Pairs of chiral quarks on the lattice from staggered fermions

A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces the four quark flavors described by the staggered fermion to two quark flavors; this pair can be taken as the up and down quarks in Lattice QCD. A domain wall formulation giving a truncation of this overlap construction is also outlined.     

QCD thermodynamics with dynamical overlap fermions

We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on _Nt=6$N_t=6$ and 8 lattices. All our runs are performed with fixed global topology. Our results are compared with staggered ones and a nice agreement is found.     

Topological susceptibility in lattice QCD with unimproved Wilson fermions

We address a long standing problem regarding topology in lattice simulations of QCD with unimproved Wilson fermions. Earlier attempt with unimproved Wilson fermions at β=5.6 to verify the suppression of topological susceptibility with decreasing quark mass (mq) was unable to unambiguously confirm the suppression. We carry out systematic calculations for two degenerate flavours at two different lattice spacings (β=5.6 and 5.8). The effects of quark mass, lattice volume and the lattice spacing on the spanning of different topological sectors are presented. We unambiguously demonstrate the suppression of the topological susceptibility with decreasing quark mass, expected from chiral Ward identity and chiral perturbation theory.     

A lattice Dirac operator for QCD with light dynamical quarks

In QCD chiral symmetry is explicitly broken by quark masses, the effect of which can be described reliably by chiral perturbation theory. Effects of explicit chiral symmetry breaking by the lattice regularisation of the Dirac operator, typically parametrised by the residual mass, should be negligible for almost all observables if the residual mass of the Dirac operator is much smaller than the quark mass. However, maintaining a small residual mass becomes increasingly expensive as the quark mass decreases towards the physical value and the continuum limit is approached. We investigate the feasibility of using a new approximately chiral Dirac operator with a small residual mass as an alternative to overlap and domain wall fermions for lattice simulations. Our Dirac operator is constructed from a Zolotarev rational approximation for the matrix sign function that is optimal for bulk modes of the hermitian kernel Dirac operator but not for the low-lying parts of its spectrum. We test our operator on various ³²³×64${32}^3\times 64$ lattices, comparing the residual mass and the performance of the Hybrid Monte Carlo algorithm at a similar lattice spacing and pion mass with a hyperbolic tangent operator as used by domain wall fermions. We find that our approximations have a significantly smaller residual mass than domain wall fermions at a similar computational cost, and still admit topological charge change.     

2 + 1 flavor simulations of QCD with improved staggered quarks

The MILC Collaboration has been performing realistic simulations of full QCD with 2 + 1 flavors of improved staggered quarks. Our simulations allow for controlled continuum and chiral extrapolations. I present results for the light pseudoscalar sector: masses and decay constants, quark masses and Gasser-Leutwyler low-energy constants. In addition I will present some results for heavy-light mesons, decay constants and semileptonic form factors, obtained in collaboration with the HPQCD and Fermilab lattice Collaborations. Such calculations will help in the extraction of CKM matrix elements from experimental measurements.     

Nonlinear dynamics of fermions during preheating

We study the role of dynamical fermions during preheating after inflation. We compute the nonequilibrium dynamics of Dirac fermions coupled to a scalar (inflaton) field at next-to-next-to-leading order in a coupling expansion of the 2PI effective action. Besides the well-known parametric production of bosons and fermions and their back-reaction on the background inflaton field, this includes direct interactions between produced particles, which have been neglected in previous studies. We present preliminary numerical results in 3+1 dimensions which indicates that, for intermediate Yukawa couplings, the latter can dramatically affect the usual picture of preheating.     

On the flavour interpretations of staggered fermions

The relationship between the flavour identifications of staggered fermions in configuration and in momentum space is clarified for interacting theories. It is demonstrated that these identification schemes are identical in the continuum limit.     

Holographic fermions with running chemical potential and dipole coupling

We explore the properties of the holographic fermions in extremal R-charged black hole background with a running chemical potential, as well as the dipole coupling between fermions and the gauge field in the bulk. We find that although the running chemical potential effect the location of the Fermi surface, it does not change the type of fermions. We also study the onset of the Fermi gap and the gap effected by running chemical potential and the dipole coupling. The spectral function in the limit ω→0$\omega \to 0$ and the existence of the Fermi liquid are also investigated. The running chemical potential and the dipole coupling altogether can make a non-Fermi liquid become the Landau–Fermi type.     

Floquet Majorana fermions in superconducting quantum dots

We consider different configurations of ac driven quantum dots coupled to superconductor leads where Majorana fermions can exist as collective quasiparticles. The main goal is to tune the existence, localization and properties of these zero energy quasiparticles by means of periodically driven external gates. In particular, we analyze the relevance of the system and driving symmetry. We predict the existence of different sweet spots with Floquet Majorana fermions in configurations where they are not present in the undriven system.     

Lattice QCD thermodynamic results with improved staggered fermions

We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of N _τ =4,6 and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential and present the isentropic equation of state on lines of constant entropy per baryon number.     

Weak localization in disordered spin-1 chiral fermions

We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities, the correction of conductivity from the coherent backscatter and non-coherent backscatter contributions cancel out in the intravalley scattering, leading to a weak localization correction to the Drude conductivity from the intervalley scattering. For the anisotropic impurities, the above cancelation is removed, we find the approximative quantum interference conductivity in the weak anisotropy case. The contributions from the chiral anomaly and classical Lorentz force are also discussed. Our work reveals some intriguing and detectable transport signatures of the novel spin-1 chiral fermions.     

Continuum symmetries of lattice models with staggered fermions

The validity of the flavour interpretation of staggered fermions is discussed in terms of the discrete symmetries of the interaction terms. Some aspects of the embedding of these symmetries in the symmetry group of the continuum limit are clarified. An explicit calculation, at first non-trivial order in 1/N, of the four-point function for a latticized Gross-Neveu model yields the same result in the continuum limit as the continuum theory for 2N fermions. A proof is then given that flavour and C, P, and T symmetries are restored in the continuum limit of 2-point correlation functions, for interactions, including the case of 4-dimensional QCD, which respect the discrete symmetries of the free action.     

Orthogonality between scales in a renormalization group for fermions

Having in mind the development of a technical tool to treat fermionic systems, we propose a Kadanoff-Wilson block renormalization transformation employing unusual averages (an inevitable artifact due to the specificity of lattice fermions and to the desired transformation properties). The free propagator is decomposed into operators associated to different momentum scales and with orthogonal relations, and the effective actions generated from the Dirac operator by the transformations present uniform exponential decay. We argue to show the usefulness of the formalism to study correlation functions of interacting fermions.     

Nuclear physics from lattice QCD

We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.