arXiv subjects

L. Lepori

Publications and source records attributed to L. Lepori.

At least 19 recordsLinked to original sources

arXiv2025

Molecular spin qudits to test generalized Bell inequalities

We show that Yb(trensal) molecular nanomagnet, embedding an electronic spin qubit coupled to a nuclear spin qudit, provides an ideal platform to probe entanglement in a qubit-qudit system.This is demonstrated by developing an optimized pulse sequence to show violation of generalized Bell inequalities and by performing realistic numerical simulations including experimentally measured decoherence. We find that the inequalities are safely violated in a wide range of parameters, proving the robustness of entanglement in the investigated system. Furthermore, we propose a scheme to study qudit-qudit entanglement on a molecular spin trimer, in which two spins 3/2 are linked via an interposed switch to turn on and off their mutual interaction.

quant-ph↗

arXiv2025

Reversing adiabatic state preparation in few-level quantum systems

We present a detailed study of an adiabatic state preparation in an effective three-level quantum system. States can be prepared with high speed and fidelity by adding a counterdiabatic (CD) quantum control protocol. As a second step, we invert the preparation protocol to get back to the initial state. This describes an overall cyclic evolution in state space. Using counterdiabatic terms, the resulting composed fast evolution can be repeated many times. We then analyze the control of Berry's phase along the adiabatic cyclic path and show that Berry's phase can act as a sensitive detector of non-perfect state transfer.

quant-ph↗

arXiv2021

Interplay between singlet and triplet pairings in multi-band two-dimensional oxide superconductors

We theoretically study the superconducting properties of multi-band two-dimensional transition metal oxide superconductors by analyzing not only the role played by conventional singlet pairings, but also by the triplet order parameters, favored by the spin-orbit couplings present in these ma- terials. In particular, we focus on the two-dimensional electron gas at the (001) interface between LaAlO3 and SrTiO3 band insulators where the low electron densities and the sizeable spin-orbit couplings affect the superconducting features. Our theoretical study is based on an extended su- perconducting mean-field analysis of the typical multi-band tight-binding Hamiltonian, as well as on a parallel analysis of the effective electronic bands in the low-momentum limit, including static on-site and inter-site intra-band attractive potentials under applied magnetic fields. The presence of triplet pairings is able to strongly reduce the singlet order parameters which, as a result, are no longer a monotonic function of the charge density. The interplay between the singlet and the triplet pairings affects the dispersion of quasi-particle excitations in the Brillouin zone and also induces anisotropy in the superconducting behavior under the action of an in-plane and of an out- of-plane magnetic fields. Finally, non-trivial topological superconducting states become stable as a function of the charge density, as well as of the magnitude and of the orientation of the magnetic field. In addition to the chiral, time-reversal breaking, topological superconducting phase, favored by the linear Rashba couplings and by the on-site attractive potentials in the presence of an out- of-plane magnetic field, we find that a time-reversal invariant topological helical superconducting phase is promoted by not-linear spin-orbit couplings and by the inter-site attractive interactions in the absence of magnetic field.

cond-mat.str-el↗

arXiv2021

Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model

Experimental platforms based on trapped ions, cold molecules, and Rydberg atoms have made possible the investigation of highly-nonlocal spin-${1/2}$ Hamiltonians with long-range couplings. Here, we study the effects of such non-local couplings in the long-range spin-${1/2}$ XXZ Heisenberg Hamiltonian. We calculate explicitly the two-spin energy spectrum, which describes all possible energetic configurations of two spins pointing in a specific direction embedded in a background of spins with opposite orientation. For fast decay of the spin-spin couplings, we find that the two-spin energy spectrum is characterized by well-defined discrete values, corresponding to bound states, separated by a set of continuum states describing the scattering region. In the deep long-range regime instead, the bound states disappear as they get incorporated by the scattering region. The presence of two-spin bound states results to be crucial to determine both two- and many-spin dynamics. On one hand, radically different two-spin spreadings can be observed by tuning the decay of the spin couplings. On the other hand, two-spin bound states enable the dynamical stabilization of effective antiferromagnetic states in the presence of ferromagnetic couplings. Finally, we propose a novel scheme based on a trapped-ion quantum simulator to experimentally realize the long-range XXZ model and to study its out-of-equilibrium properties.

cond-mat.quant-gas↗

arXiv2018

Relations between and Estimations of Fluctuation Integrals and Direct Correlation Function Integrals

New relations among the mixture direct correlation function integrals (or fluctuation integrals) in terms of concentration variables are developed. These relations indicate that, for example, for a binary mixture only one of the three direct correlation function integrals (or one of the three fluctuation integrals is independent. Different closure expressions for mixture cross direct correlation function integrals are suggested and they are joined with the exact relations to calculate all the direct correlation function integrals and fluctuation integrals in a mixture. The results indicate the possibility of introduction of simple closure expressions relating unlike- and like-interaction direct correlation integrals. It is demonstrated that the relation between the direct correlation integrals of hard-sphere mixtures can be satisfactorily represented by a simple geometric mean closure.

cond-mat.stat-mech↗

arXiv2018

Synthesis of Majorana mass terms in low-energy quantum systems

We discuss the problem of how Majorana mass terms can be generated in low-energy systems. We show that, while these terms imply the Majorana condition, the opposite is not always true when more than one flavour is involved. This is an important aspect for the low-energy realizations of the Majorana mass terms exploiting superfluid pairings, because in this case the Majorana condition is not implemented in the spinor space, but in an internal (flavour) space. Moreover, these mass terms generally involve opposite effective chiralities, similarly to a Dirac mass term. The net effect of these features is that the Majorana condition does not imply a Majorana mass term. Accordingly the obtained Majorana spinors, as well as the resulting symmetry breaking pattern and low-energy spectrum, are qualitatively different from the ones known in particle physics. This result has important phenomenological consequences, e.g. implies that these mass terms are unsuitable to induce an effective see-saw mechanism, proposed to give mass to neutrinos. Finally, we introduce and discuss schemes based on space-dependent pairings with nonzero total momentum to illustrate how genuine Majorana mass terms may emerge in low-energy quantum systems.

cond-mat.str-el↗

arXiv2018

Collision of impurities with Bose-Einstein condensates

Quantum dynamics of impurities in a bath of bosons is a long-standing problem of solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms focused on this problem, studying atomic impurities immersed in a atomic Bose-Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano-Feshbach resonance technique. Here we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity made of few $^{41}$K atoms and a BEC made of $^{87}$Rb atoms in a quasi one-dimensional configuration and under a weak harmonic axial confinement. For small values of the interspecies interaction strength (no matter the sign of it), we find that the impurity, which starts from outside the BEC, simply oscillates back and forth the BEC cloud, but the frequency of oscillation depends on the interaction strength. For intermediate couplings, after a few cycles of oscillation the impurity is captured by the BEC and strongly changes its amplitude of oscillation. In the strong interaction regime, if the interspecies interaction is attractive, a local maximum (bright soliton) in the density of BEC occurs where the impurity is trapped; instead, if the interspecies interaction is repulsive, the impurity is not able to enter in the BEC cloud and the reflection coefficient is close to one. On the other hand, if the initial displacement of the impurity is increased, the impurity is able to penetrate in the cloud leading to the appearance of a moving hole (dark soliton) in the BEC.

cond-mat.quant-gas↗

arXiv2018

Edge insulating topological phases in a two-dimensional long-range superconductor

We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases, not continuously connected with any short-range phase, occur, signaled by the violation of the area law for the Von Neumann entropy, by semi-integer Chern numbers, and by edge modes with nonzero mass. The latter feature results in the absence of single-fermion edge conductivity, present instead in the short- range limit. The definition of a topology in the bulk and the presence of a bulk-boundary correspondence is still suggested for the long-range phases. Recent experimental proposals and advances open the stimulating possibility to probe the described long-range effects in next-future realistic set-ups.

cond-mat.str-el↗

arXiv2017

Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials

We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general space-independent non-Abelian gauge potential. We first review and analyze the case of purely Abelian potentials, showing also that the so-called Hasegawa gauge yields a decomposition of the Hamiltonian into sub-matrices having minimal dimension. Explicit expressions for such matrices are derived, also for general anisotropic fluxes. Later on, we show that the introduction of a translational invariant non-Abelian coupling for multi-component spinors does not affect the dimension of the minimal Hamiltonian blocks, nor the dimension of the magnetic Brillouin zone. General formulas are presented for the U(2) case and explicit examples are investigated involving $π$ and $2π/3$ magnetic fluxes. Finally, we numerically study the effect of random flux perturbations.

cond-mat.quant-gas↗

arXiv2017

Long-range topological insulators and weakened bulk-boundary correspondence

We formalize the appearance of new types of insulators in long-range (LR) fermionic systems. These phases are not included in the "ten-fold way classification" (TWC) for the short-range (SR) topological insulators. This conclusion is obtained studying at first specific one-dimensional LR examples, in particular their phase diagrams and contents in symmetries and entanglement. The purely long-range phases (LRP) are signaled by the violation of the area-law for the Von Neumann entropy and by corresponding peculiar distributions for the entanglement spectrum (ES). The origin of the deviations from the TWC is analyzed from a more general point of view and in any dimension. In particular, it is found related with a particular type of divergences occurring in the spectrum, due to the LR couplings. A satisfying characterization for the LRP can be achieved at least for one-dimensional systems, as well as the connected definition of a nontrivial topology, provided a careful evaluation of the LR contributions. Our results lead to reconsider the definition of correlation length in LR systems. The same analysis also allows to infer, at least for one-dimensional models, the weakening of the bulk-boundary correspondence, due to the important correlations between bulk and edges, and consequently to clarify the nature of the massive edge states appearing in the topological LR. The emergence of this peculiar edge structure is signaled by the bulk ES. The stability of the LRP against finite-size effects, relevant in current experiments, and against local disorder is discussed, showing that the latter ingredient can even strengthen the effect of the LR couplings. Finally, we analyze the entanglement content of the paradigmatic LR Ising spin chain, inferring again important deviations from the SR regime, and the limitations of bulk-boundary (tensor-network based) approaches to classify LR spin models.

cond-mat.str-el↗

arXiv2017

Singular dynamics and emergence of nonlocality in long-range quantum models

We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of the equilibrium. We focus in particular on the Kitaev chains with long-range pairings and on the quantum Ising chain with long-range antiferromagnetic coupling (both having a power-law decay with exponent α). By studying the dynamic correlation functions, we find that for every finite αtwo different behaviours can be identified, one typical of short-range systems and the other connected with locality violation. The latter behaviour is shown related also with the known power-law decay tails previously observed in the static correlation functions, and originated by modes, having in general energies far from the minima of the spectrum, where particular singularities develop as a consequence of the long-rangedness of the system. We refer to these modes as to "singular" modes, and as to "singular dynamics" to their dynamics. For the Kitaev model they are manifest, at finite α, in derivatives of the quasiparticle energy, the order of the derivative at which the singularity occurs increasing with α. The features of the singular modes and their physical consequences are clarified by studying an effective theory for them and by a critical comparison of the results from this theory with the lattice ones. Moreover, a numerical study of the effects of the singular modes on the time evolution after various types of global quenches is performed. We finally present and discuss the presence of singular modes and their consequences in interacting long-range systems by investigating in the long-range Ising quantum chain, both in the deep paramagnetic regime and at criticality, where they also play a central role for the breakdown of conformal invariance.

cond-mat.str-el↗

arXiv2016

Phase diagram and non-Abelian symmetry locking for fermionic mixtures with unequal interactions

The occurrence of non-Abelian symmetry-locked states in ultracold fermionic mixtures with four components is investigated. We study the phase diagram in the presence of an attractive interaction between the species of two pairs of the mixture, and general (also repulsive) interactions between the species of each pair. This system is physically realized, e.g., in mixtures of two different earth-alkaline species, both of them with two hyperfine levels selectively populated. We find an extended region of the diagram exhibiting a two-flavors superfluid symmetry-locking (TSFL) phase. This phase is present also for not too large repulsive intra-pair interactions and it is characterized by a global non-Abelian symmetry group obtained by locking together two independent invariance groups of the corresponding normal state. Explicit estimates are reported for the mixture of the fermionic isotopes $^{171}\mathrm{Yb}$-$^{173}\mathrm{Yb}$, indicating that the TFSL phase can be achieved also without tuning the interactions between $\mathrm{Yb}$ atoms.

cond-mat.quant-gas↗

arXiv2016

PT invariant Weyl semimetals in gauge symmetric systems

Weyl semimetals typically appear in systems in which either time-reversal (T) or inversion (P}) symmetry are broken. Here we show that in the presence of gauge potentials these topological states of matter can also arise in fermionic lattices preserving both T and P. We analyze in detail the case of a cubic lattice model with $π$-fluxes, discussing the role of gauge symmetries in the formation of Weyl points and the difference between the physical and the canonical T and P symmetries. Motivated by advances in ultracold atom experiments and by the possibility of using synthetic magnetic fields, we examine the robustness of the Weyl semimetal phase in the presence of trapping potentials and random perturbations of the magnetic fluxes, which can be compared to a local disorder in realistic scenarios.

cond-mat.quant-gas↗

arXiv2013

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving non-trivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal/insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system and the topological phase transitions can be detected by analyzing its polarization in time of flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.

cond-mat.quant-gas↗

arXiv2013

Truncated Conformal Space Approach for Perturbed Wess-Zumino-Witten $SU(2)_k$ Models

We outline the application of the truncated conformal space approach (TCSA) to perturbations of $SU(2)_k$ Wess-Zumino-Witten theories. As examples of this methodology, we consider two distinct perturbations of $SU(2)_1$ and one of $SU(2)_2$. $SU(2)_1$ is first perturbed by its spin-1/2 field, a model which is equivalent to the sine-Gordon model at a particular value of its coupling $β$. The sine-Gordon spectrum is correctly reproduced as well as the corresponding finite size corrections. We next study $SU(2)_1$ with a marginal current-current perturbation. The TCSA results can be matched to perturbation theory within an appropriate treatment of the UV divergences. We find however that these results do not match field theoretic computations on the same model performed with a Lorentz invariant regulator. Finally, we consider $SU(2)_2$ perturbed by its spin-1 field, which is equivalent to three decoupled massive Majorana fermions. In this case as well the TCSA reproduces accurately the known spectrum.

hep-th↗

arXiv2013

Scaling of the entanglement spectrum near quantum phase transitions

The entanglement spectrum describing quantum correlations in many-body systems has been recently recognized as a key tool to characterize different quantum phases, including topological ones. Here we derive its analytically scaling properties in the vicinity of some integrable quantum phase transitions and extend our studies also to non integrable quantum phase transitions in one dimensional spin models numerically. Our analysis shows that, in all studied cases, the scaling of the difference between the two largest non degenerate Schmidt eigenvalues yields with good accuracy critical points and mass scaling exponents.

cond-mat.str-el↗

arXiv2012

Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.

cond-mat.stat-mech↗

arXiv2010

(3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a rotating optical lattice or, alternatively, in a synthetic magnetic field. This approach has the advantage to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. We also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions.

hep-th↗