arXiv subjects

Artur Polls

Publications and source records attributed to Artur Polls.

At least 19 recordsLinked to original sources

arXiv2025

Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential

We provide a detailed study of the properties of a few interacting spin $1/2$ fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The $N=2$ case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for $N=2, 3, 4$ and 5 particles, e.g. low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength.

cond-mat.quant-gas↗

arXiv2021

Supervised learning of few dirty bosons with variable particle number

We investigate the supervised machine learning of few interacting bosons in optical speckle disorder via artificial neural networks. The learning curve shows an approximately universal power-law scaling for different particle numbers and for different interaction strengths. We introduce a network architecture that can be trained and tested on heterogeneous datasets including different particle numbers. This network provides accurate predictions for all system sizes included in the training set and, by design, is suitable to attempt extrapolations to (computationally challenging) larger sizes. Notably, a novel transfer-learning strategy is implemented, whereby the learning of the larger systems is substantially accelerated and made consistently accurate by including in the training set many small-size instances.

cond-mat.quant-gas↗

arXiv2020

Spinodal instabilities of spin polarized asymmetric nuclear matter

We analyze the spinodal instabilities of spin polarized asymmetric nuclear matter at zero temperature for several configurations of the neutron and proton spins. The calculations are performed with the Brueckner--Hartree--Fock (BHF) approach using the Argonne V18 nucleon-nucleon potential plus a three-nucleon force of Urbana type. An analytical parametrization of the energy density, which reproduces with good accuracy the BHF results, is employed to determine the spinodal instability region. We find that, independently of the of the orientation of the neutron and proton spins, the spinodal instability region shinks when the system is polarized, being its size smaller smaller when neutron and proton spins are antiparallel than when they are oriented in a parallel way. We find also that the spinodal instability is always dominated by total density fluctuation independently of the degree of polarization of the system, and that restoration of the isospin symmetry in the liquid phase, {\it i.e.,} the so-called isospin distillation or fragmentation effect, becomes less efficient with the polarization of the system.

nucl-th↗

arXiv2020

Functional renormalization for repulsive Bose-Bose mixtures at zero temperature

We study weakly-repulsive Bose-Bose mixtures in two and three dimensions at zero temperature using the functional renormalization group (FRG). We examine the RG flows and the role of density and spin fluctuations. We study the condition for phase separation and find that this occurs at the mean-field point within the range of parameters explored. Finally, we examine the energy per particle and condensation depletion. We obtain that our FRG calculations compare favorably with known results from perturbative approaches for macroscopic properties.

cond-mat.quant-gas↗

arXiv2020

Universal dimerized quantum droplets in a one-dimensional lattice

The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive inter-component and repulsive intra-component interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by DMRG method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state. Finally, we identify conditions for the formation of a solitonic solution.

cond-mat.quant-gas↗

arXiv2020

The Hellmann-Feynman theorem at finite temperature

We present a simple derivation of the Hellmann-Feynman theorem at finite temperature. We illustrate its validity by considering three relevant examples which can be used in quantum mechanics lectures: the one-dimensional harmonic oscillator, the one-dimensional Ising model and the Lipkin model. We show that the Hellmann-Feynman theorem allows one to calculate expectation values of operators that appear in the Hamiltonian. This is particularly useful when the total free-energy is available, but there is not direct access to the thermal average of the operators themselves.

quant-ph↗

arXiv2020

Entanglement entropy in low-energy field theories at finite chemical potential

We investigate the leading area-law contribution to entanglement entropy in a system described by a general Lagrangian with O(2) symmetry containing first- and second-order time derivatives, namely breaking the Lorentz-invariance. We establish a connection between the Higgs gap present in a symmetry-broken phase and the area-law term for the entanglement entropy in the general, non-relativistic case. Our predictions for the entanglement entropy and correlation length are successfully compared to numerical results in two paradigmatic systems: the Mott insulator to superfluid transition for ultracold lattice bosons, and the ground state of ferrimagnetic systems.

cond-mat.quant-gas↗

arXiv2020

Spin-orbit coupled bosons interacting in a two-dimensional harmonic trap

A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value of $\hatσ_z \hat{L}_z$ for the eigenstates of the system, regardless of the trapping potential. The low-energy states of the repulsively interacting two-boson system are characterized. With the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is a direct energy-level crossing in the ground state of the system between states of different $J_z$, the third component of the total angular momentum, that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.

cond-mat.quant-gas↗

arXiv2020

Quantum droplets of bosonic mixtures in a one-dimensional optical lattice

We demonstrate the existence of quantum droplets in two-component one-dimensional Bose-Hubbard chains. The droplets exist for any strength of repulsive intra-species interactions provided they are balanced by comparable attractive inter-species interactions. The ground-state phase diagram is presented and the different phases are characterized by examining the density profile and off-diagonal one- and two-body correlation functions. A rich variety of phases is found, including atomic superfluid gases, atomic superfluid droplets, pair superfluid droplets, pair superfluid gases and a Mott-insulator phase. A parameter region prone to be experimentally explored is identified, where the average population per site is lower than three atoms, thus avoiding three-body losses. Finally, the bipartite entanglement of the droplets is found to have a non-trivial dependence on the number of particles.

cond-mat.quant-gas↗

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↗

arXiv2019

Entanglement structure of a quantum simulator: the two-component Bose-Hubbard model

We consider a quantum simulator of the Heisenberg chain with ferromagnetic interactions based on the two-component 1D Bose-Hubbard model at filling equal to two in the strong coupling regime. The entanglement properties of the ground state are compared between the original spin model and the quantum simulator as the interspecies interaction approaches the intraspecies one. A numerical study of the entanglement properties of the quantum simulator state is supplemented with analytical expressions derived from the simulated Hamiltonian. At the isotropic point, the entanglement properties of the simulated system are not properly predicted by the quantum simulator.

cond-mat.quant-gas↗

arXiv2018

Pairing in Nuclear Matter and Finite Nuclei

Effects of pairing with isospin $T=0$ and $T=1$ are systematically studied in a model, which is based on a realistic nucleon-nucleon interaction and allows to describe the transition from infinite nuclear matter to finite nuclei. Special attention is paid to the development of the spin-orbit term in the mean field of nucleons in finite nuclei. The spin-orbit term yields a drastic suppression of $T=0$ proton-neutron pairing but does not lead to a complete disappearance in finite nuclei. Arguments are presented, why no clear evidence of $T=0$ pairing can be observed in the binding energies of finite nuclei.

nucl-th↗

arXiv2018

Dynamic structure function of two interacting atoms in 1D

We consider two atoms trapped in a one-dimensional harmonic oscillator potential interacting through a contact interaction. We study the transition from the non-interacting to the strongly interacting Tonks-Girardeau state, as the interaction is varied from zero to infinitely large repulsive values. The dynamic structure function is computed by means of direct diagonalization calculations with a finite number of single particle modes. The response of the system against a monopolar perturbation is characterized by the moments of the dynamic structure function which are explicitly calculated from the dynamic structure function and by means of sum rules.

cond-mat.quant-gas↗

arXiv2018

Microscopic predictions of the nuclear matter liquid-gas phase transition

We present first-principle predictions for the liquid-gas phase transition in symmetric nuclear matter employing both two- and three-nucleon chiral interactions. Our discussion focuses on the sources of systematic errors in microscopic quantum many body predictions. On the one hand, we test uncertainties of our results arising from changes in the construction of chiral Hamiltonians. We use five different chiral forces with consistently derived three-nucleon interactions. On the other hand, we compare the ladder resummation in the self-consistent Green's functions approach to finite temperature Brueckner--Hartree--Fock calculations. We find that systematics due to Hamiltonians dominate over many-body uncertainties. Based on this wide pool of calculations, we estimate that the critical temperature is $T_c=16 \pm 2$ MeV, in reasonable agreement with experimental results. We also find that there is a strong correlation between the critical temperature and the saturation energy in microscopic many-body simulations.

nucl-th↗

arXiv2018

Fermionic properties of two interacting bosons in a two-dimensional harmonic trap

The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the system, e.g., the different contributions to the total energy, change as we vary both the strength and range of the atom-atom interaction. In particular, we focus on the short-range and strong interacting limit of the two-boson system and compare it to the noninteracting two-fermion system by properly symmetrizing the corresponding degenerate ground state wave functions. In that limit, we show that the density profile of the two-boson system has a tendency similar to the system of two noninteracting fermions. Similarly, the correlations induced when the interaction strength is increased result in a similar pair correlation function for both systems.

cond-mat.quant-gas↗

arXiv2017

Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap

We consider a few number of identical bosons trapped in a 2D isotropic harmonic potential and also the $N$-boson system when it is feasible. The atom-atom interaction is modelled by means of a finite-range Gaussian interaction. The spectral properties of the system are scrutinized, in particular, we derive analytic expressions for the degeneracies and their breaking for the lower-energy states at small but finite interactions. We demonstrate that the degeneracy of the low-energy states is independent of the number of particles in the noninteracting limit and also for sufficiently weak interactions. In the strongly interacting regime, we show how the many-body wave function develops holes whenever two particles are at the same position in space to avoid the interaction, a mechanism reminiscent of the Tonks-Girardeau gas in 1D. The evolution of the system as the interaction is increased is studied by means of the density profiles, pair correlations and fragmentation of the ground state for $N=2$, $3$, and $4$ bosons.

cond-mat.quant-gas↗

arXiv2016

Role of correlations on spin-polarized neutron matter

Using the Hellmann--Feynman theorem we analyze the contribution of the different terms of the nucleon-nucleon interaction to the spin symmetry energy of neutron matter. The analysis is performed within the microscopic Brueckner--Hartree--Fock approach using the Argonne V18 realistic potential plus the Urbana IX three-body force. The main contribution to the spin-symmetry energy of neutron matter comes from the S=0 channel, acting only in the non-polarized neutron matter, in particular the $^1S_0$ and the $^1D_2$ partial waves. The importance of correlations in spin-polarized neutron matter is estimated by evaluating the kinetic energy difference between the correlated system and the underlying Fermi sea.

nucl-th↗

arXiv2016

Shortcut to adiabaticity in spinor condensates

We devise a method to shortcut the adiabatic evolution of a spin-1 Bose gas with an external magnetic field as the control parameter. An initial many-body state with almost all bosons populating the Zeeman sublevel $m=0$, is evolved to a final state very close to a macroscopic spin-singlet condensate, a fragmented state with three macroscopically occupied Zeeman states. The shortcut protocol, obtained by an approximate mapping to a harmonic oscillator Hamiltonian, is compared to linear and exponential variations of the control parameter. We find a dramatic speedup of the dynamics when using the shortcut protocol.

cond-mat.quant-gas↗