arXiv subjects

Sebastiano Pilati

Publications and source records attributed to Sebastiano Pilati.

29 records · Page 2Linked to original sources

arXiv2019

Few-boson localization in a continuum with speckle disorder

The disorder-induced localization of few bosons interacting via a contact potential is investigated through the analysis of the level-spacing statistics familiar from random matrix theory. The model we consider is defined in a continuum and describes one-dimensional bosonic atoms exposed to the spatially correlated disorder due to an optical speckle field. % First, we identify the speckle-field intensity required to observe, in the single-particle case, the Poisson level-spacing statistics, which is characteristic of localized quantum systems, in a computationally and experimentally feasible system size. Then, we analyze the two-body and the three-body systems, exploring a broad interaction range, from the noninteracting limit up to moderately strong interactions. Our main result is that the contact potential does not induce a shift towards the Wigner-Dyson level-spacing statistics, which would indicate the emergence of an ergodic chaotic state, indicating that localization can occur also in interacting few-body systems in a continuum. We also analyze how the ground-state energy evolves as a function of the interaction strength

cond-mat.quant-gas↗

arXiv2018

Out-of-equilibrium dynamics of repulsive Fermi gases in quasi-periodic potentials: a Density Functional Theory study

The dynamics of a one-dimensional two-component Fermi gas in the presence of a quasi-periodic optical lattice (OL) is investigated by means of a Density Functional Theory approach. Inspired by the protocol implemented in recent cold-atom experiments, designed to identify the many-body localization transition, we analyze the relaxation of an initially prepared imbalance between the occupation number of odd and of even sites. For quasi-disorder strength beyond the Anderson localization transition, the imbalance survives for long times, indicating the inability of the system to reach local equilibrium. The late time value diminishes for increasing interaction strength. Close to the critical quasi-disorder strength corresponding to the noninteracting (Anderson) transition, the interacting system displays an extremely slow relaxation dynamics, consistent with sub-diffusive behavior. The amplitude of the imbalance fluctuations around its running average is found to decrease with time, and such damping is more effective with increasing interaction strengths. While our study addresses the setup with two equally intense OLs, very similar effects due to interactions have been observed also in recent cold-atom experiments performed in the tight-binding regime, i.e. where one of the two OLs is very deep and the other is much weaker.

cond-mat.quant-gas↗

arXiv2017

One-dimensional Repulsive Fermi Gas in a Tunable Periodic Potential

By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the Tonks-Girardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.

cond-mat.quant-gas↗

arXiv2016

Localization of interacting Fermi gases in quasiperiodic potentials

We investigate the zero-temperature metal-insulator transition in a one-dimensional two-component Fermi gas in the presence of a quasi-periodic potential resulting from the superposition of two optical lattices of equal intensity but incommensurate periods. A mobility edge separating (low energy) Anderson localized and (high energy) extended single-particle states appears in this continuous-space model beyond a critical intensity of the quasi-periodic potential. In order to discern the metallic phase from the insulating phase in the interacting many-fermion system, we employ unbiased quantum Monte Carlo (QMC) simulations combined with the many-particle localization length familiar from the modern theory of the insulating state. In the noninteracting limit, the critical optical-lattice intensity for the metal-insulator transition predicted by the QMC simulations coincides with the Anderson localization transition of the single-particle eigenstates. We show that weak repulsive interactions induce a shift of this critical point towards larger intensities, meaning that repulsion favors metallic behavior. This shift appears to be linear in the interaction parameter, suggesting that even infinitesimal interactions can affect the position of the critical point.

cond-mat.quant-gas↗

arXiv2016

Conduction in quasi-periodic and quasi-random lattices: Fibonacci, Riemann, and Anderson models

We study the ground state conduction properties of noninteracting electrons in aperiodic but non-random one-dimensional models with chiral symmetry, and make comparisons against Anderson models with non-deterministic disorder. The first model we consider is the Fibonacci lattice, which is a paradigmatic model of quasicrystals; the second is the Riemann lattice, which we define inspired by Dyson's proposal on the possible connection between the Riemann hypothesis and a suitably defined quasicrystal. Our analysis is based on Kohn's many-particle localization tensor defined within the modern theory of the insulating state. In the Fibonacci quasicrystal, where all single-particle eigenstates are critical (i.e., intermediate between ergodic and localized), the noninteracting electron gas is found to be a conductor at most electron densities, including the half-filled case; however, at various specific fillings $ρ$, including the values $ρ= 1/g^n$, where $g$ is the golden ratio and $n$ is any integer, the gas turns into an insulator due to spectral gaps. Metallic behaviour is found at half-filling in the Riemann lattice as well; however, in contrast to the Fibonacci quasicrystal, the Riemann lattice is generically an insulator due to single-particle eigenstate localization, likely at all other fillings. Its behaviour turns out to be alike that of the off-diagonal Anderson model, albeit with different system-size scaling of the band-centre anomalies. The advantages of analysing the Kohn's localization tensor instead of other measures of localization familiar from the theory of Anderson insulators (such as the participation ratio or the Lyapunov exponent) are highlighted.

cond-mat.dis-nn↗

arXiv2016

On the quantum spin glass transition on the Bethe lattice

We investigate the ground-state properties of a disorderd Ising model with uniform transverse field on the Bethe lattice, focusing on the quantum phase transition from a paramagnetic to a glassy phase that is induced by reducing the intensity of the transverse field. We use a combination of quantum Monte Carlo algorithms and exact diagonalization to compute Rényi entropies, quantum Fisher information, correlation functions and order parameter. We locate the transition by means of the peak of the Rényi entropy and we find agreement with the transition point estimated from the emergence of finite values of the Edwards-Anderson order parameter and from the peak of the correlation length. We interpret the results by means of a mean-field theory in which quantum fluctuations are treated as massive particles hopping on the interaction graph. We see that the particles are delocalized at the transition, a fact that points towards the existence of possibly another transition deep in the glassy phase where these particles localize, therefore leading to a many-body localized phase.

quant-ph↗

arXiv2015

Anderson localization in optical lattices with correlated disorder

We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are determined as a function of the disorder strength, ranging from vanishing disorder up to the critical disorder intensity where the two mobility edges merge and the whole band becomes localized. Our theoretical analysis is based both on continuous-space models which take into account the details of the spatial correlation of the speckle pattern, and also on a simplified tight-binding model with an uncorrelated distribution of the on-site energies. The mobility edges are computed via the analysis of the energy-level statistics, and we determine the universal value of the ratio between consecutive level spacings at the mobility edge. We analyze the role of the spatial correlation of the disorder, and we also discuss a qualitative comparison with available experimental data for interacting atomic Fermi gases measured in the moderate interaction regime.

cond-mat.quant-gas↗

arXiv2015

Kohn's localisation in disordered fermionic systems with and without interactions

Understanding the metal-insulator transition in disordered many-fermion systems, both with and without interactions, is one of the most challenging and consequential problems in condensed matter physics. In this paper we address this issue from the perspective of the modern theory of the insulating state (MTIS), which has already proven to be effective for band and Mott insulators in clean systems. First we consider noninteracting systems with different types of aperiodic external potentials: uncorrelated disorder (one-dimensional Anderson model), deterministic disorder (Aubry-André Hamiltonian and its modification including next-nearest neighbour hopping), and disorder with long-range correlations (self-affine potential). We show how the many-body localisation tensor defined within the MTIS may be used as a powerful probe to discriminate the insulating and the metallic phases, and to locate the transition point. Then we investigate the effect of weak repulsive interactions in the Aubry-André Hamiltonian, a model which describes a recent cold-atoms experiment. By treating the weak interactions within a mean-field approximation we obtain a linear shift of the transition point towards stronger disorder, providing evidence for delocalisation induced by interactions.

cond-mat.dis-nn↗

arXiv2015

Anderson localization of matter waves in quantum-chaos theory

We study the Anderson localization of atomic gases exposed to three-dimensional optical speckles by analyzing the statistics of the energy-level spacings. This method allows us to consider realistic models of the speckle patterns, taking into account the strongly anisotropic correlations which are realized in concrete experimental configurations. We first compute the mobility edge $E_c$ of a speckle pattern created using a single laser beam. We find that $E_c$ drifts when we vary the anisotropy of the speckle grains, going from higher values when the speckles are squeezed along the beam propagation axis, to lower values when they are elongated. We also consider the case where two speckle patterns are superimposed forming interference fringes, and we find that $E_c$ is increased compared to the case of idealized isotropic disorder. We discuss the important implications of our findings for cold-atoms experiments.

cond-mat.quant-gas↗

arXiv2014

Zero-Temperature Equation of State and Phase Diagram of Repulsive Fermionic Mixtures

We compute the zero-temperature equation of state of a mixture of two fermionic atomic species with repulsive interspecies interactions using second-order perturbation theory. We vary the interaction strength, the population and the mass imbalance, and we analyze the competition between different states: homogeneous, partially separated and fully separated. The canonical phase diagrams are determined for various mass ratios, including the experimentally relevant case of the 6Li-40K mixture. We find substantial differences with respect to the equal-mass case: phase separation occurs at weaker interaction strength, and the partially-separated state can be stable even in the limit of a large majority of heavy atoms. We highlight the effects due to correlations by making comparison with previous mean-field results.

cond-mat.quant-gas↗

arXiv2011

Fermi-Liquid Behavior of the Normal Phase of a Strongly Interacting Gas of Cold Atoms

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measure- ments shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.

cond-mat.quant-gas↗