542 research outputs found
Determination of the damping ratio in the soil from SASW test using the half-power bandwidth method and Arias intensity
Entropy growth of shift-invariant states on a quantum spin chain
We study the entropy of pure shift-invariant states on a quantum spin chain.
Unlike the classical case, the local restrictions to intervals of length
are typically mixed and have therefore a non-zero entropy which is,
moreover, monotonically increasing in . We are interested in the asymptotics
of the total entropy. We investigate in detail a class of states derived from
quasi-free states on a CAR algebra. These are characterised by a measurable
subset of the unit interval. As the entropy density is known to vanishes,
is sublinear in . For states corresponding to unions of finitely many
intervals, is shown to grow slower than . Numerical
calculations suggest a behaviour. For the case with infinitely many
intervals, we present a class of states for which the entropy increases
as where can take any value in .Comment: 18 pages, 2 figure
Matrix product state renormalization
The truncation or compression of the spectrum of Schmidt values is inherent
to the matrix product state (MPS) approximation of one-dimensional quantum
ground states. We provide a renormalization group picture by interpreting this
compression as an application of Wilson's numerical renormalization group along
the imaginary time direction appearing in the path integral representation of
the state. The location of the physical index is considered as an impurity in
the transfer matrix and static MPS correlation functions are reinterpreted as
dynamical impurity correlations. Coarse-graining the transfer matrix is
performed using a hybrid variational ansatz based on matrix product operators,
combining ideas of MPS and the multi-scale entanglement renormalization ansatz.
Through numerical comparison with conventional MPS algorithms, we explicitly
verify the impurity interpretation of MPS compression, as put forward by [V.
Zauner et al., New J. Phys. 17, 053002 (2015)] for the transverse-field Ising
model. Additionally, we motivate the conceptual usefulness of endowing MPS with
an internal layered structure by studying restricted variational subspaces to
describe elementary excitations on top of the ground state, which serves to
elucidate a transparent renormalization group structure ingrained in MPS
descriptions of ground states.Comment: 15 pages, 10 figures, published versio
Faster Methods for Contracting Infinite 2D Tensor Networks
We revisit the corner transfer matrix renormalization group (CTMRG) method of
Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and
demonstrate that its performance can be substantially improved by determining
the tensors using an eigenvalue solver as opposed to the power method used in
CTMRG. We also generalize the variational uniform matrix product state (VUMPS)
ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer
matrices and discuss similarities with the corner methods. These two new
algorithms will be crucial to improving the performance of variational infinite
projected entangled pair state (PEPS) methods.Comment: 20 pages, 5 figures, V. Zauner-Stauber previously also published
under the name V. Zaune
Transfer Matrices and Excitations with Matrix Product States
We investigate the relation between static correlation functions in the
ground state of local quantum many-body Hamiltonians and the dispersion
relations of the corresponding low energy excitations using the formalism of
tensor network states. In particular, we show that the Matrix Product State
Transfer Matrix (MPS-TM) - a central object in the computation of static
correlation functions - provides important information about the location and
magnitude of the minima of the low energy dispersion relation(s) and present
supporting numerical data for one-dimensional lattice and continuum models as
well as two-dimensional lattice models on a cylinder. We elaborate on the
peculiar structure of the MPS-TM's eigenspectrum and give several arguments for
the close relation between the structure of the low energy spectrum of the
system and the form of static correlation functions. Finally, we discuss how
the MPS-TM connects to the exact Quantum Transfer Matrix (QTM) of the model at
zero temperature. We present a renormalization group argument for obtaining
finite bond dimension approximations of MPS, which allows to reinterpret
variational MPS techniques (such as the Density Matrix Renormalization Group)
as an application of Wilson's Numerical Renormalization Group along the virtual
(imaginary time) dimension of the system.Comment: 39 pages (+8 pages appendix), 14 figure
Transfer matrices and excitations with matrix product states
We use the formalism of tensor network states to investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low-energy excitations. In particular, we show that the matrix product state transfer matrix (MPS-TM)—a central object in the computation of static correlation functions—provides important information about the location and magnitude of the minima of the low-energy dispersion relation(s), and we present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM's eigenspectrum and give several arguments for the close relation between the structure of the low-energy spectrum of the system and the form of the static correlation functions. Finally, we discuss how the MPS-TM connects to the exact quantum transfer matrix of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of the MPS, which allows one to reinterpret variational MPS techniques (such as the density matrix renormalization group) as an application of Wilson's numerical renormalization group along the virtual (imaginary time) dimension of the system
Truncating an exact Matrix Product State for the XY model: transfer matrix and its renormalisation
We discuss how to analytically obtain an -- essentially infinite -- Matrix
Product State (MPS) representation of the ground state of the XY model. On the
one hand this allows to illustrate how the Ornstein-Zernike form of the
correlation function emerges in the exact case using standard MPS language. On
the other hand we study the consequences of truncating the bond dimension of
the exact MPS, which is also part of many tensor network algorithms, and
analyze how the truncated MPS transfer matrix is representing the dominant part
of the exact quantum transfer matrix. In the gapped phase we observe that the
correlation length obtained from a truncated MPS approaches the exact value
following a power law in effective bond dimension. In the gapless phase we find
a good match between a state obtained numerically from standard MPS techniques
with finite bond dimension, and a state obtained by effective finite imaginary
time evolution in our framework. This provides a direct hint for a geometric
interpretation of Finite Entanglement Scaling at the critical point in this
case. Finally, by analyzing the spectra of transfer matrices, we support the
interpretation put forward by [V. Zauner at. al., New J. Phys. 17, 053002
(2015)] that the MPS transfer matrix emerges from the quantum transfer matrix
though the application of Wilson's Numerical Renormalisation Group along the
imaginary-time direction.Comment: 14 pages, 9 figures, significantly extended, comments welcom
On hawser force criteria for navigation lock design: Case study of maritime locks in port of Antwerp
The first part of this paper offers a general reflection upon the issue of mooring line forces and ship behaviour during filling/emptying of (maritime) navigation locks. The philosophy behind the so-called hawser force criterion and the classical approach to deal with it in design studies, is described first. Secondly, some innovations in the definition, verification and validation of the design criteria are highlighted. In the second part of this paper, a case study is presented focusing on two maritime locks in the Port of Antwerp (Belgium): the Zandvliet lock (L x W = 500m x 57m) and the Berendrecht lock (L x W = 500m x 68m). To illustrate and comment upon the hawser force issues, results of scale modelling, in situ measurements and numerical modelling are discussed, in comparison to published hawser force criteria
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