Andrea Fubini

Studying Quantum Spin Systems through Entanglement Estimators

We study the field dependence of the entanglement of formation in anisotropic S=1/2 antiferromagnetic chains displaying a T=0 field-driven quantum phase transition. The analysis is carried out via quantum Monte Carlo simulations. At zero temperature the entanglement estimators show abrupt changes at and around criticality, vanishing below the critical field, in correspondence with an exactly factorized state, and then immediately recovering a finite value upon passing through the quantum phase transition. At the quantum-critical point, a deep minimum in the pairwise-to-global entanglement ratio shows that multispin entanglement is strongly enhanced; moreover this signature represents a novel way of detecting the quantum phase transition of the system, relying entirely on entanglement estimators.

Entanglement and factorized ground states in two-dimensional quantum antiferromagnets.

Making use of exact results and quantum Monte Carlo data for the entanglement of formation, we show that the ground state of anisotropic two-dimensional S=1/2 antiferromagnets in a uniform field takes the classical-like form of a product state for a particular value and orientation of the field, at which the purely quantum correlations due to entanglement disappear. Analytical expressions for the energy and the form of such states are given, and a novel type of exactly solvable two-dimensional quantum models is therefore singled out. Moreover, we show that the field-induced quantum phase transition present in the models is unambiguously characterized by a cusp minimum in the pairwise-to-global entanglement ratio R, marking the quantum-critical enhancement of multipartite entanglement.

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.

Reading entanglement in terms of spin configurations in quantum magnets

Abstract. We consider a quantum many-body system made of N interacting S=1/2 spins on a lattice, and develop a formalism which allows to extract, out of conventional magnetic observables, the quantum probabilities for any selected spin pair to be in maximally entangled or factorized two-spin states. This result is used in order to capture the meaning of entanglement properties in terms of magnetic behavior. In particular, we consider the concurrence between two spins and show how its expression extracts information on the presence of bipartite entanglement out of the probability distributions relative to specific sets of two-spin quantum states. We apply the above findings to the antiferromagnetic Heisenberg model in a uniform magnetic field, both on a chain and on a two-leg ladder. Using Quantum Monte Carlo simulations, we obtain the above probability distributions and the associated entanglement, discussing their evolution under application of the field.

Two-spin entanglement distribution near factorized states

We study the two-spin entanglement distribution along the infinite S = 1/2 chain described by the XY model in a transverse field; closed analytical expressions are derived for the one-tangle and the concurrences Cr, with r being the distance between the two possibly entangled spins, for the values of the Hamiltonian parameters close to those corresponding to factorized ground states. The total amount of the entanglement, the fraction of such entanglement which is stored in pairwise entanglement and the way such fraction distributes along the chain are discussed, with attention focused on the dependence on the anisotropy of the exchange interaction. Near factorization a characteristic length scale naturally emerges in the system, which is specifically related with the entanglement properties and diverges at the critical point of the fully isotropic model. In general, we find that anisotropy rules a complex behavior of the entanglement properties, which results in the fact that more isotropic models, despite being characterized by a larger amount of the total entanglement, present a smaller fraction of the pairwise entanglement: the latter, in turn, is more evenly distributed along the chain, to the extent that, in the fully isotropic model at the critical field, the concurrences do not depend on r.

Ising transition in the two-dimensional quantum J1 − J2 Heisenberg model

We study the thermodynamics of the spin-S two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings in its collinear phase (J(2)/J(1)>0.5), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio J(2)/J(1) is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin and temperature dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li2VOSiO4 and related compounds.

Mesoscopic fluctuations in superconducting dots at finite temperatures

We study the thermodynamics of ultrasmall metallic grains with the mean level spacing \ensuremath{\delta} comparable or larger than the pairing correlation energy in the whole range of temperatures. A complete picture of the thermodynamics in such systems is given taking into account the effects of disorder, parity and classical and quantum fluctuations. Both spin susceptibility and specific heat turn out to be sensitive probes to detect superconducting correlations in such samples.

Nonequilibrium transfer and decoherence in quantum impurity problems

Using detailed balance and scaling properties of integrals that appear in the Coulomb gas reformulation of quantum impurity problems, we establish exact relations between the nonequilibrium transfer rates of the boundary sine-Gordon and the anisotropic Kondo model at zero temperature. Combining these results with findings from the thermodynamic Bethe ansatz, we derive exact closed form expressions for the transfer rate in the biased spin-boson model in the scaling limit. They illustrate how the crossover from weak to strong tunneling takes place. Using a conjectured correspondence between the transfer and the decoherence rate, we also determine the exact lower bound for damping of the coherent oscillation as a function of bias and dissipation strength in this paradigmic model for NMR and superposition of macroscopically distinct states (qubits).

Quantum thermodynamics of systems with anomalous dissipative coupling

The standard system-plus-reservoir approach used in the study of dissipative systems can be meaningfully generalized to a dissipative coupling involving the momentum, instead of the coordinate: the corresponding equation of motion differs from the Langevin equation, so this is called anomalous dissipation. It occurs for systems where such coupling can indeed be derived from the physical analysis of the degrees of freedom that can be treated as a dissipation bath. Starting from the influence functional corresponding to anomalous dissipation, it is shown how to derive the effective classical potential that gives the quantum thermal averages for the dissipative system in terms of classical-like calculations; the generalization to many degrees of freedom is given. The formalism is applied to a single particle in a double well and to the discrete phi(4) model. At variance with the standard case, the fluctuations of the coordinate are enhanced by anomalous dissipative coupling.

Quantum effects on the BKT phase transition of two-dimensional Josephson arrays

The phase diagram of two-dimensional Josephson arrays is studied by means of the mapping to the quantum