422 research outputs found
Density Matrix Renormalization Group of Gapless Systems
We investigate convergence of the density matrix renormalization group (DMRG)
in the thermodynamic limit for gapless systems. Although the DMRG correlations
always decay exponentially in the thermodynamic limit, the correlation length
at the DMRG fixed-point scales as , where is the number
of kept states, indicating the existence of algebraic order for the exact
system. The single-particle excitation spectrum is calculated, using a
Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the
symmetry for translationally invariant half-integer
spin-systems with local interactions. Finally, we provide a method to compute
overlaps between ground states obtained from different DMRG calculations.Comment: 11 pages, RevTex, 5 figure
Superconductivity in hole-doped C60 from electronic correlations
We derive a model for the highest occupied molecular orbital band of a C60
crystal which includes on-site electron-electron interactions. The form of the
interactions are based on the icosahedral symmetry of the C60 molecule together
with a perturbative treatment of an isolated C60 molecule. Using this model we
do a mean-field calculation in two dimensions on the [100] surface of the
crystal. Due to the multi-band nature we find that electron-electron
interactions can have a profound effect on the density of states as a function
of doping. The doping dependence of the transition temperature can then be
qualitatively different from that expected from simple BCS theory based on the
density of states from band structure calculations
Excitation and Entanglement Transfer Near Quantum Critical Points
Recently, there has been growing interest in employing condensed matter
systems such as quantum spin or harmonic chains as quantum channels for short
distance communication. Many properties of such chains are determined by the
spectral gap between their ground and excited states. In particular this gap
vanishes at critical points of quantum phase transitions. In this article we
study the relation between the transfer speed and quality of such a system and
the size of its spectral gap. We find that the transfer is almost perfect but
slow for large spectral gaps and fast but rather inefficient for small gaps.Comment: submitted to Optics and Spectroscopy special issue for ICQO'200
The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation
We have adjusted the Density Matrix Renormalization method to handle two
dimensional systems of limited width. The key ingredient for this extension is
the incorporation of symmetries in the method. The advantage of our approach is
that we can force certain symmetry properties to the resulting ground state
wave function. Combining the results obtained for system sizes up-to and finite size scaling, we derive the phase transition point and the
critical exponent for the gap in the Ising model in a Transverse Field on a two
dimensional square lattice.Comment: 9 pages, 8 figure
Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix
In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that
the many-particle eigenvalues and eigenstates of the many-body density matrix
of a block of sites cut out from an infinite chain of
noninteracting spinless fermions can all be constructed out of the one-particle
eigenvalues and one-particle eigenstates respectively. In this paper we
developed a statistical-mechanical analogy between the density matrix
eigenstates and the many-body states of a system of noninteracting fermions.
Each density matrix eigenstate corresponds to a particular set of occupation of
single-particle pseudo-energy levels, and the density matrix eigenstate with
the largest weight, having the structure of a Fermi sea ground state,
unambiguously defines a pseudo-Fermi level. We then outlined the main ideas
behind an operator-based truncation of the density matrix eigenstates, where
single-particle pseudo-energy levels far away from the pseudo-Fermi level are
removed as degrees of freedom. We report numerical evidence for scaling
behaviours in the single-particle pseudo-energy spectrum for different block
sizes and different filling fractions \nbar. With the aid of these
scaling relations, which tells us that the block size plays the role of an
inverse temperature in the statistical-mechanical description of the density
matrix eigenstates and eigenvalues, we looked into the performance of our
operator-based truncation scheme in minimizing the discarded density matrix
weight and the error in calculating the dispersion relation for elementary
excitations. This performance was compared against that of the traditional
density matrix-based truncation scheme, as well as against a operator-based
plane wave truncation scheme, and found to be very satisfactory.Comment: 22 pages in RevTeX4 format, 22 figures. Uses amsmath, amssymb,
graphicx and mathrsfs package
A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm
It has proved difficult to extend the density matrix renormalization group
technique to large two-dimensional systems. In this Communication I present a
novel approach where the calculation is done directly in two dimensions. This
makes it possible to use an infinite system method, and for the first time the
fixed point in two dimensions is studied. By analyzing several related blocking
schemes I find that there exists an algorithm for which the local energy
decreases monotonically as the system size increases, thereby showing the
potential feasibility of this method.Comment: 5 pages, 6 figure
Density Matrix Renormalization Group Method for the Random Quantum One-Dimensional Systems - Application to the Random Spin-1/2 Antiferromagnetic Heisenberg Chain -
The density matrix renormalization group method is generalized to one
dimensional random systems. Using this method, the energy gap distribution of
the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The
results are consistent with the predictions of the renormalization group theory
demonstrating the effectiveness of the present method in random systems. The
possible application of the present method to other random systems is
discussed.Comment: 13 pages, 3 figures upon reques
Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
The density matrix renormalization group (``DMRG'') discovered by White has
shown to be a powerful method to understand the properties of many one
dimensional quantum systems. In the case where renormalization eventually
converges to a fixed point we show that quantum states in the thermodynamic
limit with periodic boundary conditions can be simply represented by a special
type of product ground state with a natural description of Bloch states of
elementary excitations that are spin-1 solitons. We then observe that these
states can be rederived through a simple variational ansatz making no reference
to a renormalization construction. The method is tested on the spin-1
Heisenberg model.Comment: 13 pages uuencoded compressed postscript including figure
Fixed Point of the Finite System DMRG
The density matrix renormalization group (DMRG) is a numerical method that
optimizes a variational state expressed by a tensor product. We show that the
ground state is not fully optimized as far as we use the standard finite system
algorithm, that uses the block structure B**B. This is because the tensors are
not improved directly. We overcome this problem by using the simpler block
structure B*B for the final several sweeps in the finite iteration process. It
is possible to increase the numerical precision of the finite system algorithm
without increasing the computational effort.Comment: 6 pages, 4 figure
The Density Matrix Renormalization Group technique with periodic boundary conditions
The Density Matrix Renormalization Group (DMRG) method with periodic boundary
conditions is introduced for two dimensional classical spin models. It is shown
that this method is more suitable for derivation of the properties of infinite
2D systems than the DMRG with open boundary conditions despite the latter
describes much better strips of finite width. For calculation at criticality,
phenomenological renormalization at finite strips is used together with a
criterion for optimum strip width for a given order of approximation. For this
width the critical temperature of 2D Ising model is estimated with seven-digit
accuracy for not too large order of approximation. Similar precision is reached
for critical indices. These results exceed the accuracy of similar calculations
for DMRG with open boundary conditions by several orders of magnitude.Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev.
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