Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Continuous Subdimensional Quantum Phase Transitions via Dualities
Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Continuous Subdimensional Quantum Phase Transitions via Dualities
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来自最近邻双自旋相互作用的分形拓扑序和通过对偶性的连续亚维量子相变
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Yong Baek Kim
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作者：
K. Slagle;Yong Baek Kim
分形拓扑序描述了一种显著的物质相，它可以用具有约束动力学的分形激励和基态简并来表征，该简并随系统在三维环面上的长度呈指数增长。然而，先前的模型显示这种顺序需要许多自旋相互作用，这在实际材料或冷原子系统中可能很难实现。在这项工作中，我们提出了一个更实际的模型，它具有所谓的x立方分形拓扑顺序，但只需要最近邻的自旋相互作用。该模型生活在三维蜂窝状晶格上，每个位点上有1到2个自旋1/2自由度，单元格有6个位点。该模型由两个正交的$Z_2$拓扑有序基塔耶夫蜂窝层组成，它们通过双自旋相互作用耦合在一起。还证明了四自旋相互作用可以代替稳定3+1D $Z_2$拓扑秩序。我们还发现了模型中四个连续相变的对偶描述；其中两个描述了从x立方相到一个或两个2+1D $Z_2$拓扑顺序的正交解耦堆栈相的相变，分别映射到1+1D网格或2+1D横向场Ising模型堆栈的连续（无序到有序）相变。因此，这些相变具有亚维（1+1D或2+1D）动力学，在某些方向上具有无限相关长度，而在其他方向上具有有限相关长度。
Fracton topological order describes a remarkable phase of matter which can be characterized by fracton excitations with constrained dynamics and a ground state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of 6 sites. The model is constructed from two orthogonal stacks of $Z_2$ topologically ordered Kitaev honeycomb layers, which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D $Z_2$ topological order. We also find dual descriptions of four continuous phase transitions in our model; two of which describe phase transitions out of the X-cube phase to phases of either one or two orthogonal decoupled stacks of 2+1D $Z_2$ topological order, which are mapped to continuous (disorder to order) phase transitions of a grid of 1+1D or stack of 2+1D transverse-field Ising models, respectively. Therefore, these phase transitions have subdimensional (1+1D or 2+1D) dynamics with infinite correlation length in some directions, but finite correlation length in others.