84 research outputs found
Hidden-symmetry-protected topological phases on a one-dimensional lattice
We demonstrate the existence of topologically nontrivial phase in a
one-dimensional fermionic lattice system subjected to synthetic gauge fields,
which is beyond the standard Altland-Zirnbauer classification of topological
insulators. The topological phase can be characterized by the presence of
degenerate zero-mode edge states or a quantized Berry phase of the occupied
Bloch band. By analyzing symmetries of the system, we identify that the
topological phase and zero-mode edge states are protected by two hidden
symmetries. An extended model with hidden symmetry breaking is also studied in
order to reveal the effect of hidden symmetries on the symmetry protected
topological phase.Comment: 6 pages, 5 figure
Topological invariants for phase transition points of one-dimensional topological systems
We study topological properties of phase transition points of two
topologically non-trivial classes (D and DIII) in one dimension
by assigning a Berry phase defined on closed circles around the gap closing
points in the parameter space of momentum and a transition driving parameter.
While the topological property of the system is generally
characterized by a topological invariant, we identify that it
has a correspondence to the quantized Berry phase protected by the
particle-hole symmetry, and then give a proper definition of Berry phase to the
phase transition point. By applying our scheme to some specific models of class
D and DIII, we demonstrate that the topological phase transition can be well
characterized by the Berry phase of the transition point, which reflects the
change of Berry phases of topologically different phases across the phase
transition point.Comment: 6 pages, 5 figure
Winding numbers of phase transition points for one-dimensional topological systems
We study topological properties of phase transition points of one-dimensional
topological quantum phase transitions by assigning winding numbers defined on
closed circles around the gap closing points in the parameter space of momentum
and a transition driving parameter, which overcomes the problem of ill
definition of winding numbers on the transition points. By applying our scheme
to the extended Kitaev model and extended Su-Schrieffer-Heeger model, we
demonstrate that the topological phase transition can be well characterized by
winding numbers of transition points, which reflect the change of the winding
number of topologically different phases across the phase transition points.Comment: 5 pages, 5 figure
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