Strongly correlated electron systems: theory and simulation
Recent publications
Motivated by several anomalous experimental properties observed in the high temperature superconductor compounds, our group is intensively studing the phase diagram of strongly correlated electron systems, such as the t-J model and the Hubbard model in low spatial dimensions or for weakly coupled planes or chains. This problem is tackled using several different techniques, both numerical and analytical. From the numerical point of view we make intensive use of the Quantum Monte Carlo scheme ,developed here in SISSA [5-6],and the well established exact diagonalization technique for small clusters.
Recent progress have been
made for the implementation of the standard Green's function Monte Carlo
(GFMC) technique for models defined on a lattice.
A novel technique ''Green Function Monte Carlo with Stochastic
Reconfiguration'' (GFMCSR) has been proposed by our group [3-5].
With this novel and promising technique a very accurate
determination of the excitation spectrum of the Heisenberg model has been
already obtained[4,5]. Moreover this method can be also extended
to models affected by the sign problem[6], where GFMC was previously
unsuccesful.
Basic idea of GFMCSR, from the invited abstract for the APS-1999
As well known Quantum Monte Carlo (QMC) is a useful technique to evaluate
ground state properties of a many body hamiltonian H
even for large
system size, which is particularly important for 2D or higher
dimensional electron systems.
In most QMC methods
the ground state wavefunction 
0 of H
is filtered out by
a statistical application of the propagator
e -H t to a trial state
T , for large imaginary time t .
However the physical and interesting hamiltonians are difficult
to deal with QMC, because they contain some frustration or
some symmetry -e.g. the antisymmetry of the fermion wavefunction- which are
intrinsically difficult to handle with a statistical method.
Within QMC it is in fact easy
to assign only positive amplitudes- namely probability amplitudes- to the
propagated wavefunction t = e -H t
T but
very difficult to sample the sign of t
(x) over the electron
states x (determined by electron positions and spins).
The consequence is that typically the average sign of t
(x) over the
QMC sampled configurations is dramatically vanishing with increasing
t ,
causing an exponential growth of variance and prohibitive simulations
even for small lattice sizes.
In order to overcome this difficulty, several progress have been made with
the so called fixed node approximation (FN), which essentially constrains
the dynamic evolution of t(x)
to have the same signs of the
trial wavefunction T(x) .
To this dynamic corresponds a well defined hamiltonian
H f , leading to an approximate evolution
ft = e - Hf t
T
which converges to an approximate ground state with an energy better
than T .
In this work[6]
I essentially define a systematic way to improve and correct
the fixed node dynamic. This method is based upon the simple
requirement that after a
short imaginary time propagation via the approximate FN dynamic,
a number p of correlation functions over
t
can be further constrained to be exact by small perturbation
of the FN evolved state f t ,
which is free of the sign problem.
By iterating this process the average sign remains stable even for large
t
and the method has
the important property to be in principle exact
if all possible correlation functions are included in this correction scheme
of the FN.
In practice it is possible and useful to work with small p .
Nevertheless in many model hamiltonians a remarkable improvement of the
fixed node energies and physical expectation values are obtained with
p < 10 even for large system sizes.
Strong electron correlation and superconductivity
The strong electron correlation
, certainly present in the most physically interesting electron systems,
such as the High Temperature SuperConductors (HTSC), may lead to
qualitatively new physical properties, unexpected from
existing mean-field theories, that
drastically neglect such electron correlation.
This approximation has already made possible to perform numerical
simulation of realistic systems with sufficiently large number of atoms and
electrons, but is obviously not justified for the most interesting
correlated materials.
For the time being, there is no clear explanation, within a simple mean-field
theory, of the so high critical temperature of HTSC.
It is even less clear why these materials
show such anomalous properties like the linear T resistivity, that
contradicts the '' Fermi liquid theory'' , the most popular theory of
electrons in solids, which predicts that electron correlation is not important
at low enough temperature.
We are trying therefore to establish the phase diagram of the so called
t-J model and the Hubbard model
which certainly represent the ''strongly correlated electron system''
for HTSC [7].
Spin Liquid Resonating Valence Bond state in 2D
Recently, using at best, the new possibilty opened by the GFMCSR method,
we are trying to establish for the first time the conditions for
the existence of a ''Resonating Valence
Bond'' spin liquid ground state in two dimensional frustrated spin models
such as the triangular lattice[8], the Heisenberg model with next nearest
exchange interaction[9] and the ''so called'' ST-model [10].
Theory of 1D Insulators and Superconductors
From the analytical point of view the task is as usual to exctract the long
wavelength, low energy limit of a given lattice hamiltonian, and test the
validity of the theory by comparing numerical results and theoretical
predictions. An example is given by the successful validity of the
``Luttinger liquid theory'' in 1D for the Hubbard model and the
t-J one and the Spin-Wave Theory for 2D
antiferromagnets.
The theory of ''hole propagation in isulators and
superconductors'' has been established for general one dimensional models
[1,2].
The Berry phase approach for insulators
We study the transition between a band ionic insulator,
and a Mott-like insulator
in simple lattice Hubbard models with two inequivalent sites.
In particular we focus on the polarization, and its change upon simple lattice
distortions, such as dimerization. The polarization is calculated using the
Berry phase method.
In D=1 [11], we have recently been able to characterize the divergence of
the localization length of the insulator close to the transition point.
Fur further inquiries, please contact:
sorella@sissa.it