2,626 research outputs found
Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit
We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the
Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the
thermodynamic limit. The BMPS is built on a dual series of reduced
biorthonormal bases for the left and right Perron states of a non-Hermitian
matrix. We propose two alternative infinite-size Biorthonormal TMRG (iBTMRG)
algorithms and compare their numerical performance in both finite and infinite
systems. We show that both iBTMRGs produce a dual infinite-BMPS (iBMPS) which
are translationally invariant in the thermodynamic limit. We also develop an
efficient wave function transformation of the iBTMRG, an analogy of McCulloch
in the infinite-DMRG [arXiv:0804.2509 (2008)], to predict the wave function as
the lattice size is increased. The resulting iBMPS allows for probing bulk
properties of the system in the thermodynamic limit without boundary effects
and allows for reducing the computational cost to be independent of the lattice
size, which are illustrated by calculating the magnetization as a function of
the temperature and the critical spin-spin correlation in the thermodynamic
limit for a 2D classical Ising model.Comment: 14 pages, 9 figure
Boundary quantum critical phenomena with entanglement renormalization
We extend the formalism of entanglement renormalization to the study of
boundary critical phenomena. The multi-scale entanglement renormalization
ansatz (MERA), in its scale invariant version, offers a very compact
approximation to quantum critical ground states. Here we show that, by adding a
boundary to the scale invariant MERA, an accurate approximation to the critical
ground state of an infinite chain with a boundary is obtained, from which one
can extract boundary scaling operators and their scaling dimensions. Our
construction, valid for arbitrary critical systems, produces an effective chain
with explicit separation of energy scales that relates to Wilson's RG
formulation of the Kondo problem. We test the approach by studying the quantum
critical Ising model with free and fixed boundary conditions.Comment: 8 pages, 12 figures, for a related work see arXiv:0912.289
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
Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry
We propose a refined matrix product state representation for many-body
quantum states that are invariant under SU(2) transformations, and indicate how
to extend the time-evolving block decimation (TEBD) algorithm in order to
simulate time evolution in an SU(2) invariant system. The resulting algorithm
is tested in a critical quantum spin chain and shown to be significantly more
efficient than the standard TEBD.Comment: 5 pages, 4 figure
From density-matrix renormalization group to matrix product states
In this paper we give an introduction to the numerical density matrix
renormalization group (DMRG) algorithm, from the perspective of the more
general matrix product state (MPS) formulation. We cover in detail the
differences between the original DMRG formulation and the MPS approach,
demonstrating the additional flexibility that arises from constructing both the
wavefunction and the Hamiltonian in MPS form. We also show how to make use of
global symmetries, for both the Abelian and non-Abelian cases.Comment: Numerous small changes and clarifications, added a figur
A Comparison of Measured Crab and Vela Glitch Healing Parameters with Predictions of Neutron Star Models
There are currently two well-accepted models that explain how pulsars exhibit
glitches, sudden changes in their regular rotational spin-down. According to
the starquake model, the glitch healing parameter, Q, which is measurable in
some cases from pulsar timing, should be equal to the ratio of the moment of
inertia of the superfluid core of a neutron star (NS) to its total moment of
inertia. Measured values of the healing parameter from pulsar glitches can
therefore be used in combination with realistic NS structure models as one test
of the feasibility of the starquake model as a glitch mechanism. We have
constructed NS models using seven representative equations of state of
superdense matter to test whether starquakes can account for glitches observed
in the Crab and Vela pulsars, for which the most extensive and accurate glitch
data are available. We also present a compilation of all measured values of Q
for Crab and Vela glitches to date which have been separately published in the
literature. We have computed the fractional core moment of inertia for stellar
models covering a range of NS masses and find that for stable NSs in the
realistic mass range 1.4 +/- 0.2 solar masses, the fraction is greater than
0.55 in all cases. This range is not consistent with the observational
restriction Q < 0.2 for Vela if starquakes are the cause of its glitches. This
confirms results of previous studies of the Vela pulsar which have suggested
that starquakes are not a feasible mechanism for Vela glitches. The much larger
values of Q observed for Crab glitches (Q > 0.7) are consistent with the
starquake model predictions and support previous conclusions that starquakes
can be the cause of Crab glitches.Comment: 8 pages, including 3 figures and 1 table. Accepted for publication in
Ap
Localized spin ordering in Kondo lattice models
Using a non-Abelian density matrix renormalization group method we determine
the phase diagram of the Kondo lattice model in one dimension, by directly
measuring the magnetization of the ground-state. This allowed us to discover a
second ferromagnetic phase missed in previous approaches. The phase transitions
are found to be continuous. The spin-spin correlation function is studied in
detail, and we determine in which regions the large and small Fermi surfaces
dominate. The importance of double-exchange ordering and its competition with
Kondo singlet formation is emphasized in understanding the complexity of the
model.Comment: Revtex, 4 pages, 4 eps figures embedde
Polarimetric Properties of the Crab Pulsar between 1.4 and 8.4 GHz
New polarimetric observations of the Crab pulsar at frequencies between 1.4
and 8.4 GHz are presented. Additional pulse components discovered in earlier
observations (Moffett & Hankins 1996, astro-ph/9604163) are found to have high
levels of linear polarization, even at 8.4 GHz. No abrupt sweeps in position
angle are found within pulse components; however, the position angle and
rotational phase of the interpulse do change dramatically between 1.4 and 4.9
GHz. The multi-frequency profile morphology and polarization properties
indicate a non-standard origin of the emission. Several emission geometries are
discussed, but the one favored locates sites of emission both near the pulsar
surface and in the outer magnetosphere.Comment: 20 pages, 7 postscript figures, uses aaspp4 Latex style. To appear in
Volume 522 of The Astrophysical Journa
Measuring pro-poor sectoral analysis for Pakistan: trickle down?
The study aims to establish a pro-poor growth index called the ‘Poverty Equivalent Growth Rate’, which considers both the extent of sectoral growth and the benefits reaching the poor in Pakistan, using 21 household surveys between 1964 and 2011. The result reveals that despite the positive signs in agriculture growth, the growth process may not be classifiable as pro-poor. The result points out that compared with the non-poor, the poor overall benefited less from the revitalisation of agricultural processes; however, the trend was reversed during 2002 to 2011 when the poverty equivalent growth rates are higher than the growth rate of industry, manufacturing,
commodity producing and services value added, which shows sectoral growth favours the poor more than non-poor in Pakistan
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