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We study the entanglement spectrum of noninteracting band insulators, which can be computed from the two-point correlation function, when restricted to one part of the system. In particular, we analyze a type of partitioning of the system that maintains its full translational symmetry, by tracing over a subset of local degrees of freedom, such as sublattice sites or spin orientations. The corresponding single-particle entanglement spectrum is the band structure of an entanglement Hamiltonian in the Brillouin zone. We find that the hallmark of a nontrivial topological phase is a gapless entanglement spectrum with an entanglement Fermi surface. Furthermore, we derive a relation between the entanglement spectrum and the quantum geometry of Bloch states contained in the Fubini-Study metric. The results are illustrated with lattice models of Chern insulators and Z_2 topological insulators.
How do we uniquely identify a quantum phase, given its ground state wave-function? This is a key question for many body theory especially when we consider phases like topological insulators, that share the same symmetry but differ at the level of top
Quantum field theories have a rich structure in the presence of boundaries. We study the groundstates of conformal field theories (CFTs) and Lifshitz field theories in the presence of a boundary through the lens of the entanglement entropy. For a fam
We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite non-zero Chern number. Using an exactly solv
The theory of topological insulators and superconductors has mostly focused on non-interacting and gapped systems. This review article discusses topological phases that are either gapless or interacting. We discuss recent progress in identifying gapl
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities play complementary roles: the Fub