36 research outputs found
Entanglement from density measurements: analytical density-functional for the entanglement of strongly correlated fermions
We derive an analytical density functional for the single-site entanglement
of the one-dimensional homogeneous Hubbard model, by means of an approximation
to the linear entropy. We show that this very simple density functional
reproduces quantitatively the exact results. We then use this functional as
input for a local density approximation to the single-site entanglement of
inhomogeneous systems. We illustrate the power of this approach in a
harmonically confined system, which could simulate recent experiments with
ultracold atoms in optical lattices as well as in a superlattice and in an
impurity system. The impressive quantitative agreement with numerical
calculations -- which includes reproducing subtle signatures of the particle
density stages -- shows that our density-functional can provide entanglement
calculations for actual experiments via density measurements. Next we use our
functional to calculate the entanglement in disordered systems. We find that,
at contrast with the expectation that disorder destroys the entanglement, there
exist regimes for which the entanglement remains almost unaffected by the
presence of disordered impurities.Comment: 6 pages, 3 figure
Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
Simple analytical parametrizations for the ground-state energy of the
one-dimensional repulsive Hubbard model are developed. The charge-dependence of
the energy is parametrized using exact results extracted from the Bethe-Ansatz.
The resulting parametrization is shown to be in better agreement with highly
precise data obtained from fully numerical solution of the Bethe-Ansatz
equations than previous expressions [Lima et al., Phys. Rev. Lett. 90, 146402
(2003)]. Unlike these earlier proposals, the present parametrization correctly
predicts a positive Mott gap at half filling for any U>0. The construction is
extended to spin-dependent phenomena by parametrizing the
magnetization-dependence of the ground-state energy using further exact results
and numerical benchmarking. Lastly, the parametrizations developed for the
spatially uniform model are extended by means of a simple local-density-type
approximation to spatially inhomogeneous models, e.g., in the presence of
impurities, external fields or trapping potentials. Results are shown to be in
excellent agreement with independent many-body calculations, at a fraction of
the computational cost.Comment: New Journal of Physics, accepte
Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins
A combined analytical and numerical study is performed of the mapping between
strongly interacting fermions and weakly interacting spins, in the framework of
the Hubbard, t-J and Heisenberg models. While for spatially homogeneous models
in the thermodynamic limit the mapping is thoroughly understood, we here focus
on aspects that become relevant in spatially inhomogeneous situations, such as
the effect of boundaries, impurities, superlattices and interfaces. We consider
parameter regimes that are relevant for traditional applications of these
models, such as electrons in cuprates and manganites, and for more recent
applications to atoms in optical lattices. The rate of the mapping as a
function of the interaction strength is determined from the Bethe-Ansatz for
infinite systems and from numerical diagonalization for finite systems. We show
analytically that if translational symmetry is broken through the presence of
impurities, the mapping persists and is, in a certain sense, as local as
possible, provided the spin-spin interaction between two sites of the
Heisenberg model is calculated from the harmonic mean of the onsite Coulomb
interaction on adjacent sites of the Hubbard model. Numerical calculations
corroborate these findings also in interfaces and superlattices, where
analytical calculations are more complicated.Comment: 7 pages, 6 figure
Work statistics and Entanglement across the fermionic superfluid-insulator transition
Entanglement in many-body systems may display interesting signatures of
quantum phase transitions and similar properties are starting to be encountered
in the analysis of work fluctuations. Here, we consider the fermionic
superfluid-to-insulator transition (SIT) and relate its entanglement properties
with its work distribution statistics. The SIT is modeled by the attractive
fermionic Hubbard model in the presence of randomly distributed impurities. The
work distribution is calculated across two quench protocols, both triggering
the SIT. In the first, the concentration of impurities is increased; in the
second, the impurities' disorder strength is varied. Our results indicate that,
the critical state that induces minimization of the entanglement also maximizes
the average work. We demonstrate that, for this state, density fluctuations
vanish at all orders, hence all central moments of the work probability
distribution are exactly zero at criticality. For systems undergoing a
precursor to the transition (short chains with finite impurity potential)
numerical results confirm these predictions, with higher moments further from
the ideal result. For both protocols, at criticality, the system absorbs the
most energy with almost no penalty in terms of fluctuations: ultimately this
feature could be used to implement a quantum critical battery. The effects of
temperature on these signatures of critical behaviour are also investigated and
shown to favor work extraction for high enough temperatures
Work Statistics and Entanglement Across the Fermionic Superfluid-Insulator Transition
Entanglement in many-body systems may display quantum phase transition signatures, and analogous insights are emerging in the study of work fluctuations. Here, the fermionic superfluid-to-insulator transition (SIT) is considered and related to its entanglement properties and its work distribution statistics. Using the attractive fermionic Hubbard model with randomly distributed impurities, the work distribution is analyzed under two quench protocols triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. The results indicate that, at criticality, the entanglement is minimized while the average work is maximized. This study demonstrates that, for this state, density fluctuations vanish at all orders, resulting in all central moments of the work probability distribution being precisely zero. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal results. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature can be used to implement a quantum critical battery. The impact of temperature on this critical behaviour is also investigated and shown to favor work extraction for high enough temperatures