@article{WOS:000620345900004,
 abstract = {Symmetry plays an important role in the topological band theory to
remedy the eigenstates' gauge obstruction at the cost of a symmetry
anomaly and zero-energy boundary modes. One can also make use of the
symmetry to enumerate the topological invariants-giving a symmetry
classification table. Here we consider various topological phases
protected by different symmetries and examine how the corresponding
topological invariants evolve once the protecting symmetry is
spontaneously lost. To our surprise, we find that the topological
invariants and edge states can sometimes be robust to symmetry-breaking
quantum orders. This topological robustness persists as long as the
mean-field Hamiltonian in a symmetry-breaking ordered phase maintains
its adiabatic continuity to the noninteracting Hamiltonian. For example,
for a time-reversal symmetric topological phase in 2+1 dimensions, we
show that the Z(2) time-reversal polarization continues to be a good
topological invariant even after including distinct time-reversal
breaking order parameters. Similar conclusions are drawn for various
other symmetry-breaking cases. Finally, we discuss that the change in
the internal symmetry associated with the spontaneous symmetry breaking
has to be accounted for to reinstate the topological invariants into the
expected classification table.},
 article-number = {075139},
 author = {Raj, Arpit and Banerjee, Nepal and Das, Tanmoy},
 doi = {10.1103/PhysRevB.103.075139},
 eissn = {2469-9969},
 issn = {2469-9950},
 journal = {PHYSICAL REVIEW B},
 month = {FEB 22},
 number = {7},
 title = {Rigidity of topological invariants to symmetry breaking},
 unique-id = {WOS:000620345900004},
 volume = {103},
 year = {2021}
}