论文标题
硬方相模型的张量网络调查
Tensor network investigation of the hard-square model
论文作者
论文摘要
使用角转移矩阵重新归一化组与描述其分区函数的张量网络收缩，我们研究了硬方相模型的相变的性质，这是Baxter为其发现的统计物理学的精确解决模型之一。动机是双重的：评估张量网络对此类模型的功能，并探究了硬核玻色子的一维量子模型的2D经典类似物，这些模型最近在实验中引起了Rydberg Atoms链的实验中的重大关注。因此，我们集中在两个对角线方向上的活性和耦合常数的3D参数空间中的两个平面上。我们首先研究了迄今为止使用蒙特卡洛模拟研究的唯一案例，即相反的耦合常数。我们确认，距离可集成的三态POTTS点并不太远，在Huse-fisher手性通用类别中，从3个阶段的过渡似乎是独一无二的，尽管与蒙特卡洛相比，其指数明显不同。我们还确定了到目前为止尚未报告该模型的两个其他相变，Lifshitz障碍线以及用于足够大活动的Ising转变。 To make contact with 1D quantum models of Rydberg atoms, we then turn to a plane where the ferromagnetic coupling is kept fixed, and we show that the resulting phase diagram is very similar, the only difference being that the Ising transition becomes first-order through a tricritical Ising point, in agreement with Baxter's prediction that this plane should contain a tricritical Ising point, and in remarkable, almost quantitative agreement with the phase diagram of the该模型的1D量子版本。
Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of statistical physics for which Baxter has found an integrable manifold. The motivation is twofold: assess the power of tensor networks for such models, and probe the 2D classical analog of a 1D quantum model of hard-core bosons that has recently attracted significant attention in the context of experiments on chains of Rydberg atoms. Accordingly, we concentrate on two planes in the 3D parameter space spanned by the activity and the coupling constants in the two diagonal directions. We first investigate the only case studied so far with Monte Carlo simulations, the case of opposite coupling constants. We confirm that, away and not too far from the integrable 3-state Potts point, the transition out of the period-3 phase appears to be unique in the Huse-Fisher chiral universality class, albeit with significantly different exponents as compared to Monte Carlo. We also identify two additional phase transitions not reported so far for that model, a Lifshitz disorder line, and an Ising transition for large enough activity. To make contact with 1D quantum models of Rydberg atoms, we then turn to a plane where the ferromagnetic coupling is kept fixed, and we show that the resulting phase diagram is very similar, the only difference being that the Ising transition becomes first-order through a tricritical Ising point, in agreement with Baxter's prediction that this plane should contain a tricritical Ising point, and in remarkable, almost quantitative agreement with the phase diagram of the 1D quantum version of the model.
