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Topological crystalline insulators (TCIs) are nontrivial quantum phases ofmatter protected by crystalline (and other) symmetries. They are originallypredicted by band theories, so an important question is their stability underinteractions. In this paper, by directly studying the physical bulk propertiesof several band-theory-based nontrivial TCIs that are conceptually interestingand/or experimentally feasible, we show they are stable under interactions.These TCIs include (1) a weak topological insulator, (2) a TCI with a mirrorsymmetry and its time-reversal symmetric generalizations, (3) a doubledtopological insulator with a mirror symmetry, and (4) two TCIs withsymmetry-enforced-gapless surfaces. We describe two complementary methods thatallow us to determine the properties of the magnetic monopoles obtained bycoupling these TCIs to a U(1) gauge field. These methods involve studyingdifferent types of surface states of these TCIs. Applying these methods to ourexamples, we find all of them have nontrivial monopoles, which proves theirstability under interactions. Furthermore, we discuss two levels of relationsbetween these TCIs and symmetry enriched U(1) quantum spin liquids (QSLs).First, these TCIs are directly related to U(1) QSLs with crystallinesymmetries. Second, there is an interesting correspondence between U(1) QSLswith crystalline symmetries and U(1) QSLs with internal symmetries. Inparticular, the TCIs with symmetry-enforced-gapless surfaces are related to the"fractional topological paramagnets" introduced in Ref. 1 by Zou et al.

physical review. b./physical review. b

Bulk characterization of topological crystalline insulators: stability  under interactions and relations to symmetry enriched U(1) quantum spin  liquids