Giuseppe E. Santoro

Theory of Quantum Annealing of an Ising Spin Glass

Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. By comparing classical and quantum Monte Carlo annealing protocols on the two-dimensional random Ising model (a prototype spin glass), we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the residual energy after annealing is inversely proportional to a power of the logarithm of the annealing time, but the quantum case has a larger power that makes it faster.

EFFECTIVE THERMAL DYNAMICS FOLLOWING A QUANTUM QUENCH IN A SPIN CHAIN

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 tau(Q)(phi) from its asymptotic behavior. We show that the initial state determines tau(Q)(phi) only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of tau(Q)(phi) on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature.

Strong correlations in electron doped phthalocyanine conductors near half filling.

We propose that electron doped nontransition metal phthalocyanines such as ZnPc and MgPc, similar to those very recently reported, should constitute novel strongly correlated metals. Because of orbital degeneracy, Jahn-Teller coupling, and Hunds rule exchange, and with a large on-site Coulomb repulsion, these molecular conductors should display, particularly near half filling at two electrons/molecule, very unconventional properties, including Mott insulators, strongly correlated superconductivity, and other intriguing phases.

Periodic steady regime and interference in a periodically driven quantum system.

We study the coherent dynamics of a quantum many-body system subject to a time-periodic driving. We argue that in many cases, destructive interference in time makes most of the quantum averages time periodic, after an initial transient. We discuss in detail the case of a quantum Ising chain periodically driven across the critical point, finding that, as a result of quantum coherence, the system never reaches an infinite temperature state. Floquet resonance effects are moreover observed in the frequency dependence of the various observables, which display a sequence of well-defined peaks or dips. Extensions to nonintegrable systems are discussed.

Quantum annealing of the traveling-salesman problem

We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric traveling-salesman problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal simulated annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (two-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.

Optimization by quantum annealing : Lessons from hard satisfiability problems

The path integral Monte Carlo simulated quantum annealing algorithm is applied to the optimization of a large hard instance of the random satisfiability problem (N = 10,000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the traveling salesman problem, in the present case the linear-schedule quantum annealing performance is definitely worse than classical annealing. Nevertheless, a quantum cooling protocol based on field-cycling and able to outperform standard classical simulated annealing over short time scales is introduced.

Quantum quenches, thermalization, and many-body localization

We conjecture that thermalization following a quantum quench in a strongly correlated quantum system is closely connected to many-body delocalization in the space of quasi-particles. This scenario is tested in the anisotropic Heisenberg spin chain with different types of integrability-breaking terms. We first quantify the deviations from integrability by analyzing the level spacing statistics and the inverse participation ratio of the systems eigenstates. We then focus on thermalization, by studying the dynamics after a sudden quench of the anisotropy parameter. Our numerical simulations clearly support the conjecture, as long as the integrability-breaking term acts homogeneously on the quasiparticle space, in such a way as to induce ergodicity over all the relevant Hilbert space.

Surface lattice-dynamical approach to the reconstruction of W(100) and W(100): H

Abstract We review the surface reconstruction of the bcc (100) transition metal surface, particularly W(100) and some of the results obtained, with the method of the effective surface lattice dynamics.

Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

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 quasi-particles of the model: non-local 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 analizing their robustness with respect to a sufficiently strong integrability-breaking term.

Self-trapping vs. non-trapping of electrons and holes in organic insulators: polyethylene

We show, by electronic structure based molecular dynamics simulations, that an extra electron injected in crystalline polyethylene should fall spontaneously into a self-trapped state, a shallow donor with a large novel distortion pattern involving a pair of trans-gauche defects. Parallel calculations show instead that a hole will remain free and delocalized. We trace the difference of behavior to the intrachain nature of the hole, as opposed to the interchain one of the electron, and argue that applicability of this concept could be more general. Thus electrons (but not holes) should tend to self-trap in saturated organic insulators, but not for example in aromatic insulators, where both carriers are intrachain.