Density matrices for finite segments of Heisenberg chains of arbitrary length
Density matrices for finite segments of Heisenberg chains of arbitrary length
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任意长度的海森堡链有限段的密度矩阵
DOI：
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发表时间：
2007
期刊：
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通讯作者：
A. Klümper
中科院分区：
文献类型：
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作者：
J. Damerau;F. Göhmann;Nils P. Hasenclever;A. Klümper
我们推导出一个多重积分表示的长度为m的XXZ自旋链的L格点，这只依赖于L参数的一段基态密度矩阵。这使我们能够处理任意有限长度的链。专门的各向同性限制的XXX链，我们表明，小m的多重积分因式分解。我们猜想，这一性质适用于任意m，并建议一个指数公式的密度矩阵，其中只涉及一个双柯西型积分的指数。我们证明了我们的公式的效率，通过计算的下一个最近的邻居ZZ-相关函数的链长度范围从两个宏观数字。
We derive a multiple integral representing the ground-state density matrix of a segment of length m of the XXZ spin chain on L lattice sites, which depends on L only parametrically. This allows us to treat chains of arbitrary finite length. Specializing to the isotropic limit of the XXX chain we show for small m that the multiple integrals factorize. We conjecture that this property holds for arbitrary m and suggest an exponential formula for the density matrix which involves only a double Cauchy type integral in the exponent. We demonstrate the efficiency of our formula by computing the next-to-nearest neighbour zz-correlation function for chain lengths ranging from two to macroscopic numbers.