418 research outputs found
The open XXX spin chain in the SoV framework: scalar product of separate states
We consider the XXX open spin-1/2 chain with the most general non-diagonal
boundary terms, that we solve by means of the quantum separation of variables
(SoV) approach. We compute the scalar products of separate states, a class of
states which notably contains all the eigenstates of the model. As usual for
models solved by SoV, these scalar products can be expressed as some
determinants with a non-trivial dependance in terms of the inhomogeneity
parameters that have to be introduced for the method to be applicable. We show
that these determinants can be transformed into alternative ones in which the
homogeneous limit can easily be taken. These new representations can be
considered as generalizations of the well-known determinant representation for
the scalar products of the Bethe states of the periodic chain. In the
particular case where a constraint is applied on the boundary parameters, such
that the transfer matrix spectrum and eigenstates can be characterized in terms
of polynomial solutions of a usual T-Q equation, the scalar product that we
compute here corresponds to the scalar product between two off-shell Bethe-type
states. If in addition one of the states is an eigenstate, the determinant
representation can be simplified, hence leading in this boundary case to direct
analogues of algebraic Bethe ansatz determinant representations of the scalar
products for the periodic chain.Comment: 39 page
On determinant representations of scalar products and form factors in the SoV approach: the XXX case
In the present article we study the form factors of quantum integrable
lattice models solvable by the separation of variables (SoV) method. It was
recently shown that these models admit universal determinant representations
for the scalar products of the so-called separate states (a class which
includes in particular all the eigenstates of the transfer matrix). These
results permit to obtain simple expressions for the matrix elements of local
operators (form factors). However, these representations have been obtained up
to now only for the completely inhomogeneous versions of the lattice models
considered. In this article we give a simple algebraic procedure to rewrite the
scalar products (and hence the form factors) for the SoV related models as
Izergin or Slavnov type determinants. This new form leads to simple expressions
for the form factors in the homogeneous and thermodynamic limits. To make the
presentation of our method clear, we have chosen to explain it first for the
simple case of the Heisenberg chain with anti-periodic boundary
conditions. We would nevertheless like to stress that the approach presented in
this article applies as well to a wide range of models solved in the SoV
framework.Comment: 46 page
Long-distance asymptotic behaviour of multi-point correlation functions in massless quantum models
We provide a microscopic model setting that allows us to readily access to
the large-distance asymptotic behaviour of multi-point correlation functions in
massless, one-dimensional, quantum models. The method of analysis we propose is
based on the form factor expansion of the correlation functions and does not
build on any field theory reasonings. It constitutes an extension of the
restricted sum techniques leading to the large-distance asymptotic behaviour of
two-point correlation functions obtained previously.Comment: 25 page
Regular quantum graphs
We introduce the concept of regular quantum graphs and construct connected
quantum graphs with discrete symmetries. The method is based on a decomposition
of the quantum propagator in terms of permutation matrices which control the
way incoming and outgoing channels at vertex scattering processes are
connected. Symmetry properties of the quantum graph as well as its spectral
statistics depend on the particular choice of permutation matrices, also called
connectivity matrices, and can now be easily controlled. The method may find
applications in the study of quantum random walks networks and may also prove
to be useful in analysing universality in spectral statistics.Comment: 12 pages, 3 figure
Domain wall partition functions and KP
We observe that the partition function of the six vertex model on a finite
square lattice with domain wall boundary conditions is (a restriction of) a KP
tau function and express it as an expectation value of charged free fermions
(up to an overall normalization).Comment: 16 pages, LaTeX2
On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
We consider the problem of computing form factors of the massless XXZ
Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit
where the size M of the chain becomes large. For that purpose, we take the
particular example of the matrix element of the third component of spin between
the ground state and an excited state with one particle and one hole located at
the opposite ends of the Fermi interval (umklapp-type term). We exhibit its
power-law decrease in terms of the size of the chain M, and compute the
corresponding exponent and amplitude. As a consequence, we show that this form
factor is directly related to the amplitude of the leading oscillating term in
the long-distance asymptotic expansion of the two-point correlation function of
the third component of spin.Comment: 28 page
Emptiness formation probability of the XXZ spin-1/2 Heisenberg chain at Delta=1/2
Using a multiple integral representation for the correlation functions, we
compute the emptiness formation probability of the XXZ spin-1/2 Heisenberg
chain at anisotropy Delta=1/2. We prove it is expressed in term of the number
of alternating sign matrices.Comment: 5 page
Of global reach yet of situated contexts: an examination of the implicit and explicit selection criteria that shape digital archives of historical newspapers
A large literature addresses the processes, circumstances and motivations that have given rise to archives. These questions are increasingly being asked of digital archives, too. Here, we examine the complex interplay of institutional, intellectual, economic, technical, practical and social factors that have shaped decisions about the inclusion and exclusion of digitised newspapers in and from online archives. We do so by undertaking and analysing a series of semi-structured interviews conducted with public and private providers of major newspaper digitisation programmes. Our findings contribute to emerging understandings of factors that are rarely foregrounded or highlighted, yet fundamentally shape the depth and scope of digital cultural heritage archives and thus the questions that can be asked of them, now and in the future. Moreover, we draw attention to providers’ emphasis on meeting the needs of their end-users and how this is shaping the form and function of digital archives. The end user is not often emphasised in the wider literature on archival studies and we thus draw attention to the potential merit of this vector in future studies of digital archives
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