80 citations · 480 across the 35 of their papers we have counts for
37 papers
Consistent symmetry breaking and topological phases
Yuezhao Li, Guo Chuan Thiang
Operators invariant under a symmetry group are also invariant under any finite-index subgroup. The equivariant indices of such operators must be consistent under symmetry breaking.…
Proof of Kitaev determinant trivialization conjecture
Guo Chuan Thiang
Using ideas from algebraic -theory, we prove that a simple and naturally applicable criterion of Kitaev suffices to trivialize the Fredholm determinant of a multiplicative commu…
Large-scale quantization of trace I: Finite propagation operators
Matthias Ludewig, Guo Chuan Thiang
Inspired by parallel developments in coarse geometry in mathematics and exact macroscopic quantization in physics, we present a family of general trace formulae which are universal…
Topological Semimetals
Guo Chuan Thiang
We review the differential topology underlying the topological protection of energy band crossings in Weyl semimetals, and how they lead to the experimental signature of surface Fe…
Fock space: A bridge between Fredholm index and the quantum Hall effect
Guo Chuan Thiang, Jingbo Xia
We compute the quantized Hall conductance at various Landau levels by using the classic trace. The computations reduce to the single elementary one for the lowest Landau level. By…
Fractional index of Bargmann-Fock space and Landau levels
Guo Chuan Thiang
The lowest Landau level Hilbert space, or the Bargmann-Fock space, admits a quantized trace for the commutator of its position coordinate operators. We exploit the Carey-Pincus the…
Quantization of conductance and the coarse cohomology of partitions
Matthias Ludewig, Guo Chuan Thiang
We demonstrate how integer quantization of Hall conductance arises from the large-scale geometry of the sample. Specifically, the Hall conductance is a higher-trace pairing of the…
Topological edge states of 1D chains and index theory
Guo Chuan Thiang
We provide an elementary proof and refinement of a well-known idea from physics: a chiral-symmetric local Hamiltonian on a half-space has the same signed number of edge-localized s…
Bulk-interface correspondences for one dimensional topological materials with inversion symmetry
Guo Chuan Thiang, Hai Zhang
The interface between two materials described by spectrally gapped Hamiltonians is expected to host an in-gap interface mode, whenever a certain topological invariant changes acros…
Large-scale geometry obstructs localization
Matthias Ludewig, Guo Chuan Thiang
We explain the coarse geometric origin of the fact that certain spectral subspaces of topological insulator Hamiltonians are delocalized, in the sense that they cannot admit an ort…
Delocalized spectra of Landau operators on helical surfaces
Yosuke Kubota, Matthias Ludewig, Guo Chuan Thiang
On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely degenerate Landau levels. We consider surfaces with asymptotically co…
Topology in shallow-water waves: A spectral flow perspective
Clément Tauber, Guo Chuan Thiang
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter…
'Real' gerbes and Dirac cones of topological insulators
Kiyonori Gomi, Guo Chuan Thiang
A time-reversal invariant topological insulator occupying a Euclidean half-space determines a 'Quaternionic' self-adjoint Fredholm family. We show that the discrete spectrum data f…
Twisted crystallograpic T-duality via the Baum--Connes isomorphism
Kiyonori Gomi, Yosuke Kubota, Guo Chuan Thiang
We establish the twisted crystallographic T-duality, which is an isomorphism between Freed-Moore twisted equivariant K-groups of the position and momentum tori associated to an ext…
Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
Matthias Ludewig, Guo Chuan Thiang
We use coarse index methods to prove that the Landau Hamiltonian on the hyperbolic half-plane, and even on much more general imperfect half-spaces, has no spectral gaps. Thus the e…
The Fermi gerbe of Weyl semimetals
Alan Carey, Guo Chuan Thiang
In the gap topology, the unbounded self-adjoint Fredholm operators on a Hilbert space have third homotopy group the integers. We realise the generator explicitly, using a family of…
On spectral flow and Fermi arcs
Guo Chuan Thiang
We introduce spectral flow techniques to explain why the Fermi arcs of Weyl semimetals are topologically protected against boundary condition changes and perturbations. We first an…
Cobordism invariance of topological edge-following states
Matthias Ludewig, Guo Chuan Thiang
We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore…
Edge-following topological states
Guo Chuan Thiang
We prove that Chern insulators have topologically protected edge states which not only propagate unidirectionally along a straight line boundary, but also swerve around arbitrary-a…
Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves
Kei Yamamoto, Guo Chuan Thiang, Philipp Pirro +3
We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applicat…
Good Wannier bases in Hilbert modules associated to topological insulators
Matthias Ludewig, Guo Chuan Thiang
For a large class of physically relevant operators on a manifold with discrete group action, we prove general results on the (non-)existence of a basis of smooth well-localised Wan…
Crystallographic T-duality
Kiyonori Gomi, Guo Chuan Thiang
We introduce the notion of crystallographic T-duality, inspired by the appearance of -theory with graded equivariant twists in the study of topological crystalline materials. Be…
Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices
Kiyonori Gomi, Guo Chuan Thiang
A 2-torsion topological phase exists for Hamiltonians symmetric under the wallpaper group with glide reflection symmetry, corresponding to the unorientable cycle of the Klein bottl…
Topological phases on the hyperbolic plane: fractional bulk-boundary correspondence
Varghese Mathai, Guo Chuan Thiang
We study topological phases in the hyperbolic plane using noncommutative geometry and T-duality, and show that fractional versions of the quantised indices for integer, spin and an…