Dimensional tuning of electronic states under strong and frustrated interactions

We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can be used to experimentally detect signatures of the charge excitations.     

Tight-binding description of Landau levels of graphite in tilted magnetic fields

The electronic structure of Bernal-stacked graphite subject to tilted magnetic fields is studied theoretically. The minimal nearest-neighbor tight-binding model with the Peierls substitution is employed to describe the structure of Landau levels. We show that, while the orbital effect of the in-plane component of the magnetic field is negligible for massive Dirac fermions in the vicinity of the K point of the graphite Brillouin zone, at the H point it leads to the experimentally observable splitting of Landau levels, which grows approximately linearly with the in-plane field intensity.     

Charge-Stripe Phases Versus a Weak Anisotropy of Nearest-Neighbor Hopping

Recently, we demonstrated rigorously the stability of charge-stripe phases in 2D quantum-particle systems that are described by extended Falicov–Kimball Hamiltonians, with the quantum hopping particles being either spinless fermions or hardcore bosons. In this paper, by means of the same methods, we show that an arbitrary small anisotropy of nearest-neighbor hopping eliminates the π/2-rotation degeneracy of dimeric and axial-stripe phases and orients them in the direction of the weaker hopping. Due to the same anisotropy the obtained phase diagrams of fermions show a tendency to become similar to those of hardcore bosons. PACS numbers: 71.10.Fd, 71.10.−w, 71.27.+a, 67.40.Db     

Glueball mass calculations on an array of computers

We have calculated the mass of the 0⁺ glueball in SU(2) pure gauge theory in 4 dimensions, with very high statistics. The computation was done on an array of microprocessors with nearest-neighbor connections which run concurrently. We discuss, in detail, the implementation of the pure gauge algorithm for SU(2) and SU(3) and also the algorithm for calculating arbitrarily shaped Wilson loops on the array. The extension of these algorithms to the inclusion of dynamical fermions is also discussed. Finally, we present the results of our variational calculation of glueball masses which are in agreement with published results.     

Amplitude scaling behavior of band center states of Frenkel exciton chains with correlated off-diagonal disorder

We report the amplitude scaling behavior of Frenkel exciton chains with nearest-neighbor correlated off-diagonal random interactions. The band center spectrum and its localization properties are investigated through the integrated density of states and the inverse localization length. The correlated random interactions are produced through a binary sequence similar to the interactions in spin glass chains. We produced sets of data with different interaction strength and “wrong” sign concentrations that collapsed after scaling to the predictions of a theory developed earlier for Dirac fermions with random-varying mass. We found good agreement as the energy approaches the band center for a wide range of concentrations. We have also established the concentration dependence of the lowest order expansion coefficient of the scaling amplitudes for the correlated case. The correlation causes unusual behavior of the spectra, i.e., deviations from the Dyson-type singularity.     

Robust stationary distributed discord in the Jordan-Wigner fermion system under perturbations of the initial state

We investigate the Jordan-Wigner fermion clusters with a stationary distributed quantum pairwise discord. Such clusters appear after the Jordan-Wigner transformation of a spin chain governed by the nearest-neighbor XY Hamiltonian with the particular initial state having one polarized node. We show that the quantum discord stationarity in such systems is not destroyed by the “parasitic” polarization of at least two types. The first type appears because the initial state with a single polarized node is hardly realizable experimentally, and therefore the low polarization of neighboring nodes must be taken into account. The second is the unavoidable additional noise polarization of all nodes. Although the stationarity may not be destroyed by perturbations of the above two types, the parasitic polarizations deform the pairwise discord distribution and may destroy clusters of correlated fermions with equal pairwise discords. Such deformations are studied in this paper.     

Understanding finite size effects in quasi-long-range orders for exactly solvable chain models

In this paper, we investigate how much of the numerical artefacts introduced by finite system size and choice of boundary conditions can be removed by finite size scaling, for strongly correlated systems with quasi-long-range order. Starting from the exact ground-state wave functions of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion on finite periodic chains and finite open chains, we compute the two-point, density-density, and pair-pair correlation functions, and fit these to various asymptotic power laws. Comparing the finite-periodic-chain and finite-open-chain correlations with their infinite-chain counterparts, we find reasonable agreement among them for the power-law amplitudes and exponents, but poor agreement for the phase shifts. More importantly, for chain lengths on the order of 100, we find our finite-open-chain calculation overestimates some infinite-chain exponents (as did a recent density-matrix renormalization-group (DMRG) calculation on finite smooth chains), whereas our finite-periodic-chain calculation underestimates these exponents. We attribute this systematic difference to the different choice of boundary conditions. Eventually, both finite-chain exponents approach the infinite-chain limit: by a chain length of 1000 for periodic chains, and >2000 for open chains. There is, however, a misleading apparent finite size scaling convergence at shorter chain lengths, for both our finite-chain exponents, as well as the finite-smooth-chain exponents. Implications of this observation are discussed.     

Dynamical CPA approach to an itinerant fermionic spin glass model

We study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a -dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random medium. By means of a CPA method we derive a set of self-consistency equations for the spin glass order parameter and for the Fourier components of the local spin susceptibility. In order to solve these equations numerically we employ an approximation scheme which restricts the dynamics to a feasible number of the leading Fourier components. From a sequence of systematically improved dynamical approximations we estimate the location of the quantum critical point.Received: 5 August 2003, Published online: 2 October 2003PACS: 75.10.Nr Spin glass and other random models - 75.40.Cx Dynamic properties - 71.10.Fd Lattice fermion models     

QCD on the lattice and light hadron spectroscopy

Results in lattice Quantum Chromodynamics with fermions are reviewed. Estimates for the hadron spectrum on large lattices without and with light fermion polarization loops are discussed, and the results for different fermion regularizations are compared. The effects of the loops are found to be significant in lattice units, but to a greater part they can be reabsorbed in a redefinition of the overall scale. New estimates for the light quark masses with Wilson fermions are also presented. They differ substantially from previous estimates obtained by other methods in the continuum, and are much smaller. Finally it is argued that staggered fermions can lead to some anomalous results, which arise because of the doubling problem.     

Superheavy fermions and horizontal symmetries

The mechanism which was formerly used to obtain neutrino masses is generalized to all light fermions. Correspondingly, several sets of superheavy fermions are introduced. Assignments under a horizontal symmetry group are arranged such that the heaviest among the light fermions acquire their masses, not from the ordinary Higgs-Yukawa couplings, but from couplings to the heavy fermions. Masses of the other light fermions are then obtained through horizontal gauge interactions. Accordingly, the resulting light fermion masses exhibit a hierarchical generation structure. Because of the construction, light Higgs fields do not induce dangerous flavor-changing neutral-current interactions.     

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.     

New implementation of composite fermions in terms of subgroups of a braid group

The new implementation of composite fermions and more generally — of composite anyons is formulated, exploiting one-dimensional unitary representations of appropriately constructed subgroups of the full braid group. The nature of hypothetical fluxes attached to the Jain's composite fermions is explained via additional cyclotron trajectory loops consistently with the braid subgroup structure. It is demonstrated that composite fermions are proper 2D particles (not an auxiliary construction), but associated with braid subgroups instead of the full braid group.     

Avoidance of Majorana resonances in periodic topological superconductor-nanowire structures

Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermion in these semiconductor-superconductor-nanowire structures is tuning the semiconductor chemical potential in close proximity to the metallic superconductor. We show that presently realizable structures in experiments with tunable chemical potential lead to Majorana resonances, which are interesting in their own right, but do not manifest non-Abelian statistics. To resolve this crucial barrier to the solid state realization of Majorana fermions, we propose a new topological superconducting array structure where introducing the superconducting proximity effect from adjacent nanowires generates Majorana fermions with non-Abelian statistics.     

Hawking temperature of Kerr anti-de-Sitter black hole affected by Lorentz symmetry violating

We studied the correction of the quantum tunneling radiation of fermions with spin 1/2 in Kerr anti-de-Sitter black hole. First, the dynamic equation of spin 1/2 fermions was corrected using Lorentz’s violation theory. Second, the new expressions of the fermions quantum tunneling rate,the Hawking temperature of the black hole and the entropy of the black hole were obtained according to the corrected fermions dynamic equation. Our results show that Hawking temperature increases with the enhancement of both the coupling strength and the radial component of ether-like field, but is independent of non-radial components of ether-like field.At last, some comments are made on the results of our work.     

Gapless Chiral Superconducting ( d + id )-Wave Phase in Strongly Correlated Layered Material with a Triangular Lattice

It is shown that interlayer electron tunneling in the quasi-two-dimensional ensemble of Hubbard fermions leads to the realization of the gapless superconducting phase with the chiral (d + id)-wave order parameter symmetry, not for a single value of sodium ion concentration, but in a wide range of concentrations. Precisely this situation corresponds to experimental data on the layered sodium cobaltite intercalated by water (NaxCoO2 ⋅ yH2O). Intra-atomic electron repulsion that determines the strong electron correlation regime leads to the representation of Hubbard fermions, the interaction of which ensures Cooper instability. Intersite intralayer interactions between fermions considerably affect the positions of nodal points of the chiral order parameter and change the critical concentration at which a topological transition occurs in the 2D system of Hubbard fermions.     

Anomaly driven signatures of new invisible physics at the Large Hadron Collider

Many extensions of the Standard Model (SM) predict new neutral vector bosons at energies accessible by the Large Hadron Collider (LHC). We study an extension of the SM with new chiral fermions subject to non-trivial anomaly cancellations. If the new fermions have SM charges, but are too heavy to be created at LHC, and the SM fermions are not charged under the extra gauge field, one would expect that this new sector remains completely invisible at LHC. We show, however, that a non-trivial anomaly cancellation between the new heavy fermions may give rise to observable effects in the gauge boson sector that can be seen at the LHC and distinguished from backgrounds.     

Fermion Mass Mixing in Vacuum

Renormalization group procedure for effective particles is applied to a theory of fermions that interact only through mass mixing terms in their Hamiltonian. Problems with virtual pair production in vacuum are avoided by using the front form of Hamiltonian dynamics. Masses and states of physical fermions emerge at the end of a calculation that is carried out exactly irrespective of the strength of the mass mixing terms. An a priori infinite set of renormalization group equations for all momentum modes of fermion quantum fields is reduced to just one equation for a two-by-two mass matrix. In distinction from scalars, fermions never become tachyons but appear chirally rotated when the mass mixing interaction term is sufficiently strong.     

Chiral analog gauge theories on the lattice

We discuss a class of lattice gauge theories with fermions that have properties in common with continuum chiral gauge theories. The symmetries we gauge have often been mistaken for chiral symmetries in the literature. We show that in the continuum limit they converge to ordinary vector-like symmetries, but that at strong coupling they behave like chiral symmetries. We find lattice analogs of the technicolor mechanism and of the generation of composite massless fermions in chiral gauge theories.     

Dirac returns: Non-Abelian statistics of vortices with Dirac fermions

Topological superconductors classified as type D admit zero-energy Majorana fermions inside vortex cores, and consequently the exchange statistics of vortices becomes non-Abelian, giving a promising example of non-Abelian anyons. On the other hand, types C and DIII admit zero-energy Dirac fermions inside vortex cores. It has been long believed that an essential condition for the realization of non-Abelian statistics is non-locality of Dirac fermions made of two Majorana fermions trapped inside two well-separated vortices as in the case of type D. Contrary to this conventional wisdom, however, we show that vortices with local Dirac fermions also obey non-Abelian statistics.