Low-energy effective theories of quantum spin and quantum link models
Low-energy effective theories of quantum spin and quantum link models
复制标题
量子自旋低能有效理论和量子链接模型
DOI：
10.1103/physrevd.63.085007
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发表时间：
2000
影响因子：
5
通讯作者：
U. Wiese
中科院分区：
文献类型：
--
作者：
B. Schlittgen;U. Wiese
Quantum spin and quantum link models provide an unconventional regularization of field theory in which classical fields arise via dimensional reduction of discrete variables. This D-theory regularization leads to the same continuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state path integral techniques. We illustrate our method for the $(2+1)\mathrm{D}$ Heisenberg quantum spin model which is the D-theory regularization of the $2\mathrm{D} O(3)$ model. Similarly, we prove that in the continuum limit a $(2+1)\mathrm{D}$ quantum spin model with ${\mathrm{SU}(N)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(N)}_{R}\ifmmode\times\else\texttimes\fi{}{U(1)}_{L=R}$ symmetry is equivalent to the 2D principal chiral model. Finally, we show that $(4+1)\mathrm{D}$ $\mathrm{SU}(N)$ quantum link models reduce to ordinary 4D Yang-Mills theory.
Quantum spin and quantum link models provide an unconventional regularization of field theory in which classical fields arise via dimensional reduction of discrete variables. This D-theory regularization leads to the same continuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state path integral techniques. We illustrate our method for the $(2+1)\mathrm{D}$ Heisenberg quantum spin model which is the D-theory regularization of the $2\mathrm{D} O(3)$ model. Similarly, we prove that in the continuum limit a $(2+1)\mathrm{D}$ quantum spin model with ${\mathrm{SU}(N)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(N)}_{R}\ifmmode\times\else\texttimes\fi{}{U(1)}_{L=R}$ symmetry is equivalent to the 2D principal chiral model. Finally, we show that $(4+1)\mathrm{D}$ $\mathrm{SU}(N)$ quantum link models reduce to ordinary 4D Yang-Mills theory.