Related papers: Low-lying Dirac eigenmodes and monopoles in 3+1D c…
We analyze a generalized Dirac system, where the dispersion along the $k_{x}$ and $k_{y}$ axes is $N$-th power and linear along the $k_{z}$ axis. When we apply magnetic field, there emerge $N$ monopole-antimonopole pairs beyond a certain…
In the presence of the charged impurities, we study the weak localization (WL) effect by evaluating the quantum interference correction (QIC) to the conductivity of Dirac fermions in graphene. With the inelastic scattering rate due to…
We discuss the proximate phases of a three-dimensional system with Dirac-like dispersion. Using the cubic lattice with plaquette $\pi$-flux as a model, we find, among others phases, a chiral topological insulator and singlet topological…
We give analytical and numerical solutions for the zero modes of the Dirac operator in topological SU(2) gauge backgrounds at nonzero chemical potential. Continuation from imaginary to real chemical potential is used to systematically…
We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a…
In recent years, two-dimensional Dirac materials patterned with a superlattice structure have emerged as a rich platform for exploring correlated and topological quantum matter. In this work, we propose that by subjecting Dirac electrons to…
In the deconfinement phase of quenched SU(2) Yang-Mills theory the spectrum and localization properties of the eigenmodes of the overlap Dirac operator with antiperiodic boundary conditions are strongly dependent on the sign of the average…
We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T=0 and T\neq 0, in the case of…
When two layers of two-dimensional materials are assembled with a relative twist, moir\'e patterns arise, inducing a tremendous wealth of exotic phenomena. In this work, we consider twisting two triangular lattices hosting Dirac quantum…
The quark number density at finite imaginary chemical potential is investigated in the lattice QCD using the Dirac-mode expansion. We find the analytical formula of the quark number density in terms of the Polyakov loop in the large quark…
The structure of QCD vacuum can be studied from first principles using lattice-regularized theory. This line of research entered a qualitatively new phase recently, wherein the space-time structure (at least for some quantities) can be…
The low-lying eigenmodes of the Dirac operator associated with typical gauge field configurations in QCD encode, among other low-energy properties, the physics behind the solution to the $U_A(1)$ problem (i.e. the origin of the $\eta'$…
Low-lying Dirac modes become localized at the finite-temperature transition in QCD and other gauge theories, indicating a strong connection between localization and deconfinement. This phenomenon can be understood through the "sea/islands"…
I discuss recent results on the relation between the localisation of low-lying Dirac eigenmodes, the restoration of chiral symmetry, and deconfinement in QCD and QCD-like models, providing evidence of a close connection between the three…
We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as…
We investigate several examples of Yang-Mills gauge configurations containing center vortex structures, including intersection points between vortices and nontrivial color structures residing on the vortex world-surfaces. Various…
We study the electronic structure and the phase diagram of non-interacting fermions confined to hexagonal optical lattices. In the first part, we compare the properties of Dirac points arising in the eigenspectrum of either honeycomb or…
We show that the phases of the 4-dimensional compact U(1) lattice gauge theory are unambiguously characterized by the topological properties of minimal Dirac sheets as well as of monopole currents lines. We obtain the minimal sheets by a…
The lowest eigenmodes of the Dirac operator are related to the dynamical breaking of the chiral symmetry in Quantum Chromodynamics (QCD). In our work we construct quark propagators which exclude a varying number of the lowest Dirac…
We prove the existence of exponentially accurate quasimodes using the square of the Dirac operator on the Schwarzschild-Anti-de Sitter spacetime and the Agmon estimates. We then deduce a logarithmic lower bound for the local energy decay of…