基于张量网络算法对二维t-J模型的研究

高温超导问题是当前凝聚态物理学研究的最重要的问题之一。本文应用基于二维强关联电子无限费米子系统的投影纠缠对(gPEPS)表示下建立的虚时间演化的张量网络算法arXiv:0907.5520],对高温超导的相关的最小模型——二维t-J 模型进行了数值模拟研究,得出二维t-J模型在半占据状态与小于半占据状态时的基态,并最终得到了海森堡反铁磁无空穴的态与有空穴的态之间的相分离线,以及二维正方格子t-J 模型的单位格点基态能量。研究结果表明,二维t-J 模型的相分离线上临界点为Jc=0.95t和下临界点为Jc=3.45t；随后模拟J/t = 0.4,发现不同的掺杂会导致出现四个超导相：一个是由电荷密度波、自旋密度波与p波共存的超导相,一个是自旋单态的d s波超导配对与反铁磁背景下自旋三态p波超导配对超导相,一个是扩展s波配对超导相,一个是铁磁背景下p波的配对超导相。

2-D quantum t-J model based on the tensor network algorithm

The problem of high temperature superconductor is one of the most important problems in condensed matter. Both the phase separation line and the ground-state energy of the two-dimensional t-J model are investigated in the context of the tensor network algorithm in terms of the graded projected entangled-pair state representation (gPEPS) arXiv:0907.5520] of the ground-state wave functions. Here, there is a line of phase separation between the Heisenberg anti-ferromagnetic state without hole and a hole-rich state of the two-dimensional t-J model, which qualitatively agrees with the results based on the high-temperature expansions (HTE). The line of phase separation undergo two quantum phase transitions at Jc=0.95t and Jc=3.45t. For J/t = 0.4, a systematic computation is simulated to identify all ground states for various fillings. It is found that the regime consists of four different phases: one superconducting phase with charge density wave and spin density wave order coexisting with a p-wave superconducting state, one superconducting phase with the symmetry mixing of d s-wave superconductivity in the spin-singlet channel and p-wave superconductivity in the spin-triplet channel in the presence of an anti-ferromagnetic background, one phase with extended s-wave symmetry, and one phase with p-wave symmetry in a ferromagnetic background.