Related papers: A topological state sum model for fermions on the …
We formulate real-space dynamical mean-field theory within scattering theory. Thereby the Friedel sum rule is derived for interacting lattice fermions at zero temperature.
The Sommerfield model with a massive vector field coupled to a massless fermion in 1+1 dimensions is an exactly solvable analog of a Bank-Zaks model. The "physics" of the model comprises a massive boson and an unparticle sector that…
We develop the integral calculus for quasi-standard smooth functions defined on the ring of Fermat reals. The approach is by proving the existence and uniqueness of primitives. Besides the classical integral formulas, we show the…
A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parameterised by a pivotal functor from a spherical fusion…
We present a microscopic model of interacting fermions where the ground state degeneracy is topologically protected. The model is based on a double-wire setup with local interactions in a particle number conserving setting. A compelling…
We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition…
The concept of topological fermions, including Weyl and Dirac fermions, stems from the quantum Hall state induced by a magnetic field, but the definitions and classifications of topological fermions are formulated without using magnetic…
Statistical mechanics and thermodynamics for ideal fractional exclusion statistics with mutual statistical interactions is studied systematically. We discuss properties of the single-state partition functions and derive the general form of…
We derive low-energy effective field theories for the quantum anomalous Hall and topological superconducting phases. The quantum Hall phase is realized in terms of free fermions with nonrelativistic dispersion relation, possessing a global…
Particle-vortex duality is a powerful theoretical tool that has been used to study bosonic systems. Here we propose an analogous duality for Dirac fermions in 2+1 dimensions. The physics of a single Dirac cone is proposed to be described by…
We demonstrate that summing up series of Feynman diagrams can yield unbiased accurate results for strongly-correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of non-relativistic…
We study strongly correlated fractional topological phases on a two-sphere threaded by a magnetic dipole field with globally vanishing flux. Solving the Dirac equation in this background produces spheroidal wavefunctions forming a highly…
A free fermion without doubler is formulated on 1+D dimensional discrete Minkowski space-time. The action is not hermitian but causes no harm. In 1+3 dimensional massless case the equation describes a single species of Dirac particle in the…
Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this work, we propose an alternative approach to assessing topologically induced edge states in free…
We present the construction of the partition function of 3-dimensional gravity in the Lorentzian regime as a state sum model over a triangulation. This generalize the work of Ponzano and Regge to the case of Lorentzian signature.
We report discovery of a topological Mott insulator in strongly-correlated Dirac semimetals. Such an interaction-driven topological state has been theoretically proposed but not yet observed with unbiased large scale numerical simulations.…
This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asymptotically for a large dimension of the group, for various…
We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic…
We investigate the quantization of pure U(1) and U(2) gauge theories in the vicinity of non-trivial ground state in four-dimensional Euclidean space-time. The main goal is to make the simultaneous consideration of many vacuums possible. It…
We consider a Wilson-Dirac operator with improved chiral properties. We show that, for arbitrarily rough gauge fields, it satisfies the index theorem if we identify the zero modes with the small real eigenvalues of the fermion operator and…