O'Brien Aroon, Bartlett Stephen D, Doherty Andrew C, Flammia Steven T
Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney NSW 2006, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042163. doi: 10.1103/PhysRevE.92.042163. Epub 2015 Oct 29.
We use a simple real-space renormalization-group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously. This approach, which is based on exploiting the on-site symmetry of the model, has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse-field Ising model. Our investigation explores this approach in more generality, in a model in which the critical behavior has a richer structure but which reduces to the simpler Ising case at a special point. We demonstrate that the correlation length critical exponent as predicted from this real-space renormalization-group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality. Near the Ising special point, the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods, although the accuracy decreases away from the decoupled Ising model point.
我们使用一种简单的实空间重整化群方法来研究量子阿什金 - 泰勒模型的临界行为，该模型是一个一维量子自旋链，具有一条临界线，沿着这条线临界指数连续变化。这种基于利用模型的局域对称性的方法，已被证明在预测量子横向场伊辛模型临界行为的某些方面出奇地准确。我们的研究在一个更具普遍性的模型中探索这种方法，在该模型中临界行为具有更丰富的结构，但在一个特殊点会简化为更简单的伊辛情况。我们证明，从这种实空间重整化群方法预测的关联长度临界指数与共形场论沿临界线的相应结果大致相符。在伊辛特殊点附近，这种简单方法估计的临界指数的误差与基于更复杂方法的数值密集模拟的误差相当，尽管远离解耦的伊辛模型点时精度会降低。
