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

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

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.

Out-of-equilibrium dynamics driven by localized time-dependent perturbations at quantum phase transitions

We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium behavior is observed, even when the perturbation is very slow. We show that, close to the transition, time-dependent quantities obey scaling laws. In first-order quantum transitions, the scaling behavior is universal, and some scaling functions can be exactly computed. For continuous quantum transitions, the scaling laws are controlled by the standard critical exponents and by the renormalization-group dimension of the perturbation at the transition. Our scaling approach is applied to the quantum Ising ring which presents both first-order and continuous quantum transitions.Comment: 10 pages, 4 fig

Are Workers. Enterprises Entry Policies Conventional

One of the main reasons why workers’ enterprises (WE) still represent a relevant chunk of the economy may lie in some affinities with conventional profit maximizing firms. To prove this, we compare the entry policies of WEs and conventional firms when they can decide size at entry while having to stick to it afterwards. Even though short run differences remain, a long run coincidence appears besides that under certainty. Endogenizing size and time of entry in an uncertain dynamic environment we see that WEs enter at the same trigger and size of conventional firms. Both of them wait less and choose a dimension larger than the minimum efficient scale. This may be another way to explain why WE are still an important share of the economy (Hesse and Cihàk, 2007) despite the ongoing mantra of their imminent demise.Workers’ Enterprises, Entry, Uncertainty, Rigidity