3,544 research outputs found
Comment on "Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains"
Dukelsky, Mart\'in-Delgado, Nishino and Sierra (Europhys. Lett., 43, 457
(1998) - hereafter referred to as DMNS) investigated the matrix product method
(MPM), comparing it with the infinite-size density matrix renormalization group
(DMRG). For equivalent basis size, the MPM produces an improved variational
energy over that produced by DMRG and, unlike DMRG, produces a
translationally-invariant wavefunction. The DMRG results presented were
significantly worse than the MPM, caused by a shallow bound state appearing at
the join of the two DMRG blocks. They also suggested that the DMRG results can
be improved by using an alternate superblock construction for
the last few steps of the calculation. In this comment, we show that the DMRG
results presented by DMNS are in error and the artificial bound state produced
by the standard superblock configuration is very small even for states
kept. In addition, we calculate explicitly the energy and wavefunction for the
superblock structure and verify that the energy coincides
with that of the MPM, as conjectured by S. Ostlund and S. Rommer (Phys. Rev.
Lett., 75, 3537 (1995)).Comment: 2 pages, 1 eps figure included. eps.cls include
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for
fermions with positive weights. In the example of the Hubbard model close to
half filling it fails to reproduce all the symmetries of the ground state
leading to systematic errors at low temperatures. In a previous work [Phys.
Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by
projecting the density matrix obtained from the simulation onto the ground
state symmetry sector. For ground state properties, the accuracy of this method
depends on a {\it large overlap} between the GQMC and exact density matrices.
Thus, the method is not rigorously exact. We present the limits of the approach
by a systematic study of the method for 2 and 3 leg Hubbard ladders for
different fillings and on-site repulsion strengths. We show several indications
that the systematic errors stem from non-vanishing boundary terms in the
partial integration step in the derivation of the Fokker-Planck equation.
Checking for spiking trajectories and slow decaying probability distributions
provides an important test of the reliability of the results. Possible
solutions to avoid boundary terms are discussed. Furthermore we compare results
obtained from two different sampling methods: Reconfiguration of walkers and
the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for
fermions with positive weights. In the example of the Hubbard model close to
half filling it fails to reproduce all the symmetries of the ground state
leading to systematic errors at low temperatures. In a previous work [Phys.
Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by
projecting the density matrix obtained from the simulation onto the ground
state symmetry sector. For ground state properties, the accuracy of this method
depends on a {\it large overlap} between the GQMC and exact density matrices.
Thus, the method is not rigorously exact. We present the limits of the approach
by a systematic study of the method for 2 and 3 leg Hubbard ladders for
different fillings and on-site repulsion strengths. We show several indications
that the systematic errors stem from non-vanishing boundary terms in the
partial integration step in the derivation of the Fokker-Planck equation.
Checking for spiking trajectories and slow decaying probability distributions
provides an important test of the reliability of the results. Possible
solutions to avoid boundary terms are discussed. Furthermore we compare results
obtained from two different sampling methods: Reconfiguration of walkers and
the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl
Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux
We perform a density-matrix renormalization-group study of strongly
interacting bosons on a three-leg ladder in the presence of a homogeneous flux.
Focusing on one-third filling, we explore the phase diagram in dependence of
the magnetic flux and the inter-leg tunneling strength. We find several phases
including a Meissner phase, vortex liquids, a vortex lattice, as well as a
staggered-current phase. Moreover, there are regions where the chiral current
reverses its direction, both in the Meissner and in the staggered-current
phase. While the reversal in the latter case can be ascribed to spontaneous
breaking of translational invariance, in the first it stems from an effective
flux increase in the rung direction. Interactions are a necessary ingredient to
realize either type of chiral-current reversal
A Survey of the Galactic Plane for 6.7-GHz Methanol Masers I: l = 325.0 - 335.0 ; b = -0.53 - 0.53
We report the results of the first complete survey of an area of the Galactic
Plane for maser emission from the 6.7-GHz transition of methanol. The survey
covers a 10.6-square-degree region of the Galactic Plane in the longitude range
325-335 degrees and latitude range -0.53-0.53 degrees. The survey is sensitive
to masers with a peak flux density greater than approximately 2.6 Jy. The
weakest maser detected has a peak flux density of 2.3 Jy and the strongest a
peak flux density of 425 Jy. We detected a total of 50 distinct masers, 26 of
which are new detections. We show that many 6.7-GHz methanol masers are not
associated with IRAS sources, and that some are associated with sources that
have colours differing from those of a typical ultra-compact HII region
(UCHII). We estimate that the number of UCHII regions in the Galaxy is
significantly more than suggested by IRAS-based estimates, possibly by more
than a factor of two.Comment: 19 pages including 4 figures, using LaTeX formatted with mn.sty,
accepted for publication in MNRA
Minimally Entangled Typical Thermal State Algorithms
We discuss a method based on sampling minimally entangled typical thermal
states (METTS) that can simulate finite temperature quantum systems with a
computational cost comparable to ground state DMRG. Detailed implementations of
each step of the method are presented, along with efficient algorithms for
working with matrix product states and matrix product operators. We furthermore
explore how properties of METTS can reveal characteristic order and excitations
of systems and discuss why METTS form an efficient basis for sampling. Finally,
we explore the extent to which the average entanglement of a METTS ensemble is
minimal.Comment: 18 pages, 14 figure
Magnetism in the dilute Kondo lattice model
The one dimensional dilute Kondo lattice model is investigated by means of
bosonization for different dilution patterns of the array of impurity spins.
The physical picture is very different if a commensurate or incommensurate
doping of the impurity spins is considered. For the commensurate case, the
obtained phase diagram is verified using a non-Abelian density-matrix
renormalization-group algorithm. The paramagnetic phase widens at the expense
of the ferromagnetic phase as the -spins are diluted. For the incommensurate
case, antiferromagnetism is found at low doping, which distinguishes the dilute
Kondo lattice model from the standard Kondo lattice model.Comment: 11 pages, 2 figure
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