arXiv subjects

Luca Lepori

Publications and source records attributed to Luca Lepori.

At least 37 records · Page 2Linked to original sources

arXiv2019

Multicomponent meson superfluids in chiral perturbation theory

We show that the multicomponent meson systems can be described by chiral perturbation theory. We chiefly focus on a system of two pion gases at different isospin chemical potential, deriving the general expression of the chiral Lagrangian, the ground state properties and the spectrum of the low-energy excitations. We consider two different kinds of interactions between the two meson gases: one which does not lock the two chiral symmetry groups and one which does lock them. The former is a kind of interaction that has already been discussed in mutlicomponent superfluids. The latter is perhaps more interesting, because seems to be related to an instability. Although the pressure of the system does not show any instability, we find that for sufficiently strong locking, the spectrum of one Bogolyubov mode becomes tachyonic. This unstable branch seems to indicate a transition to an inhomogeneous phase.

hep-ph↗

arXiv2018

Solvable 2D superconductors with l-wave pairing

We analyze a family of two-dimensional BCS Hamiltonians with general l-wave pairing interactions, classifying the models in this family that are Bethe-ansatz solvable in the finite-size regime. We show that these solutions are characterized by nontrivial winding numbers, associated with topological phases, in some part of the corresponding phase diagrams. By means of a comparative study, we demonstrate benefits and limitations of the mean-field approximation, which is the standard approach in the limit of a large number of particles. The mean-field analysis also allows to extend part of the results beyond integrability, clarifying the peculiarities associable with the integrability itself.

cond-mat.str-el↗

arXiv2018

Multipartite-Entanglement Tomography of a Quantum Simulator

Multipartite entanglement tomography, namely the quantum Fisher information (QFI) calculated with respect to different collective operators, allows to fully characterize the phase diagram of the quantum Ising chain in a transverse field with variable-range coupling. In particular, it recognizes the phase stemming from long-range antiferromagnetic coupling, a capability also shared by the spin squeezing. Furthermore, the QFI locates the quantum critical points, both with vanishing and nonvanishing mass gap. In this case, we also relate the finite-size power-law exponent of the QFI to the critical exponents of the model, finding a signal for the breakdown of conformal invariance in the deep long-range regime. Finally, the effect of a finite temperature on the multipartite entanglement, and ultimately on the phase stability, is considered. In light of the current realizations of the model with trapped ions and of the potential measurability of the QFI, our approach yields a promising strategy to probe long-range physics in controllable quantum systems.

quant-ph↗

arXiv2018

Axial anomaly in multi-Weyl and triple-point semimetals

We derive the expression of the abelian axial anomaly in the so-called multi-Weyl and triple-point crossing semimetals. No simplifying restrictions are assumed on the symmetry of the spectrum. Three different computation methods are considered: the perturbative quantum field theory procedure which is based on the evaluation of the one-loop Feynman diagrams, the Nielsen-Ninomiya method, and the Atiyah-Singer index argument. It is shown that the functional form of the axial anomaly does not depend on the Lorentz symmetry, but it is determined by the gauge structure group. We discuss the stability of the anomaly - stemming from the quantisation of the anomaly coefficient - under smooth modifications of the lagrangian parameters.

cond-mat.str-el↗

arXiv2018

Effective control of chemical potentials by Rabi coupling with rf-fields in ultracold mixtures

We show that a linear term coupling the atoms of an ultracold binary mixture provides a simple method to induce an effective and tunable population imbalance between them. This term is easily realized by a Rabi coupling between different hyperfine levels of the same atomic species. The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained diagonalizing the mixing matrix of the Rabi term. This way of controlling the chemical potentials applies for both bosonic and fermionic atoms and it allows also for spatially and temporally dependent imbalances. As a first application, we show that, in the case of two attractive fermionic hyperfine levels with equal chemical potentials and coupled by the Rabi pulse, the same superfluid properties of an imbalanced binary mixture are recovered. We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions.

cond-mat.quant-gas↗

arXiv2018

Current transport properties and phase diagram of a Kitaev chain with long-range pairing

We describe a method to probe the quantum phase transition between the short-range topological phase and the long-range topological phase in the superconducting Kitaev chain with long-range pairing, both exhibiting subgap modes localized at the edges. The method relies on the effects of the finite mass of the subgap edge modes in the long-range regime (which survives in the thermodynamic limit) on the single-particle scattering coefficients through the chain connected to two normal leads. Specifically, we show that, when the leads are biased at a voltage V with respect to the superconducting chain, the Fano factor is either zero (in the short-range correlated phase) or 2e (in the long-range correlated phase). As a result, we find that the Fano factor works as a directly measurable quantity to probe the quantum phase transition between the two phases. In addition, we note a remarkable "critical fractionalization effect" in the Fano factor, which is exactly equal to e along the quantum critical line. Finally, we note that a dual implementation of our proposed device makes it suitable as a generator of large-distance entangled two-particle states.

cond-mat.str-el↗

arXiv2017

Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials

We study the effect of a non-Abelian SU(2) gauge potential on the topological semimetal induced by a magnetic field having π-flux per plaquette and acting on fermions in a cubic lattice. The Abelian π-flux term gives rise to a spectrum characterized by Weyl points. When the non-Abelian part is turned on, due to the presence of a C4 rotation symmetry, the Weyl points assume a quadratic dispersion along two directions and constitute double monopoles for the Berry curvature. We examine both analytically and numerically the main features of this system, focusing on its gapless surface modes, the so-called Fermi arcs. We discuss the stability of the system under confining hard-wall and harmonic potentials, relevant for the implementation in ultracold atom settings, and the effect of rotation symmetry breaking.

cond-mat.quant-gas↗

arXiv2017

Multipartite entanglement in topological quantum phases

We witness multipartite entanglement in the Kitaev chain -- a benchmark model of one dimensional topological insulator -- also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, both for short- and long-range pairing, are characterized by a power-law diverging finite-size scaling of multipartite entanglement. Moreover the occurring quantum phase transitions are sharply marked by the divergence of the derivative of the quantum Fisher information, even in the absence of a closing energy gap.

quant-ph↗

arXiv2017

Abelian gauge potentials on cubic lattices

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally examine applications of gauge potentials in one-dimensional rings.

cond-mat.quant-gas↗

arXiv2017

Tunable zero and first sounds in ultracold Fermi gases with Rabi coupling

We consider a weakly-interacting fermionic gas of alkali-metal atoms characterized by two hyper- fine states which are Rabi coupled. By using a Hartree approximation for the repulsive interaction we determine the zero-temperature equation of state of this Fermi gas in D spatial dimensions (D = 1, 2, 3). Then, adopting the Landau-Vlasov equation and hydrodynamic equations, we investi- gate the speed of first sound and zero sound. We show that the two sounds, which occur respectively in collisional and collisionless regimes, crucially depend on the interplay between interaction strength and Rabi coupling. Finally, we discuss for some experimentally relevant cases the effect of a trapping harmonic potential on the density profiles of the fermionic system.

cond-mat.quant-gas↗

arXiv2017

Scrutinizing the pion condensed phase

When the isospin chemical potential exceeds the pion mass, charged pions condense in the zero-momentum state forming a superfluid. Chiral perturbation theory provides a very powerful tool for studying this phase. However, the formalism that is usually employed in this context does not clarify various aspects of the condensation mechanism and makes the identification of the soft modes problematic. We re-examine the pion condensed phase using different approaches within the chiral perturbation theory framework. As a first step, we perform a low-density expansion of the chiral Lagrangian valid close to the onset of the Bose-Einstein condensation. We obtain an effective theory that can be mapped to a Gross-Pitaevskii Lagrangian in which, remarkably, all the coefficients depend on the isospin chemical potential. The low-density expansion becomes unreliable deep in the pion condensed phase. For this reason, we develop an alternative field expansion deriving a low-energy Lagrangian analog to that of quantum magnets. By integrating out the "radial" fluctuations we obtain a soft Lagrangian in terms of the Nambu-Goldstone bosons arising from the breaking of the pion number symmetry. Finally, we test the robustness of the second-order transition between the normal and the pion condensed phase when next-to-leading-order chiral corrections are included. We determine the range of parameters for turning the second-order phase transition into a first-order one, finding that the currently accepted values of these corrections are unlikely to change the order of the phase transition.

hep-ph↗

arXiv2016

Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain

We deal with the problem of studying the effective theories and the symmetries of long-range models around critical points. We focus in particular on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent $α$. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. By renormalization group approach we derive first the effective theory close to the critical line at positive chemical potential. This is the sum of two terms: a Dirac action $S_D$, found in the short-range Ising universality class, and a CS breaking term $S_{AN}$. While $S_D$ originates from low-energy excitations, $S_{AN}$ derives from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality $S_{AN}$ flows to zero if $α> 2$, while if $α< 2$ it dominates and determines the breakdown of the CS. Out of criticality $S_{AN}$ breaks, in the considered approximation, the effective Lorentz invariance (ELI) for every finite $α$. As $α$ increases, such ELI breakdown becomes less and less pronounced and in the short-range limit $α\to \infty$ the ELI is restored. To test the validity of the effective theory, we compared the two-fermion static correlations and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. From the effective theory one can also see that new phases emerge for $α< 1$. Finally we show that at every finite $α$ the critical exponents are the same as for the short-range ($α\to \infty$) model. At variance, for the critical line with negative chemical potential, only $S_{AN}$ ($S_D$) is present for $1 < α< 2$ (for $α> 2$). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change exactly where CS is broken.

cond-mat.str-el↗

arXiv2015

Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes

We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the 1D Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance $r$ as $1/r^α$, as well as a related class of fermionic Hamiltonians that generalise the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents $α$, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for $α\lesssim1$, while connected correlation functions can decay with a hybrid exponential and power-law behaviour, with a power that is $α$-dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every $α$. Along the critical lines, for all models breaking of conformal symmetry is argued at low enough $α$. For the fermionic models we show that the edge modes, massless for $α\gtrsim 1$, can acquire a mass for $α< 1$. The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.

cond-mat.str-el↗

arXiv2014

Simulation of two-flavors symmetry-locking phases in ultracold fermionic mixtures

We describe an ultracold fermionic set-up where it is possible to synthesize a superfluid phase with symmetry obtained by locking independent invariance groups of the normal state. In this phase, named two-flavors symmetry-locking phase (TFSL), non-Abelian fractional vortices with semi-integer flux and gapless non-Abelian Goldstone modes localized on them appear. Considerations on the possible experimental realization of the TFSL are also provided.

cond-mat.quant-gas↗

arXiv2014

Kitaev chains with long-range pairing

We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $α$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($α> 1$) or purely algebraically ($α< 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $α$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions.

cond-mat.str-el↗

arXiv2013

Semimetal-superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having π-flux per plaquette. The reason for such a choice is that the π-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, t_z) these Dirac points are unaltered: it is then possible to study the 3D-2D interpolation towards the π-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2D π-flux square lattice and the honeycomb geometry. We investigate by a mean field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and at half filling there is a quantum phase transition occurring at a critical (negative) interaction U_c presenting a linear critical exponent for the gap as a function of |U-U_c|. We show that in three dimensions this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of t_z.

cond-mat.str-el↗

arXiv2010

Non abelian Bianchi identities, monopoles and gauge invariance

A direct connection is proved between the Non-Abelian Bianchi Identities and the Abelian Bianchi identities for the 't Hooft tensor in a generic gauge; the existence of a magnetic current is related to the violation of NABI's. Using this relation it is shown that not all gauges are equivalent to detect monopoles on the lattice, that e.g. the Maximal Abelian Gauge is a legitimate choice while the Landau gauge is not. Nevertheless monopole condensation is found to be a gauge invariant property.

hep-lat↗

arXiv2010

Monopoles, abelian projection, and gauge invariance

A direct connection is proved between the Non-Abelian Bianchi Identities(NABI), and the abelian Bianchi identities for the 't Hooft tensor. As a consequence the existence of a non-zero magnetic current is related to the violation of the NABI's and is a gauge-invariant property. The construction allows to show that not all abelian projections can be used to expose monopoles in lattice configurations: each field configuration with non-zero magnetic charge identifies its natural projection, up to gauge transformations which tend to unity at large distances. It is shown that the so-called maximal-abelian gauge is a legitimate choice. It is also proved, starting from the NABI, that monopole condensation is a physical gauge invariant phenomenon, independent of the choice of the abelian projection.

hep-lat↗