Related papers: Microscopic lattice model for quartic semi-Dirac f…
In this paper I construct the naive lattice Dirac Hamiltonian describing the propagation of fermions in a generic 2D optical metric for different lattice and flux-lattice geometries. First, I apply a top-down constructive approach that we…
In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…
We consider the role of spontaneous lattice symmetry breaking in strongly interacting two dimensional Dirac systems. The fermion induced quantum (multi-)criticality is described by Dirac fermions coupled to a dynamical order parameter that…
On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate…
We review recent results concerning the evolution of fermionic systems. We are interested in the mean field regime, where particles experience many weak collisions. For fermions, the mean field regime is naturally linked with a…
Quantum mechanics and relativity in the continuum imply the well known spin-statistics connection. However for particles hopping on a lattice, there is no such constraint. If a lattice model yields a relativistic field theory in a continuum…
Consequences of different discretizations of the two-dimensional Dirac operator on low energy properties (e.g., the number of nodes) and their relations to gauge properties are discussed. Breaking of the gauge invariance was suggested in a…
We combine a pair of independent Weyl fermions to compose a Dirac fermion on the four-dimensional Euclidean lattice. The obtained Dirac operator is antihermitian and does not reproduce anomaly under the usual chiral transformation. To…
In solids containing elements with f orbitals, the interaction between f-electron spins and those of itinerant electrons leads to the development of low-energy fermionic excitations with a heavy effective mass. These excitations are…
Phase transitions in systems described by Bose-Fermi-Hubbard model on a lattice with two nonequivalent sublattices are investigated in this work. The case of hard-core bosons is considered and pseudospin formalism is used. Phase diagrams…
We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting the N\'{e}el state using fractionalized degrees of freedom typically inherent to quantum spin liquids. In particular we consider a long-range…
We describe an experimental protocol for introducing spin-dependent lattice structure in a cold atomic fermi gas using lasers. It can be used to realize Hubbard models whose hopping parameters depend on spin and whose interaction strength…
We study the behavior of Dirac fermions in the presence of electron correlation in a nonsymmorphic Kondo lattice system, CeAgSb2 employing high-resolution angle-resolved photoemission spectroscopy and first-principles calculations.…
The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair…
Searching for new states of matter and unusual quasiparticles in emerging materials and especially low-dimensional systems is one of the major trends in contemporary condensed matter physics. Dirac materials, which host quasiparticles which…
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
We review recent results on lattice models for spin-less fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to a model possessing supersymmetry. In the 1D case, this model displays…
We construct a model in which four dimensional chiral fermions arise on the boundaries of a five dimensional lattice with free boundary conditions in the fifth direction. The physical content is similar to Kaplan's model of domain wall…
We study theoretically the properties of the interacting Dirac liquid, a novel three-dimensional many-body system which was recently experimentally realized and in which the electrons have a chiral linear relativistic dispersion and a…
In a recent paper, Creutz has given a new action describing two species of Dirac fermions with exact chiral symmetry on the lattice. This action depends on a parameter which may be fixed at a certain value in order to get the right…