Eigenvalues of the eight-vertex model transfer matrix and the spectrum of theXYZ Hamiltonian

1988 ◽  
Vol 71 (4) ◽  
pp. 495-507 ◽  
Author(s):  
A. Kl�mper ◽  
J. Zittartz
Keyword(s):  
Transfer Matrix ◽  
Vertex Model ◽  
Model Transfer

Quantum Tavis–Cummings Model

2019 ◽  
pp. 474-488
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Strong Interaction ◽  
Building Blocks ◽  
Vertex Model ◽  
Algebraic Bethe Ansatz ◽  
Quantum Matter ◽  
Ansatz Approach

This chapter extends the algebraic Bethe ansatz to the quantum Tavis–Cummings model, an N atom generalization of the Jaynes–Cummings model to describe the strong interaction between light and quantum matter. In the case of the quantum Tavis–Cum- mings model there is no underlying vertex model to suggest the constituent building blocks of the algebraic Bethe ansatz approach, e.g.like the L-matrix or ultimately the transfer matrix. The algebraic Bethe ansatz is then first applied to the Tavis–Cummings Hamiltonian with an added Stark term using a conjecture for the transfer matrix. The original Tavis–Cummings model and its algebraic Bethe ansatz are obtained in the limit of vanishing Stark term, which requires considerable care.

Application of the Transfer Matrix Method for Multibody Systems in Dynamics of the Self-Propelled Artillery

2018 ◽  
Author(s):  
Qicheng Zha ◽  
Xiaoting Rui ◽  
Feifei Liu ◽  
Hailong Yu ◽  
Jianshu Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
The Self ◽  
System Matrix ◽  
Topological Graph ◽  
Fast Calculation ◽  
Transfer Equations ◽  
Model Transfer

Transfer Matrix Method for Multibody Systems (MSTMM) has the advantages of no need to establish the global system dynamics equations, low order of the system matrix, high programming, and fast calculation speed compared to the ordinary dynamics methods. In this paper, the topological graph of the dynamics model, transfer equations, transfer matrix of overall system and the simulation program of dynamics of the self-propelled artillery system are established by using the new version of the transfer matrix method for multibody systems and the automatic deduction theorem of overall transfer equation of systems. Realize the rapid calculation of the deviation of the pitch angle and the revolution angles of the turret versus time in the self-propelled artillery. It provides a theoretical basis and simulation means for the dynamics analysis of the self-propelled artillery.

scholarly journals THE 8V CSOS MODEL AND THE sl2 LOOP ALGEBRA SYMMETRY OF THE SIX-VERTEX MODEL AT ROOTS OF UNITY

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1899-1905 ◽  
Author(s):  
TETSUO DEGUCHI
Keyword(s):  
Transfer Matrix ◽  
Lattice Model ◽  
Algebraic Method ◽  
System Size ◽  
Spin Operator ◽  
Total Spin ◽  
Coupling Constants ◽  
Roots Of Unity ◽  
Vertex Model ◽  
Elliptic Quantum

We review an algebraic method for constructing degenerate eigenvectors of the transfer matrix of the eight-vertex Cyclic Solid-on-Solid lattice model (8V CSOS model), where the degeneracy increases exponentially with respect to the system size. We consider the elliptic quantum group Eτ,η(sl2) at the discrete coupling constants: 2N η = m1 + im2τ, where N, m1 and m2 are integers. Then we show that degenerate eigenvectors of the transfer matrix of the six-vertex model at roots of unity in the sector SZ ≡ 0 ( mod N) are derived from those of the 8V CSOS model, through the trigonometric limit. They are associated with the complete N strings. From the result we see that the dimension of a given degenerate eigenspace in the sector SZ ≡ 0 ( mod N) of the six-vertex model at Nth roots of unity is given by [Formula: see text], where [Formula: see text] is the maximal value of the total spin operator SZ in the degenerate eigenspace.

The transfer matrix of the symmetric 16-vertex model

1973 ◽  
Vol 44 (6) ◽  
pp. 437-438 ◽  
Author(s):  
B.U. Felderhof
Keyword(s):  
Transfer Matrix ◽  
Vertex Model

scholarly journals Solution of Eight-vertex Lattice Model Without Elliptic Functions

1974 ◽  
Vol 27 (4) ◽  
pp. 433 ◽  
Author(s):  
Kailash Kumar
Keyword(s):  
Eigenvalue Problem ◽  
Transfer Matrix ◽  
Elliptic Functions ◽  
Point Of View ◽  
Vertex Model ◽  
Type Problem ◽  
Matrix Eigenvalue Problem ◽  
Lattice Statistical Mechanics ◽  
Algebraic Operations ◽  
Functional Matrix

Baxter's method of solving the eight-vertex model in lattice statistical mechanics is examined from an elementary point of view. It is shown that the algebraic operations in the method can be carried out without recourse to elliptic functions. These include: construction of certain subspaces invariant uti.der the action of the transfer matrix; reduction of the transfer matrix eigenvalue problem to an equivalent ice-type problem and construction of certain matrices which commute with the transfer matrix and satisfy a functional matrix equation.

scholarly journals FLUCTUATING INTERFACES, SURFACE TENSION, AND CAPILLARY WAVES: AN INTRODUCTION

1992 ◽  
Vol 03 (05) ◽  
pp. 857-877 ◽  
Author(s):  
VLADIMIR PRIVMAN
Keyword(s):  
Surface Tension ◽  
Transfer Matrix ◽  
Lattice Models ◽  
Wave Model ◽  
Capillary Waves ◽  
Roughening Transition ◽  
Transfer Matrix Spectrum ◽  
Model Transfer ◽  
Matrix Spectrum ◽  
Long Cylinder

We present an introduction to modern theories of interfacial fluctuations and the associated interfacial parameters: surface tension and surface stiffness, as well as their interpretation within the capillary wave model. Transfer matrix spectrum properties due to fluctuation of an interface in a long-cylinder geometry are reviewed. The roughening transition and properties of rigid interfaces below the roughening temperature in 3d lattice models are surveyed with emphasis on differences in fluctuations and transfer matrix spectral properties of rigid vs. rough interfaces.

Six-Vertex Model

2019 ◽  
pp. 454-473
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Spin Chain ◽  
Quantum Spin ◽  
Square Lattice ◽  
Vertex Model ◽  
Quantum Spin Chain ◽  
Special Value ◽  
Quantum Operators ◽  
The One

This chapter considers the special case of the six-vertex model on a square lattice using a trigonometric parameterization of the vertex weights. It demonstrates how, by exploiting the Yang-Baxter relations, the six-vertex model is diagonalized and the Bethe ansatz equations are derived. The Hamiltonian of the Heisenberg quantum spin chain is obtained from the transfer matrix for a special value of the spectral parameter together with an infinite set of further conserved quantum operators. By the diagonalization of the transfer matrix the exact solution of the one-dimensional quantum spin chain Hamiltonian has automatically also been obtained, which is given by the same Bethe ansatz equations.

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