Wang Ling, Kao Ying-Jer, Sandvik Anders W
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056703. doi: 10.1103/PhysRevE.83.056703. Epub 2011 May 6.
We present a method for contracting a square-lattice tensor network in two dimensions based on auxiliary tensors accomplishing successive truncations (renormalization) of eight-index tensors for 2 × 2 plaquettes into four-index tensors. Since all approximations are done on the wave function (which also can be interpreted in terms of different kinds of tensor networks), the scheme is variational, and thus, the tensors can be optimized by minimizing the energy. Test results for the quantum phase transition of the transverse-field Ising model confirm that even the smallest possible tensors (two values for each tensor index at each renormalization level) produce much better results than the simple product (mean-field) state.
我们提出了一种在二维中收缩方形晶格张量网络的方法，该方法基于辅助张量，通过辅助张量将二维平面上八指标张量连续截断（重整化）为四指标张量。由于所有近似都是在波函数上进行的（波函数也可以用不同类型的张量网络来解释），所以该方案是变分的，因此，可以通过最小化能量来优化张量。横向场伊辛模型量子相变的测试结果证实，即使是最小可能的张量（在每个重整化级别上每个张量指标有两个值）也能产生比简单乘积（平均场）态好得多的结果。
