gets excellent results for both gapped and gapless phases. In this case, excellent accuracies are obtained by a relatively shallow architecture, with a single layer of self-attention, thus largely simplifying the original architecture. Still, the optimization of a deeper structure is possible and can be used for more challenging models, most notably highly-frustrated systems in two dimensions. The success of the ViT wave function relies on mixing both local and global operations, thus enabling the study of large systems with high accuracy.

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