49 research outputs found
XXZ-like phase in the F-AF anisotropic Heisenberg chain
By means of the Density Matrix Renormalization Group technique, we have
studied the region where -like behavior is most likely to emerge within
the phase diagram of the F-AF anisotropic extended () Heisenberg chain.
We have analyzed, in great detail, the equal-time two-spin correlation
functions, both in- and out-of- plane, as functions of the distance (and
momentum). Then, we have extracted, through an accurate fitting procedure, the
exponents of the asymptotic power-law decay of the spatial correlations. We
have used the exact solution of model () to benchmark our results,
which clearly show the expected agreement. A critical value of has been
found where the relevant power-law decay exponent is independent of the
in-plane nearest-neighbor coupling.Comment: 5 pages, 4 figures. Accepted for publication in European Physical
Journal
Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit
We present the exact solution, obtained by means of the Transfer Matrix (TM)
method, of the 1D Hubbard model with nearest-neighbor (NN) and
next-nearest-neighbor (NNN) Coulomb interactions in the atomic limit (t=0). The
competition among the interactions (, , and ) generates a plethora
of T=0 phases in the whole range of fillings. , , and are the
intensities of the local, NN and NNN interactions, respectively. We report the
T=0 phase diagram, in which the phases are classified according to the behavior
of the principal correlation functions, and reconstruct a representative
electronic configuration for each phase. In order to do that, we make an
analytic limit in the transfer matrix, which allows us to obtain
analytic expressions for the ground state energies even for extended transfer
matrices. Such an extension of the standard TM technique can be easily applied
to a wide class of 1D models with the interaction range beyond NN distance,
allowing for a complete determination of the T=0 phase diagrams.Comment: 13 pages, 7 figures, to appear in European Physical Journal
Entanglement in the F-AF zig-zag Heisenberg chain
We present a study of the entanglement properties of the F-AF zig-zag
Heisenberg chain done by means of the Density Matrix Renormalization Group
method. In particular, we have selected the concurrence as measure of
entanglement and checked its capability to signal the presence of quantum phase
transitions within the previously found ergodicity phase diagram [E. Plekhanov,
A. Avella, and F. Mancini, Phys. Rev. B \textbf{74}, 115120 (2006)]. By
analyzing the behavior of the concurrence, we have been able not only to
determine the position of the transition lines within the phase diagram of the
system, but also to identify a well defined region in the parameter space of
the model that shows a complex spin ordering indicating the presence of a new
phase of the system.Comment: 4 pages, 3 figures to be published in Journal of Optoelectronics and
Advanced Materials, presented at ESM '0
Ergodicity of the extended anisotropic 1D Heisenberg model: response at low temperatures
We present the results of exact diagonalization calculations of the isolated
and isothermal on-site static susceptibilities in the anisotropic extended
Heisenberg model on a linear chain with periodic boundary conditions. Based on
the ergodicity considerations we conclude that the isothermal susceptibility
will diverge as both in finite clusters and in the bulk system in two
non-ergodic regions of the phase diagram of the system.Comment: reported at the International Conference on Magnetism, August 20-25,
2006 Kyoto, Japa
Ergodicity in Strongly Correlated Systems
We present a concise, but systematic, review of the ergodicity issue in
strongly correlated systems. After giving a brief historical overview, we
analyze the issue within the Green's function formalism by means of the
equations of motion approach. By means of this analysis, we are able to
individuate the primary source of non-ergodic dynamics for a generic operator
and also to give a recipe to compute unknown quantities characterizing such a
behavior within the Composite Operator Method. Finally, we present examples of
non-trivial strongly correlated systems where it is possible to find a
non-ergodic behavior
Emery vs. Hubbard model for cuprate superconductors: a Composite Operator Method study
Within the Composite Operator Method (COM), we report the solution of the
Emery model (also known as p-d or three band model), which is relevant for the
cuprate high-Tc superconduc- tors. We also discuss the relevance of the
often-neglected direct oxygen-oxygen hopping for a more accurate, sometimes
unique, description of this class of materials. The benchmark of the solution
is performed by comparing our results with the available quantum Monte Carlo
ones. Both single- particle and thermodynamic properties of the model are
studied in detail. Our solution features a metal-insulator transition at half
filling. The resulting metal-insulator phase diagram agrees qual- itatively
very well with the one obtained within Dynamical Mean-Field Theory. We discuss
the type of transition (Mott-Hubbard (MH) or charge-transfer (CT)) for the
microscopic (ab-initio) parameter range relevant for cuprates getting, as
expected a CT type. The emerging single-particle scenario clearly suggests a
very close relation between the relevant sub-bands of the three- (Emery) and
the single- band (Hubbard) models, thus providing an independent and
non-perturbative proof of the validity of the mapping between the two models
for the model parameters optimal to describe cuprates. Such a result confirms
the emergence of the Zhang-Rice scenario, which has been recently questioned.
We also report the behavior of the specific heat and of the entropy as
functions of the temperature on varying the model parameters as these
quantities, more than any other, depend on and, consequently, reveal the most
relevant energy scales of the system.Comment: 20 pages, 19 figure
d-wave pairing in lightly doped Mott insulators
We define a suitable quantity that measures the pairing strength of two
electrons added to the ground state wave function by means of the anomalous
part of the one-particle Green's function. discriminates between systems
described by one-electron states, like ordinary metals and band insulators, for
which , and systems where the single particle picture does not hold,
like superconductors and resonating valence bond insulators, for which . By using a numerically exact projection technique for the Hubbard model at
, a finite value of , with d-wave symmetrry, is found at half
filling and in the lightly doped regime, thus emphasizing a qualitatively new
feature coming from electronic correlation.Comment: 4 pages, 4 figure
Non-ergodic dynamics of the extended anisotropic Heisenberg chain
The issue of ergodicity is often underestimated. The presence of
zero-frequency excitations in bosonic Green's functions determine the
appearance of zero-frequency momentum-dependent quantities in correlation
functions. The implicit dependence of matrix elements make such quantities also
relevant in the computation of susceptibilities. Consequently, the correct
determination of these quantities is of great relevance and the
well-established practice of fixing them by assuming the ergodicity of the
dynamics is quite questionable as it is not justifiable a priori by no means.
In this manuscript, we have investigated the ergodicity of the dynamics of the
-component of the spin in the 1D Heisenberg model with anisotropic
nearest-neighbor and isotropic next-nearest-neighbor interactions. We have
obtained the zero-temperature phase diagram in the thermodynamic limit by
extrapolating Exact and Lanczos diagonalization results computed on chains with
sizes . Two distinct non-ergodic regions have been found: one
for and and another for
and . On the contrary,
finite-size scaling of results, obtained by means of Exact
diagonalization on chains with sizes , indicates an ergodic
behavior of dynamics in the whole range of parameters.Comment: 6 pages, 7 figure