Analyzing in detail the first corrections to the scaling hypothesis, we develop accelerated methods for the determination of critical points from finite size data. The output of these procedures are sequences of pseudo-critical points which rapidly c
onverge towards the true critical points. In fact more rapidly than previously existing methods like the Phenomenological Renormalization Group approach. Our methods are valid in any spatial dimensionality and both for quantum or classical statistical systems. Having at disposal fast converging sequences, allows to draw conclusions on the basis of shorter system sizes, and can be extremely important in particularly hard cases like two-dimensional quantum systems with frustrations or when the sign problem occurs. We test the effectiveness of our methods both analytically on the basis of the one-dimensional XY model, and numerically at phase transitions occurring in non integrable spin models. In particular, we show how a new Homogeneity Condition Method is able to locate the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state quantities on relatively small systems.
We use the fidelity approach to quantum critical points to study the zero temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the
phase diagram, with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion U=0 and electron density n=1, the fidelity metric satisfies an hyper-scaling form which we calculate. This implies that in general, as one approaches the critical point U=0, n=1, the fidelity metric tends to a limit which depends on the path of approach. At half filling, the fidelity metric is expected to diverge as U^{-4} when U is sent to zero.
We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way we are able to obtain sequences of pseudo-critical points which display a faster convergence rate
as compared to currently used methods. The approaches are valid in any spatial dimension and for any value of the dynamic exponent. We demonstrate the effectiveness of our methods both analytically on the basis of the one dimensional XY model, and numerically considering c = 1 transitions occurring in non integrable spin models. In particular, we show that these general methods are able to locate precisely the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state properties on relatively small systems.
Isotropic XX models of one-dimensional spin-1/2 chains are investigated with the aim to elucidate the formal structure and the physical properties that allow these systems to act as channels for long-distance, high-fidelity quantum teleportation. We
introduce two types of models: I) open, dimerized XX chains, and II) open XX chains with small end bonds. For both models we obtain the exact expressions for the end-to-end correlations and the scaling of the energy gap with the length of the chain. We determine the end-to-end concurrence and show that model I) supports true long-distance entanglement at zero temperature, while model II) supports {it ``quasi long-distance} entanglement that slowly falls off with the size of the chain. Due to the different scalings of the gaps, respectively exponential for model I) and algebraic in model II), we demonstrate that the latter allows for efficient qubit teleportation with high fidelity in sufficiently long chains even at moderately low temperatures.
