Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
复制标题
拓扑有序波函数中本征符号的非厄米效应
DOI：
10.1038/s42005-020-00479-y
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发表时间：
2020
影响因子：
5.5
通讯作者：
Guang
中科院分区：
文献类型：
--
作者：
Qi Zhang;Wen;Ziqiang Wang;Guang
多体波函数中的负号在量子力学中扮演着重要的角色，因为干涉依赖于相反符号的幅度之间的抵消。双Semion模型的基态波函数包含任何局部变换都不能去除的负号。在这里，我们研究这些内在负号的量子效应。通过在张量网络表示中提出一个一般的双半离子波函数，我们证明了它的范数可以映射到具有虚相互作用的三角晶格Ashkin-Teller模型的配分函数。我们使用数值张量网络方法来求解这个具有宇称-时间对称性的非厄米模型，并确定了一个整体相图。特别地，我们发现了由非么正共形场理论描述的稠密环相和由配分函数的零点表征的宇称时对称破缺相。因此，我们的工作建立了拓扑波函数中的内禀符号与奇偶时间对称非厄米统计模型中的非酉相之间的联系。虽然波函数中的负号在多体量子力学中扮演着相关的角色，但它们对物质拓扑有序相的性质的物理影响仍然不清楚。在这里，作者用张量网络方法证明了双Semion模型的本征负号是相图中发现的非酉相和非酉相的原因。
Negative signs in many-body wavefunctions play an important role in quantum mechanics because interference relies on cancellation between amplitudes of opposite signs. The ground-state wavefunction of double semion model contains negative signs that cannot be removed by any local transformation. Here we study the quantum effects of these intrinsic negative signs. By proposing a generic double semion wavefunction in tensor network representation, we show that its norm can be mapped to the partition function of a triangular lattice Ashkin-Teller model with imaginary interactions. We use numerical tensor-network methods to solve this non-Hermitian model with parity-time symmetry and determine a global phase diagram. In particular, we find a dense loop phase described by non-unitary conformal field theory and a parity-time-symmetry breaking phase characterized by the zeros of the partition function. Therefore, our work establishes a connection between the intrinsic signs in the topological wavefunction and non-unitary phases in the parity-time-symmetric non-Hermitian statistical model. While negative signs in wave functions are known to play a relevant role in many-body quantum mechanics, their physical consequences on the nature of topologically ordered phases of matter is still unclear. Here, the authors use tensor network methods to show that the intrinsic negative signs of the double semion model are responsible for the non-unitary phases and non-unitary phase transitions found in the phase diagram.
DOI：
10.48550/arxiv.0912.3272
发表时间：
2009
期刊：
--
影响因子：
--
作者：
Castelnovo C
通讯作者：
Castelnovo C