Publications (3)0 Total impact
ABSTRACT: We study three dimensional insulators with inversion symmetry, in which other
point group symmetries, such as time reversal, are generically absent. Their
band topology is found to be classified by the parities of occupied states at
time reversal invariant momenta (TRIM parities), and by three Chern numbers.
The TRIM parities of any insulator must satisfy a constraint: their product
must be +1. The TRIM parities also constrain the Chern numbers modulo two. When
the Chern numbers vanish, a magneto-electric response parameterized by "theta"
is defined and is quantized to theta= 0, 2pi. Its value is entirely determined
by the TRIM parities. These results may be useful in the search for magnetic
topological insulators with large theta. A classification of inversion
symmetric insulators is also given for general dimensions. An alternate
geometrical derivation of our results is obtained by using the entanglement
spectrum of the ground state wave-function.
ABSTRACT: 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 topology. The entanglement spectrum has been proposed as
a ground state property that captures characteristic edge excitations. Here we
study the entanglement spectrum for topological band insulators. We first show
that insulators with topological surface states will necessarily also have
protected modes in the entanglement spectrum. Surprisingly, however, the
converse is not true. Protected entanglement modes can also appear for
insulators without physical surface states, in which case they capture a more
elusive property. This is illustrated by considering insulators with only
inversion symmetry. Inversion is shown to act in an unusual way, as an
antiunitary operator, on the entanglement spectrum, leading to this protection.
The entanglement degeneracies indicate a variety of different phases in
inversion symmetric insulators, and these phases are argued to be robust to the
introduction of interactions.
ABSTRACT: Topological band insulators are usually characterized by symmetry-protected surface modes or quantized linear-response functions (like Hall conductance). Here we present a way to characterize them based on certain bulk properties of just the ground-state wave function, specifically, the properties of its entanglement spectrum. We prove that whenever protected surface states exist, a corresponding protected “mode” exists in the entanglement spectrum as well. Besides this, the entanglement spectrum sometimes succeeds better at indicating topological phases than surface states. We discuss specifically the example of insulators with inversion symmetry which is found to act as an antiunitary symmetry on the entanglement spectrum. A Kramers degeneracy can then arise even when time-reversal symmetry is absent. This degeneracy persists for interacting systems. The entanglement spectrum is therefore a promising tool to characterize topological band insulators and superconductors beyond the free-particle approximation.
Phys. Rev. B. 82(24).