Correlation length of the 1D Hubbard Model at half-filling : equal-time one-particle Green's function

The asymptotics of the equal-time one-particle Green's function for the half-filled one-dimensional Hubbard model is studied at finite temperature. We calculate its correlation length by evaluating the largest and the second largest eigenvalues of the Quantum Transfer Matrix (QTM). In order to allow for the genuinely fermionic nature of the one-particle Green's function, we employ the fermionic formulation of the QTM based on the fermionic R-operator of the Hubbard model. The purely imaginary value of the second largest eigenvalue reflects the k_F (= pi/2) oscillations of the one-particle Green's function at half-filling. By solving numerically the Bethe Ansatz equations with Trotter numbers up to N=10240, we obtain accurate data for the correlation length at finite temperatures down into the very low temperature region. The correlation length remains finite even at T=0 due to the existence of the charge gap. Our numerical data confirm Stafford and Millis' conjecture regarding an analytic expression for the correlation length at T=0.Comment: 7 pages, 6 figure

Fermionic R-operator approach for the small-polaron model with open boundary condition

Exact integrability and algebraic Bethe ansatz of the small-polaron model with the open boundary condition are discussed in the framework of the quantum inverse scattering method (QISM). We employ a new approach where the fermionic R-operator which consists of fermion operators is a key object. It satisfies the Yang-Baxter equation and the reflection equation with its corresponding K-operator. Two kinds of 'super-transposition' for the fermion operators are defined and the dual reflection equation is obtained. These equations prove the integrability and the Bethe ansatz equation which agrees with the one obtained from the graded Yang-Baxter equation and the graded reflection equations.Comment: 10 page

Ab initio DFT study of ideal shear strength of polytypes of silicon carbide

Ab initio density functional calculations are performed to investigate the ideal shear deformation of SiC poly types (3C, 2H, 4H, and 6H). The deformation of the cubic and the hexagonal poly types in small strain region can be well represented by the elastic properties of component Si4C-tetrahedrons. The stacking pattern in the polytypes affects strain localization, which is correlated with the generalized stacking fault (GSF) energy profile of each shuffle-set plane, and the ideal shear strength. Compressive hydrostatic stress decreases the ideal shear strength, which is in contrast with the behavior of metals.Выполнены функциональные расчеты ab initio плотности с целью изучения идеальной сдвиговой деформации политипов SiC (3С, 2Н, 4Н, 6Н). Деформирование кубических и гексагональных политапов в области малых деформаций характеризуется упругими свойствами составляющих тетраэдров, Si4C. Характер укладки в политипах оказывает воздействие на локализацию деформаций (что коррелирует с профилем энергии обобщенного дефекта укладки каждой перемещенной плоскости) и идеальную прочность на сдвиг. Сжимающее гидростатическое напряжение снижает идеальную прочность на сдвиг, что отличает поведение этих материалов от металлов

Fermionic R-Operator and Algebraic Structure of 1D Hubbard Model: Its application to quantum transfer matrix

The algebraic structure of the 1D Hubbard model is studied by means of the fermionic R-operator approach. This approach treats the fermion models directly in the framework of the quantum inverse scattering method. Compared with the graded approach, this approach has several advantages. First, the global properties of the Hamiltonian are naturally reflected in the algebraic properties of the fermionic R-operator. We want to note that this operator is a local operator acting on fermion Fock spaces. In particular, SO(4) symmetry and the invariance under the partial particle hole transformation are discussed. Second, we can construct a genuinely fermionic quantum transfer transfer matrix (QTM) in terms of the fermionic R-operator. Using the algebraic Bethe Ansatz for the Hubbard model, we diagonalize the fermionic QTM and discuss its properties.Comment: 22 pages, no figure

Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model

The quantum transfer matrix (QTM) approach to integrable lattice Fermion systems is presented. As a simple case we treat the spinless Fermion model with repulsive interaction in critical regime. We derive a set of non-linear integral equations which characterize the free energy and the correlation length of $$ for arbitrary particle density at any finite temperatures. The correlation length is determined by solving the integral equations numerically. Especially in low temperature limit this result agrees with the prediction from conformal field theory (CFT) with high accuracy.Comment: 17 page

Solution of the quantum inverse problem

We derive a formula that expresses the local spin and field operators of fundamental graded models in terms of the elements of the monodromy matrix. This formula is a quantum analogue of the classical inverse scattering transform. It applies to fundamental spin chains, such as the XYZ chain, and to a number of important exactly solvable models of strongly correlated electrons, such as the supersymmetric t-J model or the the EKS model.Comment: 37 pages, AMS-Latex, AMS-Font

Bubble burst as jamming phase transition

Recently research on bubble and its burst attract much interest of researchers in various field such as economics and physics. Economists have been regarding bubble as a disorder in prices. However, this research strategy has overlooked an importance of the volume of transactions. In this paper, we have proposed a bubble burst model by focusing the transactions incorporating a traffic model that represents spontaneous traffic jam. We find that the phenomenon of bubble burst shares many similar properties with traffic jam formation by comparing data taken from US housing market. Our result suggests that the transaction could be a driving force of bursting phenomenon.Comment: 9 pages,12 figure

Praktična sinteza regulatora za precizno pozicioniranje sustava pomične podloge

This paper presents a practical feedback controller design of a ball screw-driven table system for the microdisplacement positioning. Friction of the mechanism in the micro-displacement region has nonlinear elastic properties, unlike Coulomb and/or viscous friction in the macro-displacement, resulting in different positioning responses and frequency characteristics of the plant depending on the regions. In this paper, at first, a numerical simulator with a rolling friction model is adopted to reproduce the positioning behaviors in the micro-displacement region. Based on the simulator, the stability condition of positioning in the region is clarified on the basis of frequency characteristics and, then, appropriate parameters of feedback controller are practically designed to satisfy the required positioning performance. Effectiveness of the proposed design has been verified by a series of experiments using a prototype of ball screw-driven table positioning device.U radu je prikazana sinteza regulatora s povratnom vezom u sustavu za precizno linearno pozicioniranje pomične podloge pomoću kugličnih ležajeva. Za razliku od uobičajenih modela Coulombova i/ili viskoznog trenja, trenje razmatranog sustava ima izrazito nelinearna svojstva u području mikro-pomaka, što za posljedicu ima različite odzive pozicioniranja i frekvencijski karakteristike, ovisno o radnom području. U radu je prvo razvijeno numeričko simulacijsko okruženje zasnovano na modelu trenja kotrljanja u svrhu simuliranja ponašanja sustava pozicioniranja u području mikropomaka. Potom je, zasnivajući se na simulacijskom okruženju, pomoću frekvencijske karakteristike razjašnjen problem stabilnosti sustava u promatranom radnom području te su odabrani odgovarajući parametri regulatora koji poštuju uvjet stabilnosti i zadovoljavaju željenu kvalitetu odziva. Sinteza regulatora provedena je vodeći računa o praktičnoj primjenjivosti postupka. Učinkovitost predložene sinteze potvr.ena je nizom eksperimenata na prototipu sustava za precizno linearno pozicioniranje pomične podloge pomoću kugličnih ležajeva