ترغب بنشر مسار تعليمي؟ اضغط هنا

Difference equations for the higher rank XXZ model with a boundary

53   0   0.0 ( 0 )
 نشر من قبل Takeo Kojima
 تاريخ النشر 2000
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

The higher rank analogue of the XXZ model with a boundary is considered on the basis of the vertex operator approach. We derive difference equations of the quantum Knizhnik-Zamolodchikov type for 2N-point correlations of the model. We present infinite product formulae of two point functions with free boundary condition by solving those difference equations with N=1.



قيم البحث

اقرأ أيضاً

63 - T. Kojima 2000
We study the XXZ chain with a boundary at massless regime $-1<Delta<1$. We give the free field realizations of the boundary vacuum state and its dual. Using these realizations, we give the integrable representations of the correlation functions.
103 - T. Kojima 2000
We study the SU(n) invariant massive Thirring model with boundary reflection. Our approach is based on the free field approach. We construct the free field realizations of the boundary state and its dual. For an application of these realizations, we present integral representations for the form factors of the local operators.
59 - T. Kojima 2000
Finite XXZ chain with double boundaries is considered at critical regime $-1<Delta<1$. We construct the eigenvectors of finite Hamiltonian by means of vertex operators and the quasi-boundary states. Using the free field realizations of the vertex ope rators and the quasi-boundary states, integral representations for the correlation functions are derived.
455 - Bulat Suleimanov 2012
We construct a solution of an analog of the Schr{o}dinger equation for the Hamiltonian $ H_I (z, t, q_1, q_2, p_1, p_2) $ corresponding to the second equation $P_1^2$ in the Painleve I hierarchy. This solution is produced by an explicit change of var iables from a solution of the linear equations whose compatibility condition is the ordinary differential equation $P_1^2$ with respect to $z$. This solution also satisfies an analog of the Schr{o}dinger equation corresponding to the Hamiltonian $ H_{II} (z, t, q_1, q_2, p_1, p_2) $ of Hamiltonian system with respect to $t$ which is compatible with $P_1^2$. A similar situation occurs for the $P_2^2$ equation in the Painleve II hierarchy.
Discrete Painleve equations are nonlinear, nonautonomous difference equations of second-order. They have coefficients that are explicit functions of the independent variable $n$ and there are three different types of equations according to whether th e coefficient functions are linear, exponential or elliptic functions of $n$. In this paper, we focus on the elliptic type and give a review of the construction of such equations on the $E_8$ lattice. The first such construction was given by Sakai cite{SakaiH2001:MR1882403}. We focus on recent developments giving rise to more examples of elliptic discrete Painleve equations.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا