Alessandro Cuccoli

The effective potential and effective Hamiltonian in quantum statistical mechanics

An overview on the theoretic formalism and up to date applications in quantum condensed matter physics of the effective potential and effective Hamiltonian methods is given. The main steps of their unified derivation by the so-called pure quantum self-consistent harmonic approximation (PQSCHA) are reported and explained. What makes this framework attractive is its easy implementation as well as the great simplification in obtaining results for the statistical mechanics of complicated quantum systems. Indeed, for a given quantum system the PQSCHA yields an effective system, i.e. an effective classical Hamiltonian with dependence on h(cross) and beta and classical-like expressions for the averages of observables, that has to be studied by classical methods. Anharmonic single-particle systems are analysed in order to get insight into the physical meaning of the PQSCHA, and its extension to the investigation of realistic many-body systems is pursued afterwards. The power of this approach is demonstrated through a collection of applications in different fields, such as soliton theory, rare gas crystals and magnetism. Eventually, the PQSCHA allows us also to approach quantum dynamical properties.

Long quantum channels for high-quality entanglement transfer

High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are nonperturbatively coupled to the chain by a suitable exchange interaction j0. Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value jopt0(N), where N is the channel length. We show that jopt0(N) scales as N?1/6 for large N and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, for any chain length the average quantum-state transmission fidelity exceeds 90% and decreases very little in a broad neighbourhood of jopt0(N). We emphasize that, taking the reverse point of view, should j0 be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.

Phase transitions induced by easy-plane anisotropy in the classical Heisenberg antiferromagnet on a triangular lattice: A Monte Carlo simulation

We present the results of Monte Carlo simulations for the antiferromagnetic classical XXZ model with easy-plane exchange anisotropy on the triangular lattice, which causes frustration of the spin alignment. The behaviour of this system is similar to that of the antiferromagnetic XY model on the same lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition, associated to vortex-antivortex unbinding, and of an Ising-like one due to the chirality, the latter occurring at a slightly higher temperature. Data for internal energy, specific heat, magnetic susceptibility, correlation length, and some properties associated with the chirality are reported in a broad temperature range, for lattice sizes ranging from 24x24 to 120x120; four values of the easy-plane anisotropy are considered. Moving from the strongest towards the weakest anisotropy (1%) the thermodynamic quantities tend to the isotropic model behaviour, and the two transition temperatures decrease by about 25% and 22%, respectively.

Optimal dynamics for quantum-state and entanglement transfer through homogeneous quantum systems

It is shown that eective quantum-state and entanglement transfer can be obtained by inducing a coherent dynamics in quantum wires with homogeneous intrawire interactions. This goal is accom- plished by tuning the coupling between the wire endpoints and the two qubits there attached, to an optimal value. A general procedure to determine such value is devised, and scaling laws between the optimal coupling and the length of the wire are found. The procedure is implemented in the case of a wire consisting of a spin- 1 XY chain: results for the time dependence of the quantities which characterize quantum-state and entanglement transfer are found of extremely good quality and al- most independent of the wire length. The present approach does not require ad hoc engineering of the intrawire interactions nor a specic initial pulse shaping, and can be applied to a vast class of quantum channels. One of the most commonly requested conditions in quantum communication and computation protocols is that two distant parties, typically Alice and Bob, share a couple of entangled qubits. When the physical objects encoding the qubits can travel, as in the case of optical photons, the above goal can be accomplished by creat- ing the entangled couple in a limited region of space and then letting the qubits fly where necessary. On the other hand, when qubits are realized via intrinsically localized

99%-fidelity ballistic quantum-state transfer through long uniform channels

Quantum-state transfer with fidelity higher than 0.99 can be achieved in the ballistic regime of an arbitrarily long one-dimensional chain with uniform nearest-neighbor interaction, except for the two pairs of mirror symmetric extremal bonds, say x (first and last) and y (second and last-but-one). These have to be roughly tuned to suitable values x ~ 2 N^{-1/3} and y ~ 2^{3/4} N^{-1/6}, N being the chain length. The general framework can describe the end-to-end response in different models, such as fermion or boson hopping models and XX spin chains.

Propagation of nonclassical correlations across a quantum spin chain

We study the transport of quantum correlations across a chain of interacting spin-1/2 particles. As a quantitative figure of merit, we choose a symmetric version of quantum discord and compare it with the transported entanglement, addressing various operating regimes of the spin medium. Discord turns out to be better transported for a wide range of working points and initial conditions of the system. We relate this behavior to the efficiency of propagation of a single excitation across the spin chain. Moreover, we point out the role played by a magnetic field in the dynamics of discord in the effective channel embodied by the chain. Our analysis can be interestingly extended to transport processes in more complex networks and the study of nonclassical correlations under general quantum channels.

Dipolar interaction and incoherent quantum tunneling: a Monte Carlo study of magnetic relaxation

Abstract:We study the magnetic relaxation of a system of localized spins interacting through weak dipole interactions, at a temperature large with respect to the ordering temperature but low with respect to the crystal field level splitting. The relaxation results from quantum spin tunneling but is only allowed on sites where the dipole field is very small. At low times, the magnetization decrease is proportional to

Two-dimensional quantum Heisenberg antiferromagnet: Effective-Hamiltonian approach to the thermodynamics

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