Communications in Mathematical Physics From String Nets to Nonabelions
Communications in Mathematical Physics From String Nets to Nonabelions
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从弦网到非阿贝尔负数的数学物理通信
DOI：
10.1088/0305-4470/35/50/301
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Zhenghan Wang
中科院分区：
文献类型：
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作者：
L. Fidkowski;M. Freedman;C. Nayak;K. Walker;Zhenghan Wang
我们讨论了晶格上由一组弦网所张成的希尔伯特空间，即三价图。我们提出了这样一个希尔伯特空间可以成为具有短程相互作用的晶格上量子自旋模型的低能子空间的一些途径。然后，我们解释了作用于该弦网希尔伯特空间的哈密顿量必须满足的条件，以便系统处于DFib（双斐波那契）拓扑相，即在低能量下用SO(3)3 × SO(3)3双Chern-Simons理论来描述，并使用适当的非阿贝尔统计来控制低空准粒子激发（非阿贝尔）的编织。利用弦网波函数描述了该相位的性质。我们的讨论是通过弦网波函数到色多项式和波茨模型的映射来进行的。
We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for the system to be in the DFib (Doubled Fibonacci) topological phase, that is, be described at low energy by an SO(3)3 × SO(3)3 doubled Chern-Simons theory, with the appropriate non-abelian statistics governing the braiding of the low-lying quasiparticle excitations (nonabelions). Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefunctions to the chromatic polynomial and the Potts model.