Emergent topological excitations in a two-dimensional quantum spin system
Emergent topological excitations in a two-dimensional quantum spin system
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二维量子自旋系统中的突现拓扑激发
DOI：
10.1103/physrevb.91.094426
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发表时间：
2015-02
影响因子：
3.7
通讯作者：
vik, Anders W.
中科院分区：
文献类型：
--
作者：
Shao, Hui;Guo, Wenan;S;vik, Anders W.
我们研究的拓扑（缠绕数）激发的衰减机制，由于在二维价键固态的有限尺寸效应，实现在一个$S=1/2$自旋模型（$J$-$Q$模型）和研究使用投影机蒙特卡罗模拟的价键的基础上。绕组数为$的拓扑激励|W|>0$包含畴壁，由于在波函数中出现长价键而不稳定，这与量子二聚体模型的有效描述不同。我们发现，在虚时间的缠绕数的生命时间发散的系统长度$L$的幂。可以在该时间内计算能量（即，它在缠绕数衰减之前向“准本征值”收敛）并且对于大的$L$与在具有强制畴壁的边界修改的开放晶格中计算的畴壁能量一致。构建一个简化的两态模型，并使用从模拟的实时行为作为输入，我们发现，在初始绕组扇区的实时衰减率是指数L $小。因此，缠绕数迅速成为一个定义良好的大型系统的守恒量子数，支持通过计算能量准本征值得出的结论。包括海森堡交换相互作用，使系统的量子临界点分离的价键固体从反铁磁基态（假定的“解除限制”量子临界点），我们也可以收敛的畴壁能量在这里，并发现它衰减的系统大小的幂律。因此，缠绕数在临界点也是一个涌现量子数，所有缠绕数扇区在热力学极限下都退化。这支持了用U（1）规范场理论对临界点的描述。
We study the mechanism of decay of a topological (winding-number) excitation due to finite-size effects in a two-dimensional valence-bond solid state, realized in an $S=1/2$ spin model ($J$-$Q$ model) and studied using projector Monte Carlo simulations in the valence bond basis. A topological excitation with winding number $|W|>0$ contains domain walls, which are unstable due to the emergence of long valence bonds in the wave function, unlike in effective descriptions with the quantum dimer model. We find that the life time of the winding number in imaginary time diverges as a power of the system length $L$. The energy can be computed within this time (i.e., it converges toward a "quasi-eigenvalue" before the winding number decays) and agrees for large $L$ with the domain-wall energy computed in an open lattice with boundary modifications enforcing a domain wall. Constructing a simplified two-state model and using the imaginary-time behavior from the simulations as input, we find that the real-time decay rate out of the initial winding sector is exponentially small in $L$. Thus, the winding number rapidly becomes a well-defined conserved quantum number for large systems, supporting the conclusions reached by computing the energy quasi-eigenvalues. Including Heisenberg exchange interactions which brings the system to a quantum-critical point separating the valence-bond solid from an antiferromagnetic ground state (the putative "deconfined" quantum-critical point), we can also converge the domain wall energy here and find that it decays as a power-law of the system size. Thus, the winding number is an emergent quantum number also at the critical point, with all winding number sectors becoming degenerate in the thermodynamic limit. This supports the description of the critical point in terms of a U(1) gauge-field theory.