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arXiv 1509.07571cond-mat.str-el
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基于一维海森堡反铁磁体基态的拓扑性质探讨其Kosterlitz-Escherless跃迁

Probing the Kosterlitz-Thouless transition in 1D Heisenberg antiferromagnet based on topological properties of its ground state

P. Tomczak, P. Jablonski, M. Tomczak

摘要:

从不同的角度重新研究了具有最近邻和次最近邻相互作用的反铁磁自旋- $\frac{1}{2}$海森堡链的基态中的Kosterlitz无相变:发现标量积$\langle Ψ_0| Ψ_0 \rangle$的分量与几何对象之间存在明确的对应关系.人们可以根据它们中的任何两个是否可以以连续的方式相互转换(属于同一个同伦类)来对这些对象进行分类。对上述对象的每一同伦类的“连接项"$\langle Ψ_0|\partial Ψ_0 \rangle$相对于链长(16,18,20,22,24自旋)的有限尺寸标度导致具有相当高精度的$λ$的临界值。

英文摘要:

A Kosterlitz-Thouless phase transition in the ground state of an antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain with nearest and next-nearest-neighbor interactions is re-investigated from a different perspective: An unequivocal correspondence is found between components of the scalar product $\langle Ψ_0| Ψ_0 \rangle$ and geometrical objects. One can classify these objects according to whether any two of them can be transformed into each other in a continuous way (belong to the same homotopy class). A finite size scaling of the "connection term`` $\langle Ψ_0|\partial Ψ_0 \rangle$ with respect to chain length (16, 18, 20, 22, 24 spins) for each homotopy class of above mentioned objects leads to the critical value of $λ$ with rather high accuracy.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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