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arXiv 1602.02096cond-mat.str-el
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二维量子临界点附近的热伊辛跃迁

Thermal Ising transitions in the vicinity of two-dimensional quantum critical points

Stephan Hesselmann, Stefan Wessel

摘要:

转变温度的缩放到一个有序的阶段接近量子临界点,以及量子临界区域内的序参量波动提供了有价值的信息的普遍性质的基础量子临界点。在这里,我们采用量子蒙特卡罗模拟来详细研究二维量子系统的这些关系,这些量子系统在量子临界点附近表现出有限温度伊辛跃迁线,该量子临界点属于(i)三维伊辛模型(对于正方形晶格上的横向磁场中的量子伊辛模型的情况)或(ii)讨论了蜂窝晶格上无自旋费米子半满系统在最近邻排斥作用下的${\it chiral}$伊辛跃迁。虽然第一种情况允许大规模模拟以根据量子临界点处的临界指数的已知值高精度地评估缩放预测,但是对于后一种情况,我们提取与序参量波动相关的临界指数$ν$和$η$的值,我们讨论了其他最近的估计,从基态量子蒙特卡罗计算以及分析方法。

英文摘要:

The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the underlying quantum critical point. Here, we employ quantum Monte Carlo simulations to examine these relations in detail for two-dimensional quantum systems that exhibit a finite-temperature Ising-transition line in the vicinity of a quantum critical point that belongs to the universality class of either (i) the three-dimensional Ising model for the case of the quantum Ising model in a transverse magnetic field on the square lattice or (ii) the ${\it chiral}$ Ising transition for the case of a half-filled system of spinless fermions on the honeycomb lattice with nearest-neighbor repulsion. While the first case allows large-scale simulations to assess the scaling predictions to a high precision in terms of the known values for the critical exponents at the quantum critical point, for the later case we extract values of the critical exponents $ν$ and $η$, related to the order parameter fluctuations, which we discuss in relation to other recent estimates from ground state quantum Monte Carlo calculations as well as analytical approaches.

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