9,457 research outputs found
The density-matrix renormalization group
The density-matrix renormalization group (DMRG) is a numerical algorithm for
the efficient truncation of the Hilbert space of low-dimensional strongly
correlated quantum systems based on a rather general decimation prescription.
This algorithm has achieved unprecedented precision in the description of
one-dimensional quantum systems. It has therefore quickly acquired the status
of method of choice for numerical studies of one-dimensional quantum systems.
Its applications to the calculation of static, dynamic and thermodynamic
quantities in such systems are reviewed. The potential of DMRG applications in
the fields of two-dimensional quantum systems, quantum chemistry,
three-dimensional small grains, nuclear physics, equilibrium and
non-equilibrium statistical physics, and time-dependent phenomena is discussed.
This review also considers the theoretical foundations of the method, examining
its relationship to matrix-product states and the quantum information content
of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the
January 2005 issu
Vibrational Density Matrix Renormalization Group
Variational approaches for the calculation of vibrational wave functions and
energies are a natural route to obtain highly accurate results with
controllable errors. However, the unfavorable scaling and the resulting high
computational cost of standard variational approaches limit their application
to small molecules with only few vibrational modes. Here, we demonstrate how
the density matrix renormalization group (DMRG) can be exploited to optimize
vibrational wave functions (vDMRG) expressed as matrix product states. We study
the convergence of these calculations with respect to the size of the local
basis of each mode, the number of renormalized block states, and the number of
DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for
small molecules that were intensively studied in the literature. We then
proceed to show that the complete fingerprint region of the sarcosyn-glycin
dipeptide can be calculated with vDMRG.Comment: 21 pages, 5 figures, 4 table
Density Matrix Renormalization Group Lagrangians
We introduce a Lagrangian formulation of the Density Matrix Renormalization
Group (DMRG). We present Lagrangians which when minimised yield the optimal
DMRG wavefunction in a variational sense, both within the general matrix
product ansatz, as well as within the canonical form of the matrix product that
is constructed within the DMRG sweep algorithm. Some of the results obtained
are similar to elementary expressions in Hartree-Fock theory, and we draw
attention to such analogies. The Lagrangians introduced here will be useful in
developing theories of analytic response and derivatives in the DMRG.Comment: 6 page
Corner Transfer Matrix Renormalization Group Method
We propose a new fast numerical renormalization group method,the corner
transfer matrix renormalization group (CTMRG) method, which is based on a
unified scheme of Baxter's corner transfer matrix method and White's density
matrix renormalization groupmethod. The key point is that a product of four
corner transfer matrices gives the densitymatrix. We formulate the CTMRG method
as a renormalization of 2D classical models.Comment: 8 pages, LaTeX and 4 figures. Revised version is converted to a latex
file and added an example of a computatio
Density Matrix Renormalization Group for Dummies
We describe the Density Matrix Renormalization Group algorithms for time
dependent and time independent Hamiltonians. This paper is a brief but
comprehensive introduction to the subject for anyone willing to enter in the
field or write the program source code from scratch.Comment: 29 pages, 9 figures. Published version. An open source version of the
code can be found at http://qti.sns.it/dmrg/phome.htm
Dynamical density-matrix renormalization-group method
I present a density-matrix renormalization-group (DMRG) method for
calculating dynamical properties and excited states in low-dimensional lattice
quantum many-body systems. The method is based on an exact variational
principle for dynamical correlation functions and the excited states
contributing to them. This dynamical DMRG is an alternate formulation of the
correction vector DMRG but is both simpler and more accurate. The finite-size
scaling of spectral functions is discussed and a method for analyzing the
scaling of dense spectra is described. The key idea of the method is a
size-dependent broadening of the spectrum.The dynamical DMRG and the
finite-size scaling analysis are demonstrated on the optical conductivity of
the one-dimensional Peierls-Hubbard model. Comparisons with analytical results
show that the spectral functions of infinite systems can be reproduced almost
exactly with these techniques. The optical conductivity of the Mott-Peierls
insulator is investigated and it is shown that its spectrum is qualitatively
different from the simple spectra observed in Peierls (band) insulators and
one-dimensional Mott-Hubbard insulators.Comment: 16 pages (REVTEX 4.0), 10 figures (in 13 EPS files
Phase Diagram of a 2D Vertex Model
Phase diagram of a symmetric vertex model which allows 7 vertex
configurations is obtained by use of the corner transfer matrix renormalization
group (CTMRG), which is a variant of the density matrix renormalization group
(DMRG). The critical indices of this model are identified as and
.Comment: 2 pages, 5 figures, short not
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
- …