Symmetric Mass Generation of K\"ahler-Dirac Fermions from the Perspective of Symmetry-Protected Topological Phases

We describe how to construct chiral fermion mass terms using Dirac-Kahler (DK) spinors. Classical massive DK spinors are shown to be equivalent to four generations of Dirac spinors with equal mass coupled to a background U(2,2) gauge field. Quantization breaks U(2,2) to U(2)xU(2), lifts mass spectrum degeneracy, and generates a non-trivial mass mixing matrix.

We consider the $Sp(4)$ gauge theory coupled to $N_f=2$ fundamental and $n_f=3$ antisymmetric flavours of Dirac fermions in four dimensions. This theory serves as the microscopic origin for composite Higgs models with $SU(4)/Sp(4)$ coset, supplemented by partial top compositeness. We study numerically its lattice realisation, and couple the fundamental plaquette action to Wilson-Dirac fermions in mixed representations, by adopting a (rational) hybrid Monte Carlo method, to pe...

Using a simple three dimensional lattice four-fermion model we argue that massless fermions can become massive due to interactions without the need for any spontaneous symmetry breaking. Using large scale Monte Carlo calculations within our model, we show that this non-traditional mass generation mechanism occurs at a second order quantum critical point that separates phases with the same symmetries. Universality then suggests that the new origin for the fermion mass should b...

Kondo insulators are primary candidates in the search for strongly correlated topological quantum phases, which may host topological order, fractionalization, and non-Abelian statistics. Within some Kondo insulators, the hybridization gap is predicted to protect a nontrivial topological invariant and to harbor emergent heavy Dirac fermion surface modes. We use high-energy-resolution spectroscopic imaging in real and momentum space on the Kondo insulator, SmB$_6$. On cooling t...

We show that the effective action that results from integrating out massive Kaehler-Dirac fermions propagating on a curved three dimensional space is a topological gravity theory of Chern-Simons type. In the presence of a domain wall, massless, two dimensional Kaehler-Dirac fermions appear that are localized to the wall. Potential gravitational anomalies arising for these domain wall fermions are cancelled via anomaly inflow from the bulk gravitational theory. We also study t...

We utilize the topological holographic framework to characterize and gain insights into the nature of quantum critical points and gapless phases in fermionic quantum systems. Topological holography is a general framework that describes the generalized global symmetry and the symmetry charges of a local quantum system in terms of a slab of a topological order, termed as the symmetry topological field theory (SymTFT), in one higher dimension. In this work, we consider a general...

We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d boundary state of 4d SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries, namely the loop excitations of these topological orders car...

A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct symmetry algebra. As a prominent example, the spacetime inversion symmetry $PT$ satisfies $(PT)^2=\pm 1$ for spinless/spinful systems, and each class features unique topological phases. Here, we reveal a possibility to switch the two fundamenta...

We consider a model of Dirac fermions in $2+1$ dimensions with dynamically generated, anticommuting SO(3) N\'eel and Z$_2$ Kekul\'e mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the N\'eel and Kekul\'e phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While...

We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, and three dimensions. By working out this classification, on the one hand, we demonstrate the recently proposed correspondence principle between crystalline topological phases and those with internal symmetries through explicit block-state constructions. We find that for the precise correspondence to hold it is n...