Scaling of decoherence and energy flow in interacting quantum spin systems

We address the quantum dynamics of a system composed of a qubit globally coupled to a many-body system characterized by short-range interactions. We employ a dynamic finite-size scaling framework to investigate the out-of-equilibrium dynamics arising from the sudden variation (turning on) of the interaction between the qubit and the many-body system, in particular when the latter is in proximity of a quantum first-order or continuous phase transition. Although the approach is quite general, we consider d-dimensional quantum Ising spin models in the presence of transverse and longitudinal fields, as paradigmatic quantum many-body systems. To characterize the out-of-equilibrium dynamics, we focus on a number of quantum-information oriented properties of the model. Namely, we concentrate on the decoherence features of the qubit, the energy interchanges among the qubit and the many-body system during the out-of-equilibrium dynamics, and the work distribution associated with the quench. The scaling behaviors predicted by the dynamic finite-size scaling theory are verified through extensive numerical computations for the one-dimensional Ising model, which reveal a fast convergence to the expected asymptotic behavior with increasing the system size.Comment: 16 pages, 9 figure

Phase diagram of the extended Bose Hubbard model

By means of the Density Matrix Renormalization Group technique, we accurately determine the zero-temperature phase diagram of the one-dimensional extended Bose Hubbard model with on-site and nearest-neighbor interactions. We analyze the scaling of the charge and of the neutral ground-state energy gaps, as well as of various order parameters. In this way we come to an accurate location of the boundaries between the superfluid and the insulating phases. In this last region we are able to distinguish between the conventional Mott insulating and density-wave phases, and the Haldane Insulator phase displaying long-range string ordering, as originally predicted by E.G. Dalla Torre, E. Berg and E. Altman in Phys. Rev. Lett. 97, 260401 (2006).Comment: 13 pages, 6 figures. To appear in NJP, in the focus issue on "Bose Condensation Phenomena in Atomic and Solid State Physics

Ground-state fidelity at first-order quantum transitions

We analyze the scaling behavior of the fidelity, and the corresponding susceptibility, emerging in finite-size many-body systems whenever a given control parameter $\lambda$ is varied across a quantum phase transition. For this purpose we consider a finite-size scaling (FSS) framework. Our working hypothesis is based on a scaling assumption of the fidelity in terms of the FSS variables associated to $\lambda$ and to its variation $\delta \lambda$. This framework entails the FSS predictions for continuous transitions, and meanwhile enables to extend them to first-order transitions, where the FSS becomes qualitatively different. The latter is supported by analytical and numerical analyses of the quantum Ising chain along its first-order quantum transition line, driven by an external longitudinal field.Comment: 10 pages, 6 figures. Revised versio

Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions

We study the quantum dynamics of many-body systems, in the presence of dissipation due to the interaction with the environment, under Kibble-Zurek (KZ) protocols in which one Hamiltonian parameter is slowly, and linearly in time, driven across the critical value of a zero-temperature quantum transition. In particular we address whether, and under which conditions, open quantum systems can develop a universal dynamic scaling regime similar to that emerging in closed systems. We focus on a class of dissipative mechanisms whose dynamics can be reliably described through a Lindblad master equation governing the time evolution of the system's density matrix. We argue that a dynamic scaling limit exists even in the presence of dissipation, whose main features are controlled by the universality class of the quantum transition. This requires a particular tuning of the dissipative interactions, whose decay rate $u$ should scale as $u\sim t_s^{-\kappa}$ with increasing the time scale $t_s$ of the KZ protocol, where the exponent $\kappa = z/(y_\mu+z)$ depends on the dynamic exponent $z$ and the renormalization-group dimension $y_\mu$ of the driving Hamiltonian parameter. Our dynamic scaling arguments are supported by numerical results for KZ protocols applied to a one-dimensional fermionic wire undergoing a quantum transition in the same universality class of the quantum Ising chain, in the presence of dissipative mechanisms which include local pumping, decay, and dephasing.Comment: 15 pages, 8 figure

Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities

By means of analytical and numerical methods we analyze the phase diagram of polaritons in one-dimensional coupled cavities. We locate the phase boundary, discuss the behavior of the polariton compressibility and visibility fringes across the critical point, and find a non-trivial scaling of the phase boundary as a function of the number of atoms inside each cavity. We also predict the emergence of a polaritonic glassy phase when the number of atoms fluctuates from cavity to cavity.Comment: 4 pages, 5 figures. Published versio

Schwinger terms in Weyl-invariant and diffeomorphism-invariant 2-d scalar field theory

We compute the Schwinger terms in the energy-momentum tensor commutator algebra from the anomalies present in Weyl-invariant and diffeomorphism-invariant effective actions for two dimensional massless scalar fields in a gravitational background. We find that the Schwinger terms are not sensitive to the regularization procedure and that they are independent of the background metric.Comment: 8 pages, RevTex. Conclusions and references added. To appear in Phys. Rev.