arXiv subjects

Michel Ferrero

Publications and source records attributed to Michel Ferrero.

At least 19 recordsLinked to original sources

arXiv2026

Charge and spin orders in the t-U-V-J model: a slave-spin-1 approach

Strongly-correlated fermion systems on a lattice have been a subject of intense focus in the field of condensed-matter physics. These systems are notoriously difficult to solve, even with state-of-the-art numerical methods, especially in regimes of parameters where degrees of freedom compete or cooperate at similar energy and length scales. Here, we introduce a spin-1 slave-particle technique to approximately treat the t-U-V-J fermionic model at arbitrary electron dopings in an economical manner. This formalism respectively maps the original charge and spin degrees of freedom into effective pseudo-spin and pseudo-fermion sectors, which are treated using a self-consistent cluster mean-field method. We study the phase diagram of the model under various conditions and report the appearance of charge and spin stripes within this formalism. These stripes are a consequence of the cluster mean-field treatment of the pseudo-particle sectors and have not been detected in previous slave-particle studies. The results obtained agree qualitatively well with what more reliable numerical methods capture.

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arXiv2025

Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model

Accurate simulations of the Hubbard model are crucial to understanding strongly correlated phenomena, where small energy differences between competing orders demand high numerical precision. In this work, Neural Quantum States are used to probe the strongly coupled and underdoped regime of the square-lattice Hubbard model. We systematically compare the Hidden Fermion Determinant State and the Jastrow-Backflow ansatz, parametrized by a Vision Transformer, finding that in practice, their accuracy is similar. We also test different symmetrization strategies, finding that output averaging yields the lowest energies, though it becomes costly for larger system sizes. On cylindrical systems, we consistently observe filled stripes. On the torus, our calculations display features consistent with a doped Mott insulator, including antiferromagnetic correlations and suppressed density fluctuations. Our results demonstrate both the promise and current challenges of neural quantum states for correlated fermions.

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arXiv2025

Algorithm for computing perturbation series of dynamical mean field theory

We show how to use diagrammatic techniques to compute the weak-coupling perturbation series of the self-consistent solution to a Dynamical Mean Field Theory (DMFT) problem. This approach constitutes an alternative to using diagrammatic techniques directly as an impurity solver. It allows one to bypass the need of multiple perturbative series resummations within the DMFT self-consistency loop. It can be applied at or out of equilibrium, with any diagrammatic formalism, such as real times, imaginary times, or Matsubara frequencies formalisms. As a proof of principle, we illustrate our method with the half-filled Hubbard model on the Bethe lattice in the DMFT approximation, using Quantum Quasi-Monte Carlo (QQMC) to obtain the impurity perturbation series on the real time axis.

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arXiv2025

Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models

Computing dynamical response functions in interacting lattice models is a long standing challenge in condensed matter physics. In view of recent results, the dc resistivity $\rho_\mathrm{dc}$ in the weak coupling regime of the Hubbard model is of great interest, yet it is not fully understood. The challenge lies in having to work with large lattices while avoiding analytical continuation. The weak-coupling $\rho_\mathrm{dc}$ results were so far computed at the level of the Boltzmann theory and at the level of the Kubo bubble approximation, which neglects vertex corrections. Neither theory was so far rigorously proven to give exact results even at infinitesimal coupling, and the respective dc resistivity results differ greatly. In this work we develop, cross-check and apply two state-of-the-art methods for obtaining dynamical response functions. We compute the optical conductivity at weak coupling in the Hubbard model in a fully controlled way, in the thermodynamic limit and without analytical continuation. We show that vertex corrections persist to infinitesimal coupling, with a constant ratio to the Kubo bubble. We connect our methods with the Boltzmann theory, and show that the latter applies additional approximations, which lead to quantitatively incorrect scaling of $\rho_\mathrm{dc}$ with respect to the coupling constant.

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arXiv2024

Turning qubit noise into an advantage: Automatic state preparation and long-time dynamics for impurity models on quantum computers

Noise is often regarded as a limitation of quantum computers. In this work, we show that in the dynamical mean field theory (DMFT) approach to strongly-correlated systems, it can actually be harnessed to our advantage. Indeed, DMFT maps a lattice model onto an impurity model, namely a finite system coupled to a dissipative bath. While standard approaches require a large number of high-quality qubits in a unitary context, we propose a circuit that harvests amplitude damping to reproduce the dynamics of this model with a blend of noisy and noiseless qubits. We find compelling advantages with this approach: a substantial reduction in the number of qubits, the ability to reach longer time dynamics, and no need for ground state search and preparation. This method would naturally fit in a partial quantum error correction framework.

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arXiv2024

Learning interactions between Rydberg atoms

Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully controllable, allowing for precise tuning of the microscopic physical parameters that define their implementation. We consider Rydberg-atom arrays, a promising platform for quantum simulations. Experimental control of such arrays is limited by the imprecision on the optical tweezers positions when assembling the array, hence introducing uncertainties in the simulated Hamiltonian. In this work, we introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs). We employ the Density Matrix Renormalization Group (DMRG) to generate ground-state snapshots of the transverse field Ising model realized by the array, for many realizations of the Hamiltonian parameters. Correlation functions reconstructed from these snapshots serve as input data to carry out the training. We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain, both regarding the size and the shape of the system, yielding an accurate determination of the Hamiltonian parameters with a minimal set of measurements. We prove a theorem establishing a bijective correspondence between the correlation functions and the interaction parameters in the Hamiltonian, which provides a theoretical foundation to our learning algorithm. Our work could open the road to feedback control of the positions of the optical tweezers, hence providing a decisive improvement of analog quantum simulators.

quant-ph↗

arXiv2024

Efficiency of neural quantum states in light of the quantum geometric tensor

Neural quantum state (NQS) ansätze have shown promise in variational Monte Carlo algorithms by their theoretical capability of representing any quantum state. However, the reason behind the practical improvement in their performance with an increase in the number of parameters is not fully understood. In this work, we systematically study the efficiency of a shallow neural network to represent the ground states in different phases of the spin-1 bilinear-biquadratic chain, as the number of parameters increases. We train our ansatz by a supervised learning procedure, minimizing the infidelity w.r.t. the exact ground state. We observe that the accuracy of our ansatz improves with the network width in most cases, and eventually saturates. We demonstrate that this can be explained by looking at the spectrum of the quantum geometric tensor (QGT), particularly its rank. By introducing an appropriate indicator, we establish that the QGT rank provides a useful diagnostic for the practical representation power of an NQS ansatz.

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arXiv2024

Magnetic phase diagram of the three-dimensional doped Hubbard model

We establish the phase diagram of the Hubbard model on a cubic lattice for a wide range of temperatures, dopings and interaction strengths, considering both commensurate and incommensurate magnetic orders. We use the dynamical mean-field theory together with an efficient method to compute the free energy which enable the determination of the correct ordering vectors. Besides an antiferromagnetic state close to half-filling, we identify a number of different magnetic spiral phases with ordering vectors $(q,π,π)$, $(q,q,π)$ and $(q,q,q)$ as well as a region with close competition between them, hinting at spatial phase separation or at the onset of a stripe phase. Additionally, we extensively study several thermodynamic properties with direct relevance to cold-atom experiments: the entropy, energy and double-occupancy.

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arXiv2024

Luttinger surface dominance and Fermi liquid behaviour of topological Kondo insulators SmB$_6$ and YbB$_{12}$

Defying the traditional classification into metals and insulators, several materials simultaneously display metallic thermal properties and insulating electric behaviour, as if they hosted quasiparticles carrying entropy but not charge. Among them, some materials also possess quantum oscillations in magnetic fields as if they had well-defined Fermi surfaces despite the insulating gap. This remarkable dichotomy has been observed in the topological Kondo insulators SmB$_6$ and YbB$_{12}$. Prompted by the peculiar mixed-valence nature of these compounds, involving $f$ and $d$ electrons of the lanthanide, we propose an explanation of their intriguing properties drawing inspiration from the physics of the pseudogap phase in underdoped cuprates. We argue that the $f$ and $d$ subsystems, when considered separately, act, respectively, as electron- and hole-doped Mott insulators, featuring Fermi pockets coexisting with Luttinger surfaces responsible for the pseudogap. When the two are coupled to each other a hybridisation gap opens up, and the whole turns into a topological insulator endowed with genuine chiral edge states. However, the Luttinger surfaces persist and support neutral quasiparticles. This scenario, supported by numerical simulations within the dynamical cluster approximation, effectively resolves the paradoxical phenomenology of SmB$_6$ and YbB$_{12}$.

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arXiv2024

Compact fermionic quantum state preparation with a natural-orbitalizing variational quantum eigensolving scheme

Assemblies of strongly interacting fermions, whether in a condensed-matter or a quantum chemistry context, range amongst the most promising candidate systems for which quantum computing platforms could provide an advantage. Near-term quantum state preparation is typically realized by means of the variational quantum eigensolver (VQE) algorithm. One of the main challenges to a successful implementation of VQE lies in the sensitivity to noise exhibited by deep variational circuits. On the other hand, sufficient depth must be allowed to be able to reach a good approximation to the target state. In this work, we present a refined VQE scheme that consists in topping VQE with state-informed updates of the elementary fermionic modes (spin-orbitals). These updates consist in moving to the natural-orbital basis of the current, converged variational state, a basis we argue eases the task of state preparation. We test the method on the Hubbard model in the presence of experimentally relevant noise levels. For a fixed circuit structure, the method is shown to enhance the capabilities of the circuit to reach a state close to the target state without incurring too much overhead from shot noise. Moreover, coupled with an adaptive VQE scheme that constructs the circuit on the fly, we evidence reduced requirements on the depth of the circuit as the orbitals get updated.

quant-ph↗

arXiv2024

Superconductivity and Mottness in Organic Charge Transfer Materials

The phase diagrams of quasi two-dimensional organic superconductors display a plethora of fundamental phenomena associated with strong electron correlations, such as unconventional superconductivity, metal-insulator transitions, frustrated magnetism and spin liquid behavior. We analyze a minimal model for these compounds, the Hubbard model on an anisotropic triangular lattice, using cutting-edge quantum embedding methods respecting the lattice symmetry. We demonstrate the existence of unconventional superconductivity by directly entering the symmetry-broken phase. We show that the crossover from the Fermi liquid metal to the Mott insulator is associated with the formation of a pseudogap. The predicted momentum-selective destruction of the Fermi surface into hot and cold regions provides motivation for further spectroscopic studies. Our results are in remarkable agreement with experimental phase diagrams of $κ$-BEDT organics.

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arXiv2024

Simple predictors of $T_c$ in superconducting cuprates and the role of interactions between effective Wannier orbitals in the $d-p$ 3-band model

At optimal doping, different cuprate compounds can exhibit vastly different critical temperatures for superconductivity ($T_c$), ranging from about 20 K to about 135 K. The precise properties of the lattice that determine the magnitude of the $T_c$ are currently unknown. In this paper, we investigate the dependence of the optimal doping $T_c$ on the parameters of the Emery ($d-p$) model for the CuO$_2$ planes in the cuprates. We show that the best scaling is obtained not with the parameters of the model written in the real ($d/p$-orbital) space, but rather written in the space of effective Wannier orbitals. In this basis, one obtains a model of three sublattices coupled through all possible 4-point interactions. We identify multiple predictor variables that fit the experimental $T_c$ to about $\pm4-5$ K and that remarkably depend on the leading attractive coupling constants in the transformed Hamiltonian.

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arXiv2023

Magnetism and Metallicity in Moiré Transition Metal Dichalcogenides

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.

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arXiv2022

Origin and fate of the pseudogap in the doped Hubbard model

We investigate the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations allowing for the computation of spectral properties in the infinite-size limit and, crucially, with arbitrary momentum resolution. We show that three distinct regimes are found as a function of doping and interaction strength, corresponding to a weakly correlated metal with properties close to those of the non-interacting system, a correlated metal with strong interaction effects including a reshaping of the Fermi surface, and a pseudogap regime at low doping in which quasiparticle excitations are selectively destroyed near the antinodal regions of momentum space. We study the physical mechanism leading to the pseudogap and show that it forms both at weak coupling when the magnetic correlation length is large and at strong coupling when it is shorter. In both cases, we show that spin-fluctuation theory can be modified in order to account for the behavior of the non-local component of the self-energy. We discuss the fate of the pseudogap as temperature goes to zero and show that, remarkably, this regime extrapolates precisely to the ordered stripe phase found by ground-state methods. This handshake between finite temperature and ground-state results significantly advances the elaboration of a comprehensive picture of the physics of the doped Hubbard model.

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arXiv2021

Inexorable Edge Kondo Breakdown in Topological Kondo Insulators

Kondo breakdown is one of the most intriguing problems in strongly correlated electron systems, as it is rooted in many anomalous electron behaviors found in heavy-fermion materials. In Kondo lattice systems, Kondo breakdown can arise from either strong magnetic frustrations or critical fluctuations of collective modes. Here, we reveal a new type of Kondo breakdown with a fully different origin in interacting topological Kondo insulators. By employing numerically exact quantum Monte Carlo simulations, we show that with open boundary conditions, Kondo screening is inexorably destroyed by interaction effects on edges or corners in these systems. We argue that the Kondo breakdown is enforced by the symmetries of the system, because the ground states are symmetry protected Haldane phases.

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arXiv2021

Mott insulating states with competing orders in the triangular lattice Hubbard model

The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from a metal-insulator transition, intriguing thermodynamic behavior, and a putative spin liquid phase at intermediate coupling, ultimately becoming a magnetic insulator at strong coupling. In this multimethod study, we combine a finite-temperature tensor network method, minimally entangled thermal typical states (METTS), with two Green-function-based methods, connected-determinant diagrammatic Monte Carlo and cellular dynamical mean-field theory, to establish several aspects of this model. We elucidate the evolution from the metallic to the insulating regime from the complementary perspectives brought by these different methods. We compute the full thermodynamics of the model on a width-four cylinder using METTS in the intermediate to strong coupling regime. We find that the insulating state hosts a large entropy at intermediate temperatures, which increases with the strength of the coupling. Correspondingly, and consistently with a thermodynamic Maxwell relation, the double occupancy has a minimum as a function of temperature which is the manifestation of the Pomeranchuk effect of increased localization upon heating. The intermediate coupling regime is found to exhibit both pronounced chiral as well as stripy antiferromagnetic spin correlations. We propose a scenario in which time-reversal symmetry-broken states compete with stripy-spin states at lowest temperatures.

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arXiv2021

The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature and interaction strength. Through these quantities, we identify a weak-coupling regime, a strong-coupling regime with short-range correlations and an intermediate-coupling regime with long magnetic correlation lengths. In the spin channel, we observe an additional crossover from commensurate to incommensurate correlations. In contrast, we find charge correlations to be only short ranged for all studied temperatures, which suggests that the spin and charge responses are decoupled. These findings were obtained by a novel connected determinant diagrammatic Monte Carlo algorithm for the computation of double expansions, which we introduce in this paper. This permits us to obtain numerically exact results at unprecedentedly low temperatures $T\geq 0.067$ for interactions up to $U\leq 8$, while working on arbitrarily large lattices. Our method also allows us to gain physical insights from investigating the analytic structure of perturbative series. We connect to previous work by studying smaller lattice geometries and report substantial finite-size effects.

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arXiv2021

Fast Principal Minor Algorithms for Quantum Many Body Systems

The computation of determinants plays a central role in diagrammatic Monte Carlo algorithms for strongly correlated systems. The evaluation of large numbers of determinants can often be the limiting computational factor determining the number of attainable diagrammatic expansion orders. In this work we build upon the algorithm presented in [\emph{Linear Algebra and its applications} 419.1 (2006), 107-124] which computes all principal minors of a matrix in $O(2^n)$ operations. We present multiple generalizations of the algorithm to the efficient evaluation of certain subsets of all principal minors with immediate applications to Connected Determinant Diagrammatic Monte Carlo within the normal and symmetry-broken phases as well as Continuous-time Quantum Monte Carlo. Additionally, we improve the asymptotic scaling of diagrammatic Monte Carlo formulated in real-time to $O(2^n)$ and report speedups of up to a factor $25$ at computationally realistic expansion orders. We further show that all permanent-principal-minors, corresponding to sums of bosonic Feynman diagrams, can be computed in $O(3^n)$, making diagrammatic Monte Carlo for bosonic and mixed systems a viable path worth exploring.

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