All Publications

We study the thermodynamical properties of an ideal gas of non-Abelian Chern-Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern-Simons coupling, the isospin quantum number and the hard-core parameters. Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern-Simons particles is also supplied. © 2012 Elsevier B.V.

We analyze the thermalization properties and the validity of the eigenstate thermalization hypothesis in a generic class of quantum Hamiltonians where the quench parameter explicitly breaks a Z 2 symmetry. Natural realizations of such systems are given by random matrices expressed in a block form where the terms responsible for the quench dynamics are the off-diagonal blocks. Our analysis examines both dense and sparse random matrix realizations of the Hamiltonians and the observables. Sparse random matrices may be associated with local quantum Hamiltonians and they show a different spread of the observables on the energy eigenstates with respect to the dense ones. In particular, the numerical data seem to support the existence of rare states, i.e., states where the observables take expectation values that are different compared to the typical ones sampled by the microcanonical distribution. In the case of sparse random matrices, we also extract the finite-size behavior of two different time scales associated with the thermalization process. © 2012 American Physical Society.

In recent years there has been an enormous progress in low-dimensional quantum field theory. The most important results concern the conformal properties of the critical points of the Renormalization Group and the scaling region nearby. In this respect a crucial role is played by integrable deformations of Conformal Field Theories, which can be solved using bootstrap methods coming from S-matrix theory. In these lectures I present the Form-Factor Approach to the computation of correlation functions. Non-perturbative methods of both Conformal and Integrable Field Theories find remarkable applications in low-dimensional quantum systems. © 2012 Springer-Verlag Berlin Heidelberg.

We analyze quantum quenches in integrable models and in particular we determine the initial state in the basis of eigenstates of the post-quench Hamiltonian. This leads us to consider the set of transformations of creation and annihilation operators that respect the Zamolodchikov-Faddeev algebra satisfied by integrable models. We establish that the Bogoliubov transformations hold only in the case of quantum quenches in free theories. For the most general case of interacting theories, we identify two classes of transformations. The first class induces a change in the S-matrix of the theory but not in its ground state, whereas the second class results in a 'dressing' of the operators. We consider as examples of our approach the transformations associated with a change of the interaction in the sinh-Gordon model and the Lieb-Liniger model. © 2012 IOP Publishing Ltd.

We describe the hashing technique for obtaining a fast approximation of a target quantum gate in the unitary group SU(2) represented by a product of the elements of a universal basis. The hashing exploits the structure of the icosahedral group (or other finite subgroups of SU(2)) and its pseudogroup approximations to reduce the search within a small number of elements. One of the main advantages of the pseudogroup hashing is the possibility of iterating to obtain more accurate representations of the targets in the spirit of the renormalization group approach. We describe the iterative pseudogroup hashing algorithm using the universal basis given by the braidings of Fibonacci anyons. An analysis of the efficiency of the iterations based on the random matrix theory indicates that the runtime and braid length scale polylogarithmically with the final error, comparing favorably to the Solovay-Kitaev algorithm. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi-one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature, our result for the three-body correlator agrees with the extension of the results of Cheianov [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.73.051604 73, 051604(R) (2006)], obtained for the ground state of the repulsive Lieb-Liniger gas, to the super-Tonks-Girardeau state. At finite temperature, we obtain that the three-body correlator has a weak dependence on temperature up to the degeneracy temperature TD. We also find that, for temperatures larger than TD, the values of the three-body correlator for the super-Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar, even for relatively small couplings. © 2011 American Physical Society.

We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two approaches, the form factor perturbation theory and semiclassical methods. Each of them has its own advantages. Using the first approach, one can relate the confinement phenomena of topological excitations to the semi-locality of the operator which breaks integrability. Using the second approach, one can control the bound states which arise in each phase of the theory and predict that their number cannot be more than two. © 2011 IOP Publishing Ltd and SISSA.

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a cubic optical lattice in a frustrating magnetic field which can be realized by rotating the lattice or, alternatively, using a synthetic gauge field. We show that it is possible to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse: the method relies on the peculiar position of the Dirac points in the (magnetic) Brillouin zone, and it would not generally work for other lattices (e.g., for honeycomb lattices). A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. Finally, we also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions. ©EPLA, 2010.

We study the dynamics of the quantum Ising chain following a zero-temperature quench of the transverse field strength. Focusing on the behavior of two-point spin correlation functions, we show that the correlators of the order parameter display an effective asymptotic thermal behavior; i.e., they decay exponentially to zero with a phase coherence rate and a correlation length dictated by the equilibrium law with an effective temperature set by the energy of the initial state. On the contrary, the two-point correlation functions of the transverse magnetization or the density-of-kinks operator decay as a power law and do not exhibit thermal behavior. We argue that the different behavior is linked to the locality of the corresponding operator with respect to the quasiparticles of the model: nonlocal operators, such as the order parameter, behave thermally, while local ones do not. We study which features of the two-point correlators are a consequence of the integrability of the model by analyzing their robustness with respect to a sufficiently strong integrability-breaking term. © 2010 The American Physical Society.

The tragedy and greatness of the contribution of Ludwig Boltzmann cannot be understood without taking into account for the relevant scientific developments that took place in the nineteenth century, one of the most eventful periods in the history of science. The kinetic theory opened a new theoretical perspective in understanding natural phenomena. The introduction of new categories of order and disorder changed radically the point of view of those physicists that accepted Boltzmann's thesis and led, at the same time, to strong opposition to the Viennese Scientist. In this article, we present the academic situation, scientific theories, and disputes involving the Boltzmann's theories. A short introduction on the birth of the atomistic theories opens the article, while a view on the evolution of the concept of temperature and the definition of its unit quantity closes it. © 2010 Springer Science+Business Media, LLC.

We study the energy level spacing of perturbed conformal minimal models in finite volume, considering perturbations of such models that are massive but not necessarily integrable. We compute their spectrum using a renormalization group improved truncated conformal spectrum approach. With this method we are able to study systems where more than 40 000 states are kept and where we determine the energies of the lowest several thousand eigenstates with high accuracy. We find, as expected, that the level spacing statistics of integrable perturbed minimal models are Poissonian while the statistics of nonintegrable perturbations are GOE-like. However, by varying the system size (and so controlling the positioning of the theory between its IR and UV limits) one can induce crossovers between the two statistical distributions. © 2010 IOP Publishing Ltd and SISSA.

We study the non-equilibrium time evolution of an integrable field theory in 1 +1 dimensions after sudden variation of a global parameter of the Hamiltonian. For a class of quenches defined in the text, we compute the long time limit of the one point function of a local operator as a series of form factors. Even if some subtleties force us to handle this result with care, there is strong evidence that for long times the expectation value of any local operator can be described by a generalized Gibbs ensemble with a different effective temperature for each eigenmode. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O( log∼2(1/ε)), we can approximate all SU(2) matrices to an average error ε with a cost of O(log (1/ε)) in time. The algorithm is applicable to generic quantum compiling. © 2010 The American Physical Society.

The repulsive Lieb-Liniger model can be obtained as the nonrelativistic limit of the sinh-Gordon model: all physical quantities of the latter model (S-matrix, Lagrangian, and operators) can be put in correspondence with those of the former. We use this mapping, together with the thermodynamical Bethe ansatz equations and the exact form factors of the sinh-Gordon model, to set up a compact and general formalism for computing the expectation values of the Lieb-Liniger model both at zero and finite temperatures. The computation of one-point correlators is thoroughly detailed and when possible compared with known results in the literature. © 2010 The American Physical Society.

We analyze the evolution of the effective potential and the particle spectrum of two-parameter families of non-integrable quantum field theories. These theories are defined by deformations of conformal minimal models M m by using the operators Φ1,3, Φ1,2 and Φ2,1. This present work extends the analysis, previously done for the universality classes of Ising/tricritical Ising/RSOS models, to all minimal models. We establish the symmetry and the duality properties of the various models also identifying the limiting theories that emerge when m → ∞. © 2009 IOP Publishing Ltd.

We present a novel method to compute expectation values in the Lieb-Liniger model both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas. © 2009 The American Physical Society.

We study the effect of an optical lattice (OL) on the ground-state properties of one-dimensional ultracold bosons with three-body attractive interactions and two-body repulsive interactions, which are described by a cubic-quintic Gross-Pitaevskii equation with a periodic potential. Without the optical lattice and with a vanishing two-body interaction term, normalizable soliton solutions of the Townes type are possible only at a critical value of the interaction strength, at which an infinite degeneracy of the ground state occurs; a repulsive two-body interaction makes such localized solutions unstable. We show that the OL opens a stability window around the critical point when the strength of the periodic potential is above a critical threshold. We also consider the effect of an external parabolic trap, studying how the stability properties depend on the matching between minima of the periodic potential and the minimum of the parabolic trap. © 2009 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

We study the nonequilibrium dynamics of the quantum Ising model following an abrupt quench of the transverse field. We focus on the on-site autocorrelation function of the order parameter, and extract the phase-coherence time τQφ from its asymptotic behavior. We show that the initial state determines τQφ only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of τQφ on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature. © 2009 The American Physical Society.

We analyze the evolution of the particle spectrum of the tricritical Ising model by varying the couplings of the energy and vacancy density fields. The particle content changes from the spectrum of a supersymmetric theory (either of an exact or a spontaneously broken supersymmetric theory) to the spectrum of seven particles related to the underlying E7 structure. In the low temperature phase some of these excitations are topologically charged particles that are stable under an arbitrary variation of the parameters. The high and low temperature phases of the model are related by duality. In some regions of the two couplings there are also present false vacua and sequences of bound states. In order to study the non-integrable features of this model we employ the form factor perturbation theory and the truncated conformal space approach. © 2008 IOP Publishing Ltd.

We study the ground-state properties of a one-dimensional Bose gas with N -body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schrödinger equation, we compute the chemical potential and the ground-state energy. For N=3, a localized soliton wave function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parametrized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of N -body attractive contact interactions in higher dimensions is presented. © 2008 The American Physical Society.