Luigi Amico

Topology-Induced Anomalous Defect Production by Crossing a Quantum Critical Point

We study the influence of topology on the quench dynamics of a system driven across a quantum critical point. We show how the appearance of certain edge states, which fully characterize the topology of the system, dramatically modifies the process of defect production during the crossing of the critical point. Interestingly enough, the density of defects is no longer described by the Kibble-Zurek scaling, but determined instead by the nonuniversal topological features of the system. Edge states are shown to be robust against defect production, which highlights their topological nature.

Ground-state factorization and correlations with broken symmetry

We show how the phenomenon of factorization in a quantum many-body system is of collective nature. To this aim we study the quantum discord Q in the one-dimensional XY model in a transverse field. We analyze the behavior of Q at both the critical point and at the non-critical factorizing field. The factorization is found to be governed by an exponential scaling law for Q. We also address the thermal effects fanning out from the anomalies occurring at zero temperature. Close to the quantum phase transition, Q exhibits a finite-temperature crossover with universal scaling behavior, while the factorization phenomenon results in a non-trivial pattern of correlations present at low temperature.

Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point

We study the adiabatic dynamics of Majorana fermions across a quantum phase transition. We show that the Kibble?Zurek scaling, which describes the density of bulk defects produced during the critical point crossing, is not valid for edge Majorana fermions. Therefore, the dynamics governing an edge state quench is nonuniversal and depends on the topological features of the system. Besides, we show that the localization of Majorana fermions is a necessary ingredient to guarantee robustness against defect production.

Divergence of the entanglement range in low-dimensional quantum systems

We study the pairwise entanglement close to separable ground states of a class of one dimensional quantum spin models. At T=0 we find that such ground states separate regions, in the space of the Hamiltonian parameters, which are characterized by qualitatively different types of entanglement, namely parallel and antiparallel entanglement; we further demonstrate that the range of the Concurrence diverges while approaching separable ground states, therefore evidencing that such states, with uncorrelated fluctuations, are reached by a long range reshuffling of the entanglement. We generalize our results to the analysis of quantum phase transitions occurring in bosonic and fermionic systems. Finally, the effects of finite temperature are considered: At T>0 we evidence the existence of a region where no pairwise entanglement survives, so that entanglement, if present, is genuinely multipartite.

Integrable models for confined fermions: applications to metallic grains

Abstract We study integrable models for electrons in metals when the single particle spectrum is discrete. The electron–electron interactions are BCS-like pairing, Coulomb repulsion, and spin-exchange coupling. These couplings are, in general, nonuniform in the sense that they depend on the levels occupied by the interacting electrons. By using the realization of spin-1/2 operators in terms of electrons the models describe spin-1/2 models with nonuniform long range interactions and external magnetic field. The integrability and the exact solution arise since the model Hamiltonians can be constructed in terms of Gaudin models. Uniform pairing and the resulting orthodox model correspond to an isotropic limit of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.

Dynamical Mean Field Theory of the Bose-Hubbard Model

Quantum dynamics of the Bose-Hubbard Model is investigated through a semiclassical hamiltonian picture provided by the Time-Dependent Variational Principle method. The system is studied within a factorized slow/fast dynamics. The semiclassical requantization procedure allows one to account for the strong quantum nature of the system when

Quantum phase transition between cluster and antiferromagnetic states

t/U\ll 1

Statistical mechanics of the cluster Ising model

. The phase diagram is in good agreement with Quantum Monte Carlo results and third order strong coupling perturbative expansion.

The BCS model and the off-shell Bethe ansatz for vertex models

We study a Hamiltonian system describing a three–spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied and used to investigate the quantum phase transition. Our findings in one dimension corroborate the analysis of the two-dimensional generalization of the system, indicating, at a mean-field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state.

Time-dependent mean field theory of the superfluid-insulator phase transitions

We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.