45 research outputs found
Low-Dimensional Spin Systems: Hidden Symmetries, Conformal Field Theories and Numerical Checks
We review here some general properties of antiferromagnetic Heisenberg spin
chains, emphasizing and discussing the role of hidden symmetries in the
classification of the various phases of the models. We present also some recent
results that have been obtained with a combined use of Conformal Field Theory
and of numerical Density Matrix Renormalization Group techniques.Comment: To be published in the proceedings of the XIII Conference on
"Symmetries in Physics", held in Bregenz (Voralberg, Austria), 21-24/7/2003.
Plain LaTeX2e, 4 EPS figure
On critical phases in anisotropic spin-1 chains
Quantum spin-1 chains may develop massless phases in presence of Ising-like
and single-ion anisotropies. We have studied c=1 critical phases by means of
both analytical techniques, including a mapping of the lattice Hamiltonian onto
an O(2) nonlinear sigma model, and a multi-target DMRG algorithm which allows
for accurate calculation of excited states. We find excellent quantitative
agreement with the theoretical predictions and conclude that a pure Gaussian
model, without any orbifold construction, describes correctly the low-energy
physics of these critical phases. This combined analysis indicates that the
multicritical point at large single-ion anisotropy does not belong to the same
universality class as the Takhtajan-Babujian Hamiltonian as claimed in the
past. A link between string-order correlation functions and twisting vertex
operators, along the c=1 line that ends at this point, is also suggested.Comment: 9 pages, 3 figures, svjour format, submitted to Eur. Phys. J.
Effective mapping of spin-1 chains onto integrable fermionic models. A study of string and Neel correlation functions
We derive the dominant contribution to the large-distance decay of
correlation functions for a spin chain model that exhibits both Haldane and
Neel phases in its ground state phase diagram. The analytic results are
obtained by means of an approximate mapping between a spin-1 anisotropic
Hamiltonian onto a fermionic model of noninteracting Bogolioubov quasiparticles
related in turn to the XY spin-1/2 chain in a transverse field. This approach
allows us to express the spin-1 string operators in terms of fermionic
operators so that the dominant contribution to the string correlators at large
distances can be computed using the technique of Toeplitz determinants. As
expected, we find long-range string order both in the longitudinal and in the
transverse channel in the Haldane phase, while in the Neel phase only the
longitudinal order survives. In this way, the long-range string order can be
explicitly related to the components of the magnetization of the XY model.
Moreover, apart from the critical line, where the decay is algebraic, we find
that in the gapped phases the decay is governed by an exponential tail
multiplied by algebraic factors. As regards the usual two points correlation
functions, we show that the longitudinal one behaves in a 'dual' fashion with
respect to the transverse string correlator, namely both the asymptotic values
and the decay laws exchange when the transition line is crossed. For the
transverse spin-spin correlator, we find a finite characteristic length which
is an unexpected feature at the critical point. We also comment briefly the
entanglement features of the original system versus those of the effective
model. The goodness of the approximation and the analytical predictions are
checked versus density-matrix renormalization group calculations.Comment: 28 pages, plain LaTeX, 2 EPS figure
Folds and Buckles at the Nanoscale: Experimental and Theoretical Investigation of the Bending Properties of Graphene Membranes
The elastic properties of graphene crystals have been extensively investigated, revealing unique properties in the linear and nonlinear regimes, when the membranes are under either stretching or bending loading conditions. Nevertheless less knowledge has been developed so far on folded graphene membranes and ribbons. It has been recently suggested that fold-induced curvatures, without in-plane strain, can affect the local chemical reactivity, the mechanical properties, and the electron transfer in graphene membranes. This intriguing perspective envisages a materials-by-design approach through the engineering of folding and bending to develop enhanced nano-resonators or nano-electro-mechanical devices. Here we present a novel methodology to investigate the mechanical properties of folded and wrinkled graphene crystals, combining transmission electron microscopy mapping of 3D curvatures and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations
Phase separation and pairing regimes in the one-dimensional asymmetric Hubbard model
We address some open questions regarding the phase diagram of the
one-dimensional Hubbard model with asymmetric hopping coefficients and balanced
species. In the attractive regime we present a numerical study of the passage
from on-site pairing dominant correlations at small asymmetries to
charge-density waves in the region with markedly different hopping
coefficients. In the repulsive regime we exploit two analytical treatments in
the strong- and weak-coupling regimes in order to locate the onset of phase
separation at small and large asymmetries respectively.Comment: 13 pages, RevTeX 4, 12 eps figures, some additional refs. with
respect to v1 and citation errors fixe
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.Comment: 5 pages, 4 .eps figure
Correlation length and the scaling parameter in the Renormalization Group
The basic procedure of renormalization group theory is used to split the free energy into a Kadanoff block formation part, and a renormalized block-block interaction part. The study of this redistribution as a function of the scaling parameter s shows that there is a stationarity value s* of s, which turns out to have the same critical behavior as the correlation length. It is suggested that s* can be used as an appropriate measure and definition of the correlation length, even for noncritical regions. The calculation of s* is thereby performed explicitly for the Gaussian, and numerically for the S4 model. A sharp separation between noncorrelated and correlated regimes is also found for the Gaussian model, well above the critical temperature. For the S4 model, the results suggest that ξ is characterized by a high-temperature Gaussian branch and by a genuine S4 branch at low temperatures, connected by a "plateau" in the intermediate region
Scaling of excitations in dimerized and frustrated spin-1/2 chains
We study the finite-size behavior of the low-lying excitations of spin-1/2
Heisenberg chains with dimerization and next-to-nearest neighbors interaction,
J_2. The numerical analysis, performed using density-matrix renormalization
group, confirms previous exact diagonalization results, and shows that, for
different values of the dimerization parameter \delta, the elementary triplet
and singlet excitations present a clear scaling behavior in a wide range of
\ell=L/\xi (where L is the length of the chain and \xi is the correlation
length). At J_2=J_2c, where no logarithmic corrections are present, we compare
the numerical results with finite-size predictions for the sine-Gordon model
obtained using Luscher's theory. For small \delta we find a very good agreement
for \ell > 4 or 7 depending on the excitation considered.Comment: 4 pages, 4 eps figures, RevTeX 4 class, same version as in PR
Pairing, crystallization and string correlations of mass-imbalanced atomic mixtures in one-dimensional optical lattices
We numerically determine the very rich phase diagram of mass-imbalanced
binary mixtures of hardcore bosons (or equivalently -- fermions, or
hardcore-Bose/Fermi mixtures) loaded in one-dimensional optical lattices.
Focusing on commensurate fillings away from half filling, we find a strong
asymmetry between attractive and repulsive interactions. Attraction is found to
always lead to pairing, associated with a spin gap, and to pair crystallization
for very strong mass imbalance. In the repulsive case the two atomic components
remain instead fully gapless over a large parameter range; only a very strong
mass imbalance leads to the opening of a spin gap. The spin-gap phase is the
precursor of a crystalline phase occurring for an even stronger mass imbalance.
The fundamental asymmetry of the phase diagram is at odds with recent
theoretical predictions, and can be tested directly via time-of-flight
experiments on trapped cold atoms.Comment: 4 pages, 4 figures + Supplementary Materia