DMRG studies of critical SU(N) spin chains

The DMRG method is applied to integrable models of antiferromagnetic spin chains for fundamental and higher representations of SU(2), SU(3), and SU(4). From the low energy spectrum and the entanglement entropy, we compute the central charge and the primary field scaling dimensions. These parameters allow us to identify uniquely the Wess-Zumino-Witten models capturing the low energy sectors of the models we consider.Comment: 14 pages, 8 figures; final version, to appear in Ann. Phy

Master equation for spin-spin correlation functions of the XXZ chain

We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the one hand to the previously obtained multiple integral formulas for the spin-spin correlation functions and on the other hand to their expansion in terms of the form factors of the local spin operators. Hence, it provides a direct analytic link between these two representations of the correlation functions and a complete re-summation of the corresponding series. The master equation method also allows one to obtain multiple integral representations for dynamical correlation functions.Comment: 24 page

Density Matrices for a Chain of Oscillators

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model.Comment: 15 pages,8 figure

Spectrum and Thermodynamics of the one-dimensional supersymmetric t-J model with 1/r21/r^2 exchange and hopping

We derive the spectrum and the thermodynamics of the one-dimensional supersymmetric t-J model with long range hopping and spin exchange using a set of maximal-spin eigenstates. This spectrum confirms the recent conjecture that the asymptotic Bethe-ansatz spectrum is exact. By empirical determining the spinon degeneracies of each state, we are able to explicitly construct the free energy.Comment: 13 pages, Latex, (published in PRB46, 6639 (1992)

Анализ качества защемления консольной балки в зависимости от физических и геометрических параметров

In this work, it was supposed to find out the fulfillment of the pinching conditions of a cantilever beam, namely, the equality to zero of the magnitude of the deflection and the angle of rotation in the transverse boundary section of the rod. The paper presents the dependence of the values of the angle of rotation and deflection of the cantilever beam on such parameters as: section geometry, applied force, and embedment material. Practical deviation from these boundary conditions can be dangerous for the reliability of the connection. The aim of the work is to identify the compliance of the pinching material and the analysis of the degree of error in the calculation of perfectly elastic bodies for bending. The structure was calculated in ANSYS WORKBENCH, using the static structure module. To find the angular displacements, the commands of the APDL scripting language were used. Based on the data obtained, dependency tables were compiled to determine the behavior of the embedment for various physical and geometric parameters of the structure. Using the obtained data of calculations it became possible to determine the nature of the dependencies of the magnitude of the deflection on the values included in the calculation. The results are presented in the form of graphs, figures and tables. Based on the data on linear and angular displacements, conclusions were made about the nature of the influence of these quantities on the characteristics of the stress-strain state of the whole structure. Analyzing the obtained graphs, it became possible to determine the linear relationship between the load and deflection in the boundary section of the beam. The influence of the embedding material on displacements cannot be described by a similar law, which indicates possible errors in the calculation of the stress-strain state of the structure. It is also worth noting that an increase in the yield strength of a material when considering embedding from elastic materials is characterized by an increase in angular displacements and a simultaneous decrease in linear displacements. For concrete, these figures differ significantly.В данной работе предполагалось выяснить выполнение условий защемления консольной балки, а именно равенство нулю величины прогиба и угла поворота в поперечном граничном сечении стержня. В работе представлена зависимость величин угла поворота и прогиба консольной балки от таких параметров, как: геометрия сечения, прикладываемая сила и материал заделки. Практическое отклонение от данных граничных условий может являться опасным для надежности соединения. Целью работы является выявление податливости материала защемления и анализ степени погрешности при расчете идеально упругих тел на изгиб. На основе полученных данных были составлены таблицы зависимостей для определения поведения заделки при различных физических и геометрических параметрах конструкции. Используя полученные данные расчетов стало возможно определить характер зависимостей величины прогиба от включенных в расчет величин. Результаты приведены в виде графиков, рисунков и таблиц.У даній роботі передбачалося з'ясувати виконання умов защемлення консольної балки, а саме рівність нулю величини прогину і кута повороту в поперечному граничному перерізі стержня. У роботі представлена залежність величин кута повороту і прогину консольної балки від таких параметрів, як: геометрія перетину, що прикладається сила і матеріал закладення. Практичне відхилення від даних граничних умов може бути небезпечним для надійності з'єднання. Метою роботи є виявлення податливості матеріалу защемлення і аналіз ступеня похибки при розрахунку ідеально пружних тіл на вигин. На основі отриманих даних були складені таблиці залежностей для визначення поведінки закладення при різних фізичних і геометричних параметрах конструкції. Використовуючи отримані дані розрахунків стало можливо визначити характер залежностей величини прогину від включених в розрахунок величин. Результати наведені у вигляді графіків, малюнків і таблиць

Gutzwiller-Jastrow Wavefunctions for the 1/r Hubbard Model

In this work, we study the wavefunctions of the one dimensional 1/r Hubbard model in the strong interaction limit U = ∞. A set of Gutzwiller-Jastorw wavefunctions are shown to be eigen-functions of the Hamiltonian. The entire excitation spectrum and the thermodynamics are also studied in terms of more generalized Jastrow wavefunctions. For the wavefunctions and integrability conditions at finite on-site energy, further investigations are needed