Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice
Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice
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DOI：
10.1103/physrevx.3.031010
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发表时间：
2013-08-26
影响因子：
12.5
通讯作者：
Herbut, Igor F.
中科院分区：
文献类型：
--
作者：
Assaad, Fakher F.;Herbut, Igor F.
在数值模拟中，通常通过计算适当的局部序参数的两点相关函数来检测自发破缺的对称性。然而，这种方法计算局部阶次参数的平方，因此当它很小时，需要非常大的系统尺寸和高精度才能获得可靠的结果。或者，可以通过引入局部对称破缺场来钉扎阶次，然后测量距钉扎中心无限远的感应局部阶次参数。这里，在射影辅助场量子蒙特卡罗算法的范围内，针对蜂窝晶格上的哈伯德模型对该方法进行了详细测试。随着分辨率的提高，我们发现随着相互作用的增加，半金属态和绝缘反铁磁态之间存在直接且连续的量子相变。单粒子间隙（以哈伯德 U 为单位测量）跟踪交错磁化强度。通过有限尺寸缩放获得了出色的数据崩溃，其临界指数值符合转变的 Gross-Neveu 普遍性类别。
In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is small, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetry-breaking field and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary-field quantum Monte Carlo algorithm. With our enhanced resolution, we find a direct and continuous quantum phase transition between the semimetallic and the insulating antiferromagnetic states with increase of the interaction. The single-particle gap, measured in units of Hubbard U, tracks the staggered magnetization. An excellent data collapse is obtained by finite-size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.