Department of Physics, State Key Laboratory of Surface Physics and Laboratory of Advanced Materials, Fudan University, Shanghai 200433, China.
Department of Physics and Astronomy, California State University, Northridge, California 91330, USA.
Phys Rev Lett. 2014 Apr 4;112(13):137202. doi: 10.1103/PhysRevLett.112.137202.
Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductor--anyon superconductor. Such an exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in a realistic system where time-reversal symmetry is breaking (T breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneous T breaking. We find that our model has two topological degenerate ground states, which exhibit nonvanishing scalar chirality order and are protected by finite excitation gap. Furthermore, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest-neighbor kagome Heisenberg model.
卡利梅尔-劳克林（KL）手性自旋液体（CSL）是一种没有时间反演对称性的量子自旋液体，它被认为是一种奇异超导体——任意子超导体的母体状态。这种奇异的状态已经被人们研究了二十多年，但仍然不清楚它是否能存在于一个时间反演对称性自发破缺（T 破缺）的现实系统中。通过使用密度矩阵重整化群，我们表明 KL CSL 存在于一个具有自发 T 破缺的各向异性 kagome 海森堡模型中。我们发现，我们的模型有两个拓扑简并的基态，它们表现出非零标量手性序，并受到有限激发能隙的保护。此外，我们通过从纠缠谱中提取的特征边缘共形场理论和从模矩阵中提取的准粒子交织统计，将这个状态确定为 KL CSL。我们还研究了这个 CSL 相如何随着系统接近最近邻 kagome 海森堡模型而演变。
