arXiv subjects

L. Campos Venuti

Publications and source records attributed to L. Campos Venuti.

12 recordsLinked to original sources

arXiv2015

Finding critical points using improved scaling Ansaetze

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 converge 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.

cond-mat.stat-mech↗

arXiv2008

The fidelity approach to the Hubbard model

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.

cond-mat.stat-mech↗

arXiv2008

Rapidly-converging methods for the location of quantum critical points from finite-size data

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.

cond-mat.stat-mech↗

arXiv2007

Long-distance entanglement and quantum teleportation in XX spin chains

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.

quant-ph↗

arXiv2007

Qubit Teleportation and Transfer across Antiferromagnetic Spin Chains

We explore the capability of spin-1/2 chains to act as quantum channels for both teleportation and transfer of qubits. Exploiting the emergence of long-distance entanglement in low-dimensional systems [Phys. Rev. Lett. 96, 247206 (2006)], here we show how to obtain high communication fidelities between distant parties. An investigation of protocols of teleportation and state transfer is presented, in the realistic situation where temperature is included. Basing our setup on antiferromagnetic rotationally invariant systems, both protocols are represented by pure depolarizing channels. We propose a scheme where channel fidelity close to one can be achieved on very long chains at moderately small temperature.

quant-ph↗

arXiv2006

Long-distance entanglement in spin systems

Most quantum system with short-ranged interactions show a fast decay of entanglement with the distance. In this Letter, we focus on the peculiarity of some systems to distribute entanglement between distant parties. Even in realistic models, like the spin-1 Heisenberg chain, sizable entanglement is present between arbitrarily distant particles. We show that long distance entanglement appears for values of the microscopic parameters which do not coincide with known quantum critical points, hence signaling a transition detected only by genuine quantum correlations.

quant-ph↗

arXiv2006

Stable particles in anisotropic spin-1 chains

Motivated by field-theoretic predictions we investigate the stable excitations that exist in two characteristic gapped phases of a spin-1 model with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a region close to the phase boundary where a stable breather exists besides the stable particles, that form the Haldane triplet at the Heisenberg isotropic point. The numerical data, obtained by means of the Density Matrix Renormalization Group, confirm this picture in the so-called large-D phase for which we give also a quantitative analysis of the bound states using standard perturbation theory. However, the situation turns out to be considerably more intricate in the Haldane phase where, to the best of our data, we do not observe stable breathers contrarily to what could be expected from the sine-Gordon model, but rather only the three modes predicted by a novel anisotropic extension of the Non-Linear Sigma Model studied here by means of a saddle-point approximation.

cond-mat.str-el↗

arXiv2005

Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions

We discuss on general grounds some local indicators of entanglement, that have been proposed recently for the study and classification of quantum phase transitions. In particular, we focus on the capability of entanglement in detecting quantum critical points and related exponents. We show that the singularities observed in all local measures of entanglement are a consequence of the scaling hypothesis. In particular, as every non-trivial local observable is expected to be singular at criticality, we single out the most relevant one (in the renormalization group sense) as the best-suited for finite-size scaling analysis. The proposed method is checked on a couple of one-dimensional spin systems. The present analysis shows that the singular behaviour of local measures of entanglement is fully encompassed in the usual statistical mechanics framework.

quant-ph↗

arXiv2005

Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems

We study the relation between the recently defined localizable entanglement and generalized correlations in quantum spin systems. Differently from the current belief, the localizable entanglement is always given by the average of a generalized string. Using symmetry arguments we show that in most spin 1/2 and spin 1 systems the localizable entanglement reduces to the spin-spin or string correlations, respectively. We prove that a general class of spin 1 systems, which includes the Heisenberg model, can be used as perfect quantum channel. These conclusions are obtained in analytic form and confirm some results found previously on numerical grounds.

cond-mat.str-el↗

arXiv2005

Particle Content of the Nonlinear Sigma Model with Theta-Term: a Lattice Model Investigation

Using new as well as known results on dimerized quantum spin chains with frustration, we are able to infer some properties on the low-energy spectrum of the O(3) Nonlinear Sigma Model with a topological theta-term. In particular, for sufficiently strong coupling, we find a range of values of theta where a singlet bound state is stable under the triplet continuum. On the basis of these results, we propose a new renormalization group flow diagram for the Nonlinear Sigma Model with theta-term.

cond-mat.stat-mech↗

arXiv2002

Doping dependence of the spin gap in a 2-leg ladder

A spin-fermion model relevant for the description of cuprates ladders is studied in a path integral formalism, where, after integrating out the fermions, an effective action for the spins in term of a Fermi-determinant results. The determinant can be evaluated in the long-wavelength, low-frequency limit to all orders in the coupling constant, leading to a non-linear sigma model with doping dependent coupling constants. An explicit evaluation shows, that the spin-gap diminishes upon doping as opposed to previous mean-field treatments.

cond-mat.str-el↗

arXiv1999

Spin Chains in an External Magnetic Field. Closure of the Haldane Gap and Effective Field Theories

We investigate both numerically and analytically the behaviour of a spin-1 antiferromagnetic (AFM) isotropic Heisenberg chain in an external magnetic field. Extensive DMRG studies of chains up to N=80 sites extend previous analyses and exhibit the well known phenomenon of the closure of the Haldane gap at a lower critical field H_c1. We obtain an estimate of the gap below H_c1. Above the lower critical field, when the correlation functions exhibit algebraic decay, we obtain the critical exponent as a function of the net magnetization as well as the magnetization curve up to the saturation (upper critical) field H_c2. We argue that, despite the fact that the SO(3) symmetry of the model is explicitly broken by the field, the Haldane phase of the model is still well described by an SO(3) nonlinear sigma-model. A mean-field theory is developed for the latter and its predictions are compared with those of the numerical analysis and with the existing literature.

cond-mat.str-el↗