"Monodromy matrix"의 두 판 사이의 차이
Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
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| 18번째 줄: | 18번째 줄: | ||
:<math> | :<math> | ||
t=\operatorname{tr} T=A+D | t=\operatorname{tr} T=A+D | ||
| − | </math> | + | </math> |
| 82번째 줄: | 82번째 줄: | ||
==computational resource== | ==computational resource== | ||
* https://docs.google.com/file/d/0B8XXo8Tve1cxNWJ5NWNIXzRieGc/edit | * https://docs.google.com/file/d/0B8XXo8Tve1cxNWJ5NWNIXzRieGc/edit | ||
| − | + | ||
[[분류:integrable systems]] | [[분류:integrable systems]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:migrate]] | [[분류:migrate]] | ||
2020년 12월 28일 (월) 04:19 기준 최신판
introduction
- monodromy matrix
\[ T(\lambda)= \left( \begin{array}{cc} A(\lambda ) & B(\lambda ) \\ C(\lambda ) & D(\lambda ) \end{array} \right) \]
- describes the transport of the spin around the circular chain
- YBE implies the following RTT=TTR relation in spin chains
\[ RTT=TTR \]
- transfer matrix
\[ t=\operatorname{tr} T=A+D \]
definition
- \(\lambda\) : spectral parameter
- \(R(\lambda)\) : R-matrix
- define the Lax matrix
\[ \begin{eqnarray} L_{0 n}(\lambda) &=& R_{0 n}(\lambda - {i\over 2}) \\ &=& \left( \begin{array}{cc} \alpha_{n} & \beta_{n} \\ \gamma_{n} & \delta_{n} \end{array} \right) \,, \qquad n = 1 \,, 2 \,, \ldots \,, N \,, \end{eqnarray} \] where \(\alpha_{n}\), \(\beta_{n}\), \(\gamma_{n}\), \(\delta_{n}\) are operators on \[ \begin{eqnarray} \stackrel{\stackrel{1}{\downarrow}}{V} \otimes \cdots \otimes \stackrel{\stackrel{n}{\downarrow}}{V} \otimes \cdots \otimes \stackrel{\stackrel{N}{\downarrow}}{V} \end{eqnarray} \]
- monodromy matrix
\[ \begin{eqnarray} T_{0}(\lambda) &=& L_{0 N}(\lambda) \cdots L_{0 1}(\lambda) \\ &=& \left(\begin{array}{cc} \alpha_{N} & \beta_{N} \\ \gamma_{N} & \delta_{N} \end{array} \right) \cdots \left(\begin{array}{cc} \alpha_{1} & \beta_{1} \\ \gamma_{1} & \delta_{1} \end{array} \right) \\ &=& \left( \begin{array}{cc} A(\lambda ) & B(\lambda ) \\ C(\lambda ) & D(\lambda ) \end{array} \right) \label{monodromy} \end{eqnarray} \] where \(A(\lambda ) ,B(\lambda ) , C(\lambda ) , D(\lambda )\) are operators acting on \(V^{\otimes N}\)