Related papers: Topological Phases in Neuberger-Dirac operator

We initiate the study of the effects of strongly-coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time reversal…

We discuss the construction and properties of an approximate solution of the Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac operator. In particular we study the behavior of its eigenmodes in smooth instanton…

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the…

We present a general approach to obtain effective field theories for topological crystalline insulators whose low-energy theories are described by massive Dirac fermions. We show that these phases are characterized by the responses to…

We write down a minimal basis for dimension-six gauge-invariant four-fermion operators, with some operator replacements with respect to previous ones which make it simpler for calculations. Using this basis we classify all four-fermion…

At stronger gauge-field couplings, the domain wall fermion (DWF) residual mass, a measure of chiral symmetry breaking, grows rapidly. This measure is largely due to near zero fermion eigenmodes of logarithm of the 4D transfer matrix along…

Topological phase transitions in band models are usually associated to the gap closing between the highest valance band and the lowest conduction band, which can give rise to different types of nodal structures, such as Dirac/Weyl points,…

We analyze general solutions of the Ginsparg-Wilson relation for lattice Dirac operators and formulate a necessary condition for such operators to have non-zero index in the topologically nontrivial background gauge fields.

The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by the massless Dirac fermion. We address the stability of this quantum critical…

We use the Riemann-Hilbert approach, together with string and Toda equations, to study the topological expansion in the quartic random matrix model. The coefficients of the topological expansion are generating functions for the numbers…

There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely related to obstructions to the existence of…

We investigate spontaneous chiral symmetry breaking in SU(N) gauge theories at large N using overlap fermions. The exact zero modes and the low-lying modes of the Dirac operator provide the tools to gain insight into the interplay between…

We investigate a chiral property of the domain-wall fermion (DWF) system using the four-dimensional hermitian Wilson-Dirac operator $H_W$. A formula expressing the Ward-Takahashi identity quark mass $m_{5q}$ with eigenvalues of this…

The phase diagrams of an arbitrary number $N_{\text{w}}$ of diagonally and perpendicularly coupled Su-Schrieffer-Heeger wires are identified. The diagonally coupled wires exhibit rich topological phase diagrams with insulating phases…

We propose a nonperturbative gauge invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d + 1 dimensions with quantum gauge fields that reside on one…

We analyze topological charge contributions from classical SU(2) center vortices with shapes of planes and spheres using different topological charge definitions, namely the center vortex picture of topological charge, a discrete version of…

The Dirac equation in $(2+1)$ dimensions on the toroidal surface is studied for a massless fermion particle under the action of external fields. Using the covariant approach based on general relativity, the Dirac operator stemming from a…

In this work we investigate non-Hermitian topological phase transitions using real-space edge states as a paradigmatic tool. We focus on the simplest non-Hermitian variant of the Su-Schrieffer-Hegger model, including a parameter that…

We show that topological phases with fractional excitations can occur in two-dimensional ultracold dipolar gases on a particular class of optical lattices. Due to the dipolar interaction and lattice confinement, a quantum dimer model…

We briefly review the overlap formalism for chiral gauge theories, the overlap Dirac operator for massless fermions and its connection to domain wall fermions. We describe properties of the overlap Dirac operator, and methods to implement…