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Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions

机译:完整的通勤投影仪汉密尔顿人的互动对称保护的拓扑阶段的费米子

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摘要

Using the decorated domain wall procedure, we construct finite-depth local unitaries that realize fermionic symmetry-protected topological (SPT) phases. This results in explicit full commuting projector Hamiltonians, where "full" implies the fact that the ground state as well as all excited states of these Hamiltonians realize the nontrivial SPT phase. We begin by constructing explicit examples of 1+1D phases protected by the symmetry group G = Z(2)(T) x Z(2)(F), which also has a free fermion realization in class BDI, and by the symmetry group G = Z(4) x Z4(F), which does not. We then turn to 2+1D, and construct the square roots of the Levin-Gu bosonic SPT phase, protected by Z(2) x Z(2)(F) symmetry, in a concrete model of fermions and spins on the triangular lattice. Edge states and the anomalous symmetry action on them are explicitly derived. Although this phase has a free fermion representation as two copies of p + ip superconductors combined with their p - ip counterparts with a different symmetry charge, the full set of commuting projectors is only realized in the strongly interacting version, which also implies that it admits a many-body localized realization.
机译:使用装饰域墙壁程序,我们构建了有限深度的本地统一,实现了Fermionic对称保护的拓扑(SPT)阶段。这导致明确的完整通勤投影仪Hamiltonians,其中“完全”意味着地面状态以及这些哈密顿人的所有激动的国家实现了非竞争SPT阶段。我们首先构建由对称组G = Z(2)(T)×Z(2)(F)保护的1 + 1D相的明确示例,其在BDI类中也具有自由差异的Fermion实现,并由对称组g = z(4)x z4(f),其不。然后我们转到2 + 1d,并构建左沟玻色子SPT相的平方根,受z(2)x z(2)(f)对称的保护,在一个混凝土模型和三角形格子上的旋转。明确地派生了边缘状态和它们上的异常对称动作。虽然该阶段具有自由的FERMION表示作为与具有不同对称电荷的P-IP对应器的P + IP超导体的两个副本,但是整套通勤投影仪仅在强烈的交互版本中实现,这也意味着它承认许多身体的本地化实现。

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