arXiv subjects

A. Trombettoni

Publications and source records attributed to A. Trombettoni.

At least 37 records · Page 2Linked to original sources

arXiv2019

Dynamics and correlations in Motzkin and Fredkin spin chains

The Motzkin and Fredkin quantum spin chains are described by frustration-free Hamiltonians recently introduced and studied because of their anomalous behaviors in the correlation functions and in the entanglement properties. In this paper we analyze their quantum dynamical properties, focusing in particular on the time evolution of the excitations driven by a quantum quench, looking at the correlations functions of spin operators defined along different directions, and discussing the results in relation with the cluster decomposition property.

cond-mat.stat-mech↗

arXiv2018

Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions

We study the dynamics of Fermi-Pasta-Ulam chains with both harmonic and anharmonic power-law long-range interactions. We show that the dynamics is described in the continuum limit by a generalized fractional Boussinesq differential equation, whose derivation is performed in full detail. We also discuss a version of the model where couplings are alternating in sign.

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↗

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

Haldane Topological Orders in Motzkin Spin Chains

Motzkin spin chains are frustration-free models whose ground-state is a combination of Motzkin paths. The weight of such path contributions can be controlled by a deformation parameter t. As a function of the latter these models, beside the formation of domain wall structures, exhibit a Berezinskii-Kosterlitz-Thouless phase transition for t=1 and gapped Haldane topological orders with constant decay of the string order parameters for t < 1. By means of numerical calculations we show that the topological properties of the Haldane phases depend on the spin value. This allows to classify different kinds of hidden antiferromagnetic Haldane gapped regimes associated to nontrivial features like symmetry-protected topological order. Our results from one side allow to clarify the physical properties of Motzkin frustration-free chains and from the other suggest them as a new interesting and paradigmatic class of local spin Hamiltonians.

cond-mat.stat-mech↗

arXiv2017

Excitations and stability of weakly interacting Bose gases with multi-body interactions

We consider weakly interacting bosonic gases with local and non-local multi-body interactions. By using the Bogoliubov approximation, we first investigate contact interactions, studying the case in which the interparticle potential can be written as a sum of N-body δ-interactions, and then considering general contact potentials. Results for the quasi-particle spectrum and the stability are presented. We then examine non-local interactions, focusing on two different cases of 3-body non-local interactions. Our results are used for systems with 2- and 3-body δ-interactions and applied for realistic values of the trap parameters. Finally, the effect of conservative 3-body terms in dipolar systems and soft-core potentials (that can be simulated with Rydberg dressed atoms) is also studied.

cond-mat.quant-gas↗

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

Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains

We compute the ground state correlation functions of an exactly solvable chain of integer spins, recently introduced in [R. Movassagh and P. W. Shor, arXiv:1408.1657], whose ground-state can be expressed in terms of a uniform superposition of all colored Motzkin paths. Our analytical results show that for spin s$\ge$2 there is a violation of the cluster decomposition property. This has to be contrasted with s=1, where the cluster property holds. Correspondingly, for s=1 one gets a light-cone profile in the propagation of excitations after a local quench, while the cone is absent for s=2, as shown by time dependent density-matrix-renormalization-group. Moreover, we introduce an original solvable model of half-integer spins which we refer to as Fredkin spin chain, whose ground-state can be expressed in terms of superposition of all Dyck paths. For this model we exactly calculate the magnetization and correlation functions, finding that for s=1/2, a cone-like propagation occurs while for higher spins, s$\ge$3/2, the colors prevent any cone formation and clustering is violated, together with square root deviation from the area law for the entanglement entropy.

cond-mat.str-el↗

arXiv2016

One-dimensional long-range percolation: a numerical study

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability $C/ r^{1+σ}$, where $r$ is the distance length between distinct sites. We introduce and test an order $N$ Monte Carlo algorithm and we determine as a function of $σ$ the critical value $C_{c}$ at which percolation occurs. The critical exponents in the range $0<σ<1$ are reported and compared with mean-field and $\varepsilon$-expansion results. Our analysis is in agreement, up to a numerical precision $\approx 10^{-3}$, with the mean field result for the anomalous dimension $η=2-σ$, showing that there is no correction to $η$ due to correlation effects.

cond-mat.stat-mech↗

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↗

arXiv2016

Holographic optical traps for atom-based topological Kondo devices

The topological Kondo (TK) model has been proposed in solid-state quantum devices as a way to realize non-Fermi liquid behaviors in a controllable setting. Another motivation behind the TK model proposal is the demand to demonstrate the quantum dynamical properties of Majorana fermions, which are at the heart of their potential use in topological quantum computation. Here we consider a junction of crossed Tonks-Girardeau gases arranged in a star-geometry (forming a Y -junction), and we perform a theoretical analysis of this system showing that it provides a physical realization of the topological Kondo model in the realm of cold atom systems. Using computer-generated holography, we experimentally implement a Y-junction suitable for atom trapping, with controllable and independent parameters. The junction and the transverse size of the atom waveguides are of the order of 5 micrometers, leading to favorable estimates for the Kondo temperature and for the coupling across the junction. Since our results show that all the required theoretical and experimental ingredients are available, this provides the demonstration of an ultracold atom device that may in principle exhibit the topological Kondo effect.

cond-mat.mes-hall↗

arXiv2015

$c$-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow

In this paper we study the $c$-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the $c$-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency $β^2$, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points ($β^2 <8π$) to the infrared limit is in good quantitative agreement with the expected $Δc=1$ result. The behavior of the $c$-function in the other parts of the flow diagram is also discussed. Finally, we point out that also including higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i. e. going beyond local potential approximation) is crucial to get sensible results even when a single frequency is used.

cond-mat.stat-mech↗

arXiv2015

Conformal invariance in three dimensional percolation

The aim of the paper is to present numerical results supporting the presence of conformal invariance in three dimensional statistical mechanics models at criticality and to elucidate the geometric aspects of universality. As a case study we study three dimensional percolation at criticality in bounded domains. Both on discrete and continuous models of critical percolation, we test by numerical experiments the invariance of quantities in finite domains under conformal transformations focusing on crossing probabilities. Our results show clear evidence of the onset of conformal invariance in finite realizations especially for the continuum percolation models. Finally we propose a simple analytical function approximating the crossing probability among two spherical caps on the surface of a sphere and confront it with the numerical results.

cond-mat.stat-mech↗

arXiv2015

Josephson effect in fermionic superfluids across the BEC-BCS crossover

We report on the observation of the Josephson effect between two strongly interacting fermionic superfluids coupled through a thin tunneling barrier. We prove that the relative population and phase are canonically conjugate dynamical variables, coherently oscillating throughout the entire crossover from molecular Bose-Einstein condensates (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluids. We measure the plasma frequency and we extract the Josephson coupling energy, both exhibiting a non-monotonic behavior with a maximum near the crossover regime. We also observe the transition from coherent to dissipative dynamics, which we directly ascribe to the propagation of vortices through the superfluid bulk. Our results highlight the robust nature of resonant superfluids, opening the door to the study of the dynamics of superfluid Fermi systems in the presence of strong correlations and fluctuations.

cond-mat.quant-gas↗

arXiv2015

Superfluid flow above the critical velocity

Superfluidity and superconductivity have been studied widely since the last century in many different contexts ranging from nuclear matter to atomic quantum gases. The rigidity of these systems with respect to external perturbations results in frictionless motion for superfluids and resistance-free electric current in superconductors. This peculiar behaviour is lost when external perturbations overcome a critical threshold, i.e. above a critical magnetic field or a critical current for superconductors. In superfluids, such as liquid helium or ultracold gases, the corresponding quantities are critical rotation rate and critical velocity, respectively. Enhancing the critical values is of great fundamental and practical value. Here we demonstrate that superfluidity can be achieved for flow above the critical velocity through quantum interference induced resonances. This has far reaching consequences for the fundamental understanding of superfluidity and superconductivity and opens up new application possibilities in quantum metrology, e.g. in rotation sensing.

cond-mat.quant-gas↗

arXiv2015

Strongly correlated states of trapped ultracold fermions in deformed Landau levels

We analyze the strongly correlated regime of a two-component trapped ultracold fermionic gas in a synthetic non-Abelian U(2) gauge potential, that consists of both a magnetic field and a homogeneous spin-orbit coupling. This gauge potential deforms the Landau levels (LLs) with respect to the Abelian case and exchanges their ordering as a function of the spin-orbit coupling. In view of experimental realizations, we show that a harmonic potential combined with a Zeeman term, gives rise to an angular momentum term, which can be used to test the stability of the correlated states obtained through interactions. We derive the Haldane pseudopotentials (HPs) describing the interspecies contact interaction within a lowest LL approximation. Unlike ordinary fractional quantum Hall systems and ultracold bosons with short-range interactions in the same gauge potential, the HPs for sufficiently strong non-Abelian fields show an unconventional non-monotonic behaviour in the relative angular momentum. Exploiting this property, we study the occurrence of new incompressible ground states as a function of the total angular momentum. In the first deformed Landau level (DLL) we obtain Laughlin and Jain states. Instead, in the second DLL three classes of stabilized states appear: Laughlin states, a series of intermediate strongly correlated states and finally vortices of the integer quantum Hall state. Remarkably, in the intermediate regime, the non-monotonic HPs of the second DLL induce two-particle correlations which are reminiscent of paired states such as the Haffnian state. Via exact diagonalization in the disk geometry, we compute experimentally relevant observables such as density profiles and correlations, and we study the entanglement spectra as a further tool to characterize the obtained strongly correlated states.

cond-mat.quant-gas↗

arXiv2014

Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking

We study the occurrence of spontaneous symmetry breaking (SSB) for O(N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N=1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions.

hep-th↗