Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain

We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment of length $m$. On this occasion we also supply a proof of the basic integral formula for the density matrix presented in an earlier publication.Comment: 35 page

Syntactic Control of Interference Revisited

In Syntactic Control of Interference (POPL, 1978), J. C. Reynolds proposes three design principles intended to constrain the scope of imperative state effects in Algol-like languages. The resulting linguistic framework seems to be a very satisfactory way of combining functional and imperative concepts, having the desirable attributes of both purely functional languages (such as pcf) and simple imperative languages (such as the language of while programs). However, Reynolds points out that the obvious syntax for interference control has the unfortunate property that fi-reductions do not always preserve typings. Reynolds has subsequently presented a solution to this problem (ICALP, 1989), but it is fairly complicated and requires intersection types in the type system. Here, we present a much simpler solution which does not require intersection types. We first describe a new type system inspired in part by linear logic and verify that reductions preserve typings. We then define a class of bireflective models, which provide a categorical analysis of structure underlying the new typing rules; a companion paper Bireflectivity, in this volume, exposes wider ramifications of this structure. Finally, we describe a concrete model for an illustrative programming language based on the new type system; this improves on earlier such efforts in that states are not assumed to be structured using locations

Short-distance thermal correlations in the XXZ chain

Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in the infinite chain. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field for various anisotropies in the massless regime $- 1 < \Delta < 1$. It turns out that the new formulae are numerically efficient and allow us to obtain the correlations functions over the full parameter range with arbitrary precision.Comment: 25 pages, 5 colored figure

Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain

We study the generating function of the spin-spin correlation functions in the ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain without magnetic field. We have found its fundamental functional relations from those for general correlation functions, which originate in the quantum Knizhink-Zamolodchikov equation. Using these relations, we have calculated the explicit form of the generating functions up to n=6. Accordingly we could obtain the spin-spin correlator up to k=5.Comment: 10 page

Exact evaluation of density matrix elements for the Heisenberg chain

We have obtained all the density matrix elements on six lattice sites for the spin-1/2 Heisenberg chain via the algebraic method based on the quantum Knizhnik-Zamolodchikov equations. Several interesting correlation functions, such as chiral correlation functions, dimer-dimer correlation functions, etc... have been analytically evaluated. Furthermore we have calculated all the eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a result the exact von Neumann entropy for the reduced density matrix on six lattice sites has been obtained.Comment: 33 pages, 4 eps figures, 3 author

Traces on the Sklyanin algebra and correlation functions of the eight-vertex model

We propose a conjectural formula for correlation functions of the Z-invariant (inhomogeneous) eight-vertex model. We refer to this conjecture as Ansatz. It states that correlation functions are linear combinations of products of three transcendental functions, with theta functions and derivatives as coefficients. The transcendental functions are essentially logarithmic derivatives of the partition function per site. The coefficients are given in terms of a linear functional on the Sklyanin algebra, which interpolates the usual trace on finite dimensional representations. We establish the existence of the functional and discuss the connection to the geometry of the classical limit. We also conjecture that the Ansatz satisfies the reduced qKZ equation. As a non-trivial example of the Ansatz, we present a new formula for the next-nearest neighbor correlation functions.Comment: 35 pages, 2 figures, final versio

Exact results for the sigma^z two-point function of the XXZ chain at Delta=1/2

We propose a new multiple integral representation for the correlation function of the XXZ spin-1/2 Heisenberg chain in the disordered regime. We show that for Delta=1/2 the integrals can be separated and computed exactly. As an example we give the explicit results up to the lattice distance m=8. It turns out that the answer is given as integer numbers divided by 2^[(m+1)^2].Comment: 8 page

Percutaneous endoscopic gastrojejunostomy for a patient with an intractable small bowel injury after repeat surgeries: a case report

<p>Abstract</p> <p>Introduction</p> <p>The management of intestinal injury can be challenging, because of the intractable nature of the condition. Surgical treatment for patients with severe adhesions sometimes results in further intestinal injury. We report a conservative management strategy using percutaneous endoscopic gastrojejunostomy for an intractable small bowel surgical injury after repeated surgeries.</p> <p>Case presentation</p> <p>A 78-year-old Japanese woman had undergone several abdominal surgeries including urinary cystectomy for bladder cancer. After this operation, she developed peritonitis as a result of a small bowel perforation thought to be due to an injury sustained during the operation, with signs consistent with systemic inflammatory response syndrome: body temperature 38.5°C, heart rate 92 beats/minute, respiratory rate 23 breaths/minute, white blood cell count 11.7 × 10⁹/L (normal range 4-11 × 10⁹/μL). Two further surgical interventions failed to control the leak, and our patient's clinical condition and nutritional status continued to deteriorate. We then performed percutaneous endoscopic gastrojejunostomy, and continuous suction was applied as an alternative to a third surgical intervention. With this endoscopic intervention, the intestinal leak gradually closed and oral feeding became possible.</p> <p>Conclusion</p> <p>We suggest that the technique of percutaneous endoscopic gastrojejunostomy combined with a somatostatin analog is a feasible alternative to surgical treatment for small bowel leakage, and is less invasive than a nasojejunal tube.</p