Current browse context:
cond-mat.str-el
Change to browse by:
References & Citations
Condensed Matter > Strongly Correlated Electrons
Title: Theory of weak symmetry breaking of translations in $\mathbb{Z}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice $\mathbb{Z}_2$ charge-flux attachment
(Submitted on 22 Dec 2020 (v1), last revised 17 May 2021 (this version, v2))
Abstract: We study $\mathbb{Z}_2$ topologically ordered states enriched by translational symmetry by employing a recently developed 2D bosonization approach that implements an exact $\mathbb{Z}_2$ charge-flux attachment in the lattice. Such states can display `weak symmetry breaking' of translations, in which both the Hamiltonian and ground state remain fully translational invariant but the symmetry is `broken' by its anyon quasi-particles, in the sense that its action maps them into a different super-selection sector. We demonstrate that this phenomenon occurs when the fermionic spinons form a weak topological superconductor in the form of a 2D stack of 1D Kitaev wires, leading to the amusing property that there is no local operator that can transport the $\pi$-flux quasi-particle across a single Kitaev wire of fermonic spinons without paying an energy gap in spite of the vacuum remaining fully translational invariant. We explain why this phenomenon occurs hand-in-hand with other previously identified peculiar features such as ground state degeneracy dependence on the size of the torus and the appearance of dangling boundary Majorana modes in certain $\mathbb{Z}_2$ topologically ordered states. Moreover, by extending the $\mathbb{Z}_2$ charge-flux attachment to open lattices and cylinders, we construct a plethora of exactly solvable models providing an exact description of their dispersive Majorana gapless boundary modes. We also review the $\mathbb{Z}\times (\mathbb{Z}_2)^3$ classification of 2D BdG Hamiltonians (Class D) enriched by translational symmetry and provide arguments on its robust stability against interactions and self-averaging disorder that preserves translational symmetry.
Submission history
From: Peng Rao [view email][v1] Tue, 22 Dec 2020 19:00:04 GMT (727kb,D)
[v2] Mon, 17 May 2021 12:26:09 GMT (754kb,D)
Link back to: arXiv, form interface, contact.