CONTRACTOR RENORMALIZATION GROUP THEORY OF THE EVEN-LEG SPIN TORI

2010 ◽  
Vol 24 (27) ◽  
pp. 2725-2731
Author(s):  
QIHUI CHEN ◽  
PENG LI
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Ground State ◽  
Group Method ◽  
Renormalization Group Theory ◽  
Hierarchical Data ◽  
Core Group ◽  
Ground State Energies

The contractor renormalization (CORE) group method is applied to the even-leg spin tori to reveal their ground-state energies and the lowest excitation gaps. The spin tori are referred to the spin ladders that are closed along the rung direction. We designed an improved iterative CORE algorithm and applied it to the even-leg tori. The improvement is made by introducing an extrapolation based on a sequence of hierarchical data that is obtained by varying the size of the elementary block. Quite good results are obtained and compared with the ones by other methods.

scholarly journals Renormalization group theory of the generalized multi-vertex sine-Gordon model

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Takashi Yanagisawa
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Regularization Method ◽  
Dimensional Regularization ◽  
Group Method ◽  
Regular Tetrahedron ◽  
Renormalization Group Theory ◽  
Renormalization Group Method ◽  
Triangle Condition ◽  
Sine Gordon Model

Abstract We investigate the renormalization group theory of the generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by $\cos(k_j\cdot \phi)$, where $k_j$ ($j=1,2,\ldots,M$) are momentum vectors and $\phi$ is an $N$-component scalar field. The beta functions are calculated for the sine-Gordon model with multiple cosine interactions. The second-order correction in the renormalization procedure is given by the two-point scattering amplitude for tachyon scattering. We show that new vertex interaction with the momentum vector $k_{\ell}$ is generated from two vertex interactions with vectors $k_i$ and $k_j$ when $k_i$ and $k_j$ meet the condition $k_{\ell}=k_i\pm k_j$, called the triangle condition. A further condition $k_i\cdot k_j=\pm 1/2$ is required within the dimensional regularization method. The renormalization group equations form a set of closed equations when $\{k_j\}$ form an equilateral triangle for $N=2$ or a regular tetrahedron for $N=3$. The Wilsonian renormalization group method gives qualitatively the same result for beta functions.

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