Characterization of monofloral honeys by ash contents through a hierarchical design (original) (raw)
A local and integrable lattice regularization of the massive Thirring model
Nuclear Physics B, 1995
The light{cone lattice approach to the massive Thirring model is reformulated using a local and integrable lattice Hamiltonian written in terms of discrete fermi elds. Several subtle points concerning boundary conditions, normal{ordering, continuum limit, nite renormalizations and decoupling of fermion doublers are elucidated. The relations connecting the six{vertex anisotropy and the various coupling constants of the continuum are analyzed in detail. IFUM{510{FT UPRF{95{424
The phase diagram of the three dimensional Thirring model
Physics Letters B, 1999
We present Monte Carlo simulation results for the three dimensional Thirring model on moderate sized lattices using a hybrid molecular dynamics algorithm which permits an odd or non-integer number N f of fermion flavors. We find a continuous chiral symmetry breaking transition for N f ≃ 3 with critical exponents consistent with expectations from previous studies. For N f = 5 the order of the transition is difficult to determine on the lattice sizes explored. We present a phase diagram for the model in the (1/g 2 , N f ) plane and contrast our findings with expectations based on approximate solutions of the continuum Schwinger-Dyson equations.
Physical Review B, 2015
We investigate the phase diagram of spinless fermions with nearest and next-nearest neighbour densitydensity interactions on the honeycomb lattice at half-filling. Using Exact Diagonalization techniques of the full Hamiltonian and constrained subspaces, combined with a careful choice of finite-size clusters, we determine the different charge orderings that occur for large interactions. In this regime we find a two-sublattice Néel-like state, a charge modulated state with a tripling of the unit cell, a zigzag phase and a novel charge ordered states with a 12 site unit cells we call Néel domain wall crystal, as well as a region of phase separation for attractive interactions. A sizeable region of the phase diagram is classically degenerate, but it remains unclear whether an order-by-disorder mechanism will lift the degeneracy. For intermediate repulsion we find evidence for a Kekulé or plaquette bond-order wave phase. We also investigate the possibility of a spontaneous Chern insulator phase (dubbed topological Mott insulator), as previously put forward by several mean-field studies. Although we are unable to detect convincing evidence for this phase based on energy spectra and order parameters, we find an enhancement of current-current correlations with the expected spatial structure compared to the non-interacting situation. While for the studied t−V1−V2 model the phase transition to the putative topological Mott insulator is preempted by the phase transitions to the various ordered states, our findings might hint at the possibility for a topological Mott insulator in an enlarged Hamiltonian parameter space, where the competing phases are suppressed.
Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice
EPL (Europhysics Letters), 2011
We investigate a spinless Fermi gas trapped in a honeycomb optical lattice with attractive nearest-neighbor interactions. At zero temperature, mean-field theory predicts three quantum phase transitions, two being topological. At low interactions, the system is semi-metallic. Increasing the interaction further, the semi-metal destabilizes into a fully gapped superfluid. At larger interactions, a topological transition occurs and this superfluid phase becomes gapless, with Dirac-like dispersion relations. Finally, increasing again the interaction, a second topological transition occurs and the gapless superfluid is replaced by a different fully gapped superfluid phase. We analyze these different quantum phases as the temperature and the lattice filling are varied.
Nucl Phys B, 1994
A system of electrons in the two-dimensional honeycomb lattice with Coulomb interactions is described by a renormalizable quantum field theory similar but not equal to QED 3. Renormalization group techniques are used to investigate the infrared behavior of the system that flows to a fixed point with non-Fermi liquid characteristics. There are anomalous dimensions in the ferionic observables, no quasiparticle pole, and anomalous screening of the Coulomb interaction. These results are robust as the Fermi level is not changed by the interaction. The system resembles in the infrared the one-dimensional Luttinger liquid.
Theory of interacting electrons on the honeycomb lattice
Physical Review B, 2009
The general low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac four-component field dictated by the lattice is identified as D2 × Uc(1)×time reversal, where D2 is the dihedral group, and Uc(1) is a subgroup of the SUc(2) "chiral" group of the non-interacting Lagrangian, that represents translations in Dirac language. The Lagrangian describing spinless particles respecting this symmetry is parameterized by six independent coupling constants. We show how first imposing the rotational, then Lorentz, and finally chiral symmetry to the quartic terms -in conjunction with the Fierz transformations -eventually reduces the set of couplings to just two, in the "maximally symmetric" local interacting theory. We identify the two critical points in such a Lorentz and chirally symmetric theory as describing metalinsulator transitions into the states with either time-reversal or chiral symmetry being broken. The latter is proposed to govern the continuous transition in both the Thirring and Nambu-Jona-Lasinio models in 2+1 dimensions and with a single Dirac field. In the site-localized, "atomic", limit of the interacting Hamiltonian, under the assumption of emergent Lorentz invariance, the low-energy theory describes the continuous transitions into the insulator with either a finite Haldane's (circulating currents) or Semenoff's (staggered density) masses, both in the universality class of the Gross-Neveu model. The simple picture of the metal-insulator transition on a honeycomb lattice emerges at which the residue of the quasiparticle pole at the metallic, and the mass-gap in the insulating phase both vanish continuously as the critical point is approached. In contrast to these two critical quantities, we argue that the Fermi velocity is non-critical as a consequence of the dynamical exponent being fixed to unity by the emergent Lorentz invariance near criticality. Possible effects of the long-range Coulomb interaction, and the critical behavior of the specific heat and conductivity are discussed.
Correspondence between a shaken honeycomb lattice and the Haldane model
Physical Review A
We investigate the correspondence between the tight-binding Floquet Hamiltonian of a periodically modulated honeycomb lattice and the Haldane model. We show that-though the two systems share the same topological phase diagram, as reported in a breakthrough experiment with ultracold atoms in a stretched honeycomb lattice [Jotzu et al., Nature 515, 237 (2014)]-the corresponding Hamiltonians are not equivalent, the one of the shaken lattice presenting a much richer structure.
Nuclear Physics B, 1994
A system of electrons in the two-dimensional honeycomb lattice with Coulomb interactions is described by a renormalizable quantum field theory similar but not equal to QED 3 . Renormalization group techniques are used to investigate the infrared behavior of the system that flows to a fixed point with non-Fermi liquid characteristics. There are anomalous dimensions in the fermionic observables, no quasiparticle pole, and anomalous screening of the Coulomb interaction. These results are robust as the Fermi level is not changed by the interaction. The system resembles in the infrared the one-dimensional Luttinger liquid. 1
Spectrum of the non-abelian phase in Kitaev’s honeycomb lattice model
Annals of Physics, 2008
The spectral properties of Kitaev's honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the 2 n -fold ground state degeneracy in the presence of 2n well separated vortices and the lifting of the degeneracy due to their short-range interactions. The calculations are performed on an infinite lattice. In addition to the analytic treatment, a numerical study of finite size systems is performed which is in exact agreement with the theoretical considerations. The general spectral properties of the non-abelian phase are considered for various finite toroidal systems.
Phase diagram for the Harper model of the honeycomb lattice
Journal of Physics: Condensed Matter, 2018
The Harper equation arising out of a tight-binding model of electrons on a honeycomb lattice subject to a uniform magnetic field perpendicular to the plane is studied. Contrasting and complementary approaches involving von Neumann entropy, fidelity, fidelity susceptibility, multifractal analysis are employed to characterize the phase diagram. The phase diagram consists of three phases: two metallic phases and an insulating phase. A variant model where next nearest neighbor hopping is included, exhibits a mobility edge and does not allow for a simple single phase diagram characterizing all the eigenstates.