Related papers: Random-mass Dirac fermions in an imaginary vector …
The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions…
We summarize our recent investigations of lattice QCD with dynamical overlap fermions. We sketch algorithmic issues and our approach to solving them. We show our measurement of the topological susceptibility. We describe a computation of…
Quantum criticality within Dirac fermions harbors a plethora of exotic phenomena, attracting sustained attention in the past decades. Here, we explore the imaginary-time relaxation dynamics in a typical Dirac quantum criticality belonging…
We connect between the problem of thermodynamics of localized magnetic moments in a Dirac semimetal, the interaction with relativistic electrons leading to the effective ferromagnetic exchange between the moments, and the existing theories…
Particle fractionalization is believed to orchestrate the physics of many strongly correlated systems, yet its direct experimental detection remains a challenge. We propose a simple measurement for an ultracold matter system, in which…
This paper presents a theory of interaction-induced band-flattening in strongly correlated electron systems. We begin by illustrating an inherent connection between flat bands and index theorems, and presenting a generic prescription for…
In the previous paper we studied Dirac fermions in a non-Abelian random vector potential by using lattice supersymmetry. By the lattice regularization, the system of disordered Dirac fermions is defined without any ambiguities. We showed…
In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a…
A delocalization phenomenon is studied in a class of non-Hermitian random quantum-mechanical problems. Delocalization arises in response to a sufficiently large constant imaginary vector potential. The transition is related to depinning of…
We present quantum Lattice Boltzmann simulations of the Dirac equation for quantum-relativistic particles with random mass. By choosing zero-average random mass fluctuation, the simulations show evidence of localization and ultra-slow Sinai…
Let $x \in S^{n-1}$ be a unit eigenvector of an $n \times n$ random matrix. This vector is delocalized if it is distributed roughly uniformly over the real or complex sphere. This intuitive notion can be quantified in various ways. In these…
A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution…
I review how the phenomenology of localization applies to fermions in lattice gauge theory, present measurements of the localization length and other quantities, and discuss the consequences for things like the overlap kernel.
There is increased interest in time-dependent (non-autonomous) Hamiltonians, stemming in part from the active field of Floquet quantum materials. Despite this, dispersive time-decay bounds, which reflect energy transport in such systems,…
In the dilute instanton gas model of the QCD vacuum, one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues. Following Horvath, {\it et al.} we examine this question using…
The one-loop effective potential of a thermodynamic fermion loop under constant magnetic field is studied. As expected, it can be interpreted literally as a discretized sum of $(D-2)$-dimensional energy density above the Dirac sea.…
Local field effects on the rate of spontaneous emission and Lamb shift in a dense gas of atoms are discussed taking into account correlations of atomic center-of-mass coordinates. For this the exact retarded propagator in the medium is…
Random Dirac fermions in a two-dimensional space are studied numerically. We realize them on a square lattice using the $\pi$-flux model with random hopping. The system preserves two symmetries, the time-reversal symmetry and the symmetry…
We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density…
Effects of fermion-vacuum polarization by a singular configuration of an external static vector field are considered in (2 + 1)-dimensional spacetime. Expressions for the induced vacuum charge and magnetic flux are obtained.