4,677 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
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
Development and application of operational techniques for the inventory and monitoring of resources and uses for the Texas coastal zone. Volume 2: Appendices
There are no author-identified significant results in this report
Development and application of operational techniques for the inventory and monitoring of resources and uses for the Texas coastal zone. Volume 1: Text
The author has identified the following significant results. Image interpretation and computer-assisted techniques were developed to analyze LANDSAT scenes in support of resource inventory and monitoring requirements for the Texas coastal region. Land cover and land use maps, at a scale of 1:125,000 for the image interpretation product and 1:24,000 for the computer-assisted product, were generated covering four Texas coastal test sites. Classification schemes which parallel national systems were developed for each procedure, including 23 classes for image interpretation technique and 13 classes for the computer-assisted technique. Results indicate that LANDSAT-derived land cover and land use maps can be successfully applied to a variety of planning and management activities on the Texas coast. Computer-derived land/water maps can be used with tide gage data to assess shoreline boundaries for management purposes
Eastern Asian emissions of anthropogenic halocarbons deduced from aircraft concentration data
The Montreal Protocol restricts production of ozone-depleting halocarbons worldwide. Enforcement of the protocol has relied mainly on annual government statistics of production and consumption of these compounds (bottom-up approach). We show here that aircraft observations of halocarbon:CO enhancement ratios on regional to continental scales can be used to infer halocarbon emissions, providing independent verification of the bottom-up approach. We apply this top-down approach to aircraft observations of Asian outflow from the TRACE-P mission over the western Pacific (March April 2001) and derive emissions from eastern Asia (China, Japan, and Korea). We derive an eastern Asian carbon tetrachloride (CCl ) source of 21.5 Gg yr , several-fold larger than previous estimates and amounting to 30% of the global budget for this gas. Our emission estimate for CFC-11 from eastern Asia is 50% higher than inventories derived from manufacturing records. Our emission estimates for methyl chloroform (CH ) and CFC-12 are in agreement with existing inventories. For halon 1211 we find only a strong local source originating from the Shanghai area. Our emission estimates for the above gases result in a 40% increase in the ozone depletion potential (ODP) of Asian emissions relative to previous estimates, corresponding to a 10% global increase in ODP
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
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
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