Combinatorial Aspects of Correlation Functions of the XXZ Heisenberg Chain in Limiting Cases
- 作者: Bogoliubov N.1, Malyshev C.2
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隶属关系:
- St.Petersburg Department of Steklov Mathematical Institute, ITMO University
- St.Petersburg Department of Steklov Mathematical Institute
- 期: 卷 216, 编号 1 (2016)
- 页面: 8-22
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237736
- DOI: https://doi.org/10.1007/s10958-016-2884-0
- ID: 237736
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详细
We discuss the connection between quantum integrable models and some aspects of enumerative combinatorics and the theory of partitions. As a basic example, we consider the spin XXZ Heisenberg chain in the limiting cases of zero and infinite anisotropy. The representation of the Bethe wave functions via Schur functions allows us to apply the theory of symmetric functions to calculating the thermal correlation functions as well as the form factors in the determinantal form. We provide a combinatorial interpretation of the correlation functions in terms of nests of self-avoiding lattice paths. The suggested interpretation is in turn related to the enumeration of boxed plane partitions. The asymptotic behavior of the thermal correlation functions is studied in the limit of small temperature provided that the characteristic parameters of the system are large enough. The leading asymptotics of the correlators are found to be proportional to the squared numbers of boxed plane partitions.
作者简介
N. Bogoliubov
St.Petersburg Department of Steklov Mathematical Institute, ITMO University
编辑信件的主要联系方式.
Email: bogoliubov@pdmi.ras.ru
俄罗斯联邦, St.Petersburg
C. Malyshev
St.Petersburg Department of Steklov Mathematical Institute
Email: bogoliubov@pdmi.ras.ru
俄罗斯联邦, St.Petersburg