arXiv subjects

Ettore Vitali

Publications and source records attributed to Ettore Vitali.

18 recordsLinked to original sources

arXiv2026

Tuning Interatomic Forces with Magnetic Fields: Feshbach Resonances in Lithium-6

Feshbach resonances, first studied in the context of nuclear reactions, have since become a cornerstone of modern atomic physics. They offer a remarkable degree of control over interatomic (and even intermolecular) interactions by tuning external magnetic fields. This tunability arises from the interplay between quantum scattering and the internal structure of atoms or nuclei. In this work, we explore the essential physics of Feshbach resonances using only basic quantum mechanics, aiming to make this powerful concept accessible to educators and students alike.

physics.ed-ph↗

arXiv2024

Monte Carlo Methods in the Manifold of Hartree-Fock-Bogoliubov Wave Functions

We explore the possibility to implement random walks in the manifold of Hartree-Fock-Bogoliubov wave functions. The goal is to extend state-of-the-art quantum Monte Carlo approaches, in particular the constrained-path auxiliary-field quantum Monte Carlo technique, to systems where finite pairing order parameters or complex pairing mechanisms, e.g., Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing or triplet pairing, may be expected. Leveraging the flexibility to define a vacuum state tailored to the physical problem, we discuss a method to use imaginary-time evolution of Hartree-Fock-Bogoliubov states to compute ground state correlations, extending beyond situations spanned by current formalisms. Illustrative examples are provided.

cond-mat.str-el↗

arXiv2024

Spectrum of density, spin and pairing fluctuations of an attractive two-dimensional Fermi gas

We leverage random phase approximation and unbiased auxiliary-field quantum Monte Carlo methods to compute dynamical correlations for a dilute homogeneous two-dimensional attractive Fermi gas. Our main purpose is to quantitatively study the collective excitations of the system to generate robust benchmark results and to shed light into fermionic superfluidity in the strongly correlated regime. In particular we are motivated by a recent paper suggesting that the Higgs mode can be detected in the spectrum of spin fluctuations. Despite the fact that we are somewhat limited by finite-size effects, our study pinpoints indeed a clear peak in the spin channel at low momentum, but a detailed analysis suggests that such a peak, though certainly interesting, does not correspond to the Higgs mode. We propose a different explanation for the shape of the spin structure factor. On the other hand, our results clearly show that the Higgs mode can be detected in the density channel at very small wave vectors, although very good resolution is necessary.

cond-mat.quant-gas↗

arXiv2023

Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at $1/3$-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU($N$) physics.

cond-mat.str-el↗

arXiv2022

Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram

We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an anti-ferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods, established the stripe order as the ground state near $1/8$ doping at strong interactions. In this work, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about $1/5$ doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes in the pure Hubbard model.

cond-mat.str-el↗

arXiv2021

Exotic Superfluid Phases in Spin Polarized Systems on Optical Lattices

Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly $500$ atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between interaction and superfluidity in an exotic phase of matter.

cond-mat.quant-gas↗

arXiv2020

Fermionic Superfluidity: From Cold Atoms to Neutron Stars

From flow without dissipation of energy to the formation of vortices when placed within a rotating container, the superfluid state of matter has proven to be a very interesting physical phenomenon. Here we present the key mechanisms behind superfluidity in fermionic systems and apply our understanding to an exotic system found deep within the universe -- the superfluid found deep within a neutron star. A defining trait of a superfluid is the pairing gap, which the cooling curves of neutron stars depend on. The extreme conditions surrounding a neutron star prevent us from directly probing the superfluid's properties, however, we can experimentally realize conditions resembling the interior through the use of cold atoms prepared in a laboratory and simulated on a computer. Experimentalists are becoming increasingly adept at realizing cold atomic systems in the lab that mimic the behavior of neutron stars and superconductors. In their turn, computational physicists are leveraging the power of supercomputers to simulate interacting atomic systems with unprecedented accuracy. This paper is intended to provide a pedagogical introduction to the underlying concepts and the possibility of using cold atoms as a tool that can help us make significant strides towards understanding exotic physical systems.

cond-mat.quant-gas↗

arXiv2020

Dynamical structure factor of a fermionic supersolid on an optical lattice

Interfacing unbiased quantum Monte Carlo simulations with state-of-art analytic continuation techniques, we obtain exact numerical results for dynamical density and spin correlations in the attractive Hubbard model, describing a spin-balanced two-dimensional cold Fermi gas on an optical lattice. We focus on half-filling, where on average one fermion occupies each lattice site, and the system displays an intriguing supersolid phase: a superfluid with a checkerboard density modulation. The coexistence of $U(1)$ broken symmetry and the density modulations makes this regime very challenging and interesting for the calculation of dynamical properties. We compare our unbiased results with state-of-the-art Generalized Random Phase Approximation calculations: both approaches agree on a well-defined low-energy Nambu-Goldstone collective mode in the density correlations, while the higher energy structures appear to differ significantly. We also observe an interesting high-energy spin mode. We argue that our results provide a robust benchmark for Generalized Random Phase Approximation techniques, which are widely considered to be the method of choice for dynamical correlations in Fermi gases. Also, our calculations yield new physical insight in the high-energy behavior of the dynamical structure factor of the attractive Hubbard model, which is a well known prototype lattice model for superconductors and is a fertile field to target the observation of collective modes in strongly correlated systems.

cond-mat.quant-gas↗

arXiv2020

Magnetic and charge orders in the ground state of the Emery model -- accurate numerical results

We perform extensive auxiliary-field quantum Monte Carlo (AFQMC) calculations for the three-band Hubbard (Emery) model in order to study the ground-state properties of Copper-Oxygen planes in the cuprates. Employing cutting-edge AFQMC techniques with a self-consistent gauge constraint in auxiliary-field space to control the sign problem, we reach supercells containing around 500 atoms to capture collective modes in the charge and spin orders and characterize the behavior in the thermodynamic limit. The self-consistency scheme interfacing with generalized Hartree-Fock calculations allows high accuracy in AFQMC to resolve small energy scales, which is crucial for determining the complex candidate orders in such a system. We present detailed information on the charge order, spin order, momentum distribution, and localization properties as a function of charge-transfer energy for the the under-doped regime. In contrast with the stripe and spiral orders under hole-doping, we find that the corresponding 1/8 electron-doped system exhibits purely antiferromagnetic order in the three-band model, consistent with the asymmetry between electron and hole-doping in the phase diagram of cuprates.

cond-mat.supr-con↗

arXiv2020

Absence of superconductivity in the pure two-dimensional Hubbard model

We study the superconducting pairing correlations in the ground state of the doped Hubbard model -- in its original form without hopping beyond nearest neighbor or other perturbing parameters -- in two dimensions at intermediate to strong coupling and near optimal doping. The nature of such correlations has been a central question ever since the discovery of cuprate high-temperature superconductors. Despite unprecedented effort and tremendous progress in understanding the properties of this fundamental model, a definitive answer to whether the ground state is superconducting in the parameter regime most relevant to cuprates has proved exceedingly difficult to establish. In this work, we employ two complementary, state-of-the-art many-body computational methods, constrained path (CP) auxiliary-field quantum Monte Carlo (AFQMC) and density matrix renormalization group (DMRG) methods, deploying the most recent algorithmic advances in each. Systematic and detailed comparisons between the two methods are performed. The DMRG is extremely reliable on small width cylinders, where we use it to validate the AFQMC. The AFQMC is then used to study wide systems as well as fully periodic systems, to establish that we have reached the thermodynamic limit. The ground state is found to be non-superconducting in the moderate to strong coupling regime in the vicinity of optimal hole doping.

cond-mat.str-el↗

arXiv2019

Dynamical BCS theory of a two-dimensional attractive Fermi gas: effective interactions from Quantum Monte Carlo calculations

The primary work presented in this paper focuses on the calculation of density-density dynamical correlations in an attractive two dimensional Fermi gas in several physically interesting regimes, including the strongly correlated BEC-BCS crossover regime. We use state-of-the-art dynamical BCS theory and we address the possibility to renormalize the interaction strength, using unbiased Quantum Monte Carlo results as an asset to validate the predictions. We propose that a suitable interplay between dynamical BCS theory, which is computationally very cheap and yields results directly in real time domain, and Quantum Monte Carlo methods, which are exact but way more demanding and limited to imaginary time domain, can be a very promising idea to study dynamics in many body systems. We illustrate the idea and provide quantitative results for a few values of the interaction strength in the cold gas.

cond-mat.quant-gas↗

arXiv2019

Calculating ground state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches

We introduce an efficient and numerically stable technique to make use of a BCS trial wave function in the computation of correlation functions of strongly correlated quantum fermion systems. The technique is applicable to any projection approach involving paths of independent-fermion propagators, for example in mean-field or auxiliary-field quantum Monte Carlo (AFQMC) calculations. Within AFQMC, in the absence of the sign problem, the methodology allows the use of a BCS reference state which can greatly reduce the required imaginary time of projection, and improves Monte Carlo sampling efficiency and statistical accuracy for systems where pairing correlations are important. When the sign problem is present, the approach provides a powerful generalization of the constrained-path AFQMC technique which usually uses Slater determinant trial wave functions. As a demonstration of the capability of the methodology, we present benchmark results for the attractive Hubbard model, both spin-balanced (no sign problem) and with a finite spin polarization (with sign problem).

cond-mat.str-el↗

arXiv2018

Metal-insulator transition in the ground-state of the three-band Hubbard model at half-filling

The three-band Hubbard model is a fundamental model for understanding properties of the Copper-Oxygen planes in cuprate superconductors. We use cutting-edge auxiliary-field quantum Monte Carlo (AFQMC) methods to investigate ground state properties of the model in the parent compound. Large supercells combined with twist averaged boundary conditions are studied to reliably reach the thermodynamic limit. Benchmark quality results are obtained on the magnetic correlations and charge gap. A key parameter of this model is the charge-transfer energy $Δ$ between the Oxygen p and the Copper d orbitals, which appears to vary significantly across different families of cuprates and whose ab initio determination is subtle. We show that the system undergoes a quantum phase transition from an antiferromagnetic insulator to a paramagnetic metal as $Δ$ is lowered to 3 eV.

cond-mat.supr-con↗

arXiv2018

Magnetic orders in the hole doped three-band Hubbard model: spin spirals, nematicity, and ferromagnetic domain walls

The Copper-Oxygen planes in cuprates have been at the center of the search for a theory of high-temperature superconductivity. We conduct an extensive study of the ground state of the three-band Hubbard (Emery) model in the underdoped regime. We focus on the magnetic and charge orders, and present results from generalized Hartree-Fock (GHF) calculations. The ground-state properties at the thermodynamic limit are challenging to pin down because of sensitivity to computational details including the shapes and sizes of the supercells. We employ large-scale computations with various technical improvements to determine the orders within GHF. The ground state exhibits a rich phase diagram with hole doping as the charge transfer energy is varied, including ferromagnetic domain walls embedded in an antiferromagnetic background, spin spirals, and nematic order.

cond-mat.supr-con↗

arXiv2017

Response functions for the two-dimensional ultracold Fermi gas: dynamical BCS theory and beyond

Response functions are central objects in physics. They provide crucial information about the behavior of physical systems, and they can be directly compared with scattering experiments involving particles like neutrons, or photons. Calculations of such functions starting from the many-body Hamiltonian of a physical system are challenging, and extremely valuable. In this paper we focus on the two-dimensional (2D) ultracold Fermi atomic gas which has been realized experimentally. We present an application of the dynamical BCS theory to obtain response functions for different regimes of interaction strengths in the 2D gas with zero-range attractive interaction. We also discuss auxiliary-field quantum Monte Carlo (AFQMC) methods for the calculation of imaginary-time correlations in these dilute Fermi gas systems. Illustrative results are given and comparisons are made between AFQMC and dynamical BCS theory results to assess the accuracy of the latter.

cond-mat.quant-gas↗

arXiv2017

Visualizing the BEC-BCS crossover in the two-dimensional Fermi gas: pairing gaps and dynamical response functions from ab initio computations

Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi gas from first principles. Applying state-of-art analytic continuation techniques, we obtain the spectral function, and the density and spin structure factors providing unique tools to visualize the BEC-BCS crossover. These quantities will allow for a direct comparison with experiments.

cond-mat.quant-gas↗

arXiv2016

Computation of dynamical correlation functions for many fermion systems with auxiliary-field quantum Monte Carlo

We address the calculation of dynamical correlation functions for many fermion systems at zero temperature, using the auxiliary-field quantum Monte Carlo method. The two-dimensional Hubbard hamiltonian is used as a model system. Although most of the calculations performed here are for cases where the sign problem is absent, the discussions are kept general for applications to physical problems when the sign problem does arise. We study the use of twisted boundary conditions to improve the extrapolation of the results to the thermodynamic limit. A strategy is proposed to drastically reduce finite size effects relying on a minimization among the twist angles. This approach is demonstrated by computing the charge gap at half-filling. We obtain accurate results showing the scaling of the gap with the interaction strength $U$, connecting to the scaling of the unrestricted Hartree-Fock method at small $U$ and Bethe Ansatz exact result in one dimension at large $U$. A new algorithm is then proposed to compute dynamical Green functions and correlation functions which explicitly varies the number of particles during the random walks in the manifold of Slater determinants. In dilute systems, such as ultracold Fermi gases, this algorithm enables calculations with much more favorable complexity, with computational cost proportional to basis size or the number of lattice sites.

cond-mat.str-el↗

arXiv2016

Low-density phases of $^3$He monolayers adsorbed on graphite

Quantum Monte Carlo simulations at zero temperature of a $^3$He monolayer adsorbed on graphite, either clean or preplated with $^4$He, unexpectedly point to a gas-liquid phase transition at a very low areal density of the order of 0.01Å$^{-2}$. This result stems from an essentially unbiased calculation of the ground state energy for an infinite, defect-free substrate which interacts with He atoms via a realistic potential, whereas the interaction between two He atoms includes two- and three-body terms. The sensitivity of the gas-liquid coexistence region on the model Hamiltonian employed is discussed.

cond-mat.stat-mech↗