Limit Of Fermions Research Articles

The fermionic limit of the -function Bose gas: a pseudopotential approach

We use first-order perturbation theory near the fermionic limit of the delta-function Bose gas in one dimension (i.e., a system of weakly interacting fermions) to study three situations of physical interest. The calculation is done using a pseudopotential which takes the form of a two-body delta''-function interaction. The three cases considered are the behavior of the system with a hard wall, with a point where the strength of the pseudopotential changes discontinuously, and with a region of finite length where the pseudopotential strength is non-zero (this is sometimes used as a model for a quantum wire). In all cases, we obtain exact expressions for the density to first order in the pseudopotential strength. The asymptotic behaviors of the densities are in agreement with the results obtained from bosonization for a Tomonaga-Luttinger liquid, namely, an interaction dependent power-law decay of the density far from the hard wall, a reflection from the point of discontinuity, and transmission resonances for the interacting region of finite length. Our results provide a non-trivial verification of the Tomonaga-Luttinger liquid description of the delta-function Bose gas near the fermionic limit.

SPIN STRUCTURE FUNCTIONS AND INTRINSIC MOTION OF THE CONSTITUENTS

The spin structure functions of the system of quasifree fermions on mass shell are studied in a consistently covariant approach. Comparison with the basic formulas following from the quark-parton model reveals the importance of the fermion motion inside the target for the correct evaluation of the spin structure functions. In particular it is shown, that regarding the moment Γ1, both the approaches are equivalent for the static fermions, but differ by the factor 1/3 in the limit of massles fermions (m ≪ p0, in target rest frame). Some other sum rules are discussed as well.

From the square lattice to the checkerboard lattice: Spin-wave and large-nlimit analysis

Within a spin wave analysis and a fermionic large-n limit, it is shown that the antiferromagnetic Heisenberg model on the checkerboard lattice may have different ground states, depending on the spin size $S$. Through an additional exchange interaction that corresponds to an inter-tetrahedra coupling, the stability of the N\'eel state has been explored for all cases from the square lattice to the isotropic checkerboard lattice. Away from the isotropic limit and within the linear spin wave approximation, it is shown that there exists a critical coupling for which the local magnetization of the N\'eel state vanishes for any value of the spin $S$. One the other hand, using the Dyson-Maleev approximation, this result is valid only in the case $S= \frac12$ and the limit between a stable and an unstable N\'eel state is at S=1. For $S= \frac12$, the fermionic large-n limit suggests that the ground state is a valence bond solid build with disconnected 4-spins singlets. This analysis indicates that for low spin and in the isotropic limit, the checkerboard antiferromagnet may be close to an instability between an ordered S=0 ground state and a magnetized ground state.

Spin structure functions and intrinsic motion of the constituents

The spin structure functions of the system of quasifree fermions on mass shell are studied in a consistently covariant approach. A comparison with the basic formulas following from the quark-parton model reveals the importance of the fermion motion inside the target for the correct evaluation of the spin structure functions. In particular it is shown that, regarding the moment ${\ensuremath{\Gamma}}_{1},$ both the approaches are equivalent for the static fermions but differ by a factor $1/3$ in the limit of massles fermions $(m\ensuremath{\ll}{p}_{0},$ in the target rest frame). Some other sum rules are discussed as well.

Single-particle path integral for composite fermions and the renormalization of the effective mass

To study composite fermions around an even denominator fraction, we adapt the phase space single-particle path integral technique for interacting electrons in zero magnetic field developed recently by D.S. Golubev and A.D. Zaikin, Phys. Rev. B {\bf 59}, 9195 (1999). This path integral description gives an intuitive picture of composite fermion propagation very similar to the Caldeira-Leggett treatment of a particle interacting with an external environment. We use the new description to explain the origin of the famous cancellation between the self-energy and the vertex corrections in semi-classical transport measurements. The effective range of the cancellation is given by the size of the propagating particle, which for the Coulomb interaction scales with the temperature T as T^{-1/4} |log T|^{-1} in the semi-classical limit. Using this scheme we find that the effective mass in the semi-classical limit for composite fermions in GaAs is approximately 6 times the bare mass.

Integrable chain model with additional staggered model parameter

The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented. The XXZ model with staggered disposition along a chain of both, the anisotropy \pm\Delta, as well as shifts of the spectral parameters are considered and the corresponding integrable model is constructed. The Hamiltonian of the model is computed in fermionic and spin formulations. It involves three neighbour site interactions and therefore can be considered as a zig-zag ladder model. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found. The model has a free fermionic limit at \Delta=0 and the integrable boundary terms are found in this case. This construction is quite general and can be applied to other known integrable models.

MASS AND COUPLING CONSTANT LIMITS FROM CONVERGENCE CONDITIONS ON THE EFFECTIVE CHARGE IN QED

The massless fermion limit of QED is discussed. For on-shell renormalization the high energy behavior fixes no lower limit on the mass of the lightest fermion if the fine structure constant α is allowed to vary. The choice of an arbitrary (spacelike) subtraction point does, however, fix a lower limit on the mass of the lightest fermion, for any subtraction scale μ, if the effective charge α eff (μ) respects both quantum mechanical superposition and renormalization scale invariance. Limits on the values of α or the electron mass are obtained within the Standard Electroweak Model by requiring convergence of α eff (MZ).

PERTURBATION THEORY FOR SINGULAR POTENTIALS IN QUANTUM MECHANICS

We study perturbation theory in certain quantum mechanics problems in one dimension in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of the unusual techniques which are required to obtain perturbative expansions of the energies in such cases. These include a point-splitting prescription with a δ′′ function for expanding around the Dirichlet (fermionic) limit of the δ function potential, and performing a similarity transformation to a non-Hermitian potential in the Calogero–Sutherland model. As an application of the first technique, we study the ground state of the δ function Bose gas near the fermionic limit.

The domain wall fermion chiral condensate in quenched QCD

We examine the chiral limit of domain wall fermions in quenched QCD. One expects that in a quenched simulation, exact fermion zero modes will give a divergent, 1/ m behavior in the chiral condensate for sufficiently small valence quark masses. Unlike other fermion formulations, domain wall fermions clearly demonstrate this behavior.

Radiative Higgs boson decaysH→ff¯γbeyond the standard model

Neutral Higgs boson radiative decays of the form h_0, H, A \to f\bar{f}\gamma, in the light fermion limit $m_f->0, are calculated in the two Higgs doublet model at one-loop level. Comparisons with the calculation within the standard model are given, which indicates that these two models are distinguishable in the decay mode fermion-antifermion -photon. Our results show that the concerned process may stand as an implement to identify the Higgs belongings in case there is a intermediate mass Higgs detected.

Critical dynamics of the hybrid Monte Carlo algorithm

We investigate the critical dynamics of the Hybrid Monte Carlo algorithm approaching the chiral limit of standard Wilson fermions. Our observations are based on time series of lengths O(500) for a variety of observables. The lattice sizes are 16 3 × 32 and 24 3 × 40. We work at β = 5.6, and κ = 0.156, 0.157, 0.1575, 0.158, with 0.83 > m π m ϱ > 0.55 . We find surprisingly small integrated autocorrelation times for local and extended observables. The dynamical critical exponent z of the exponential autocorrelation time is compatible with 2. We estimate the total computational effort to scale between V 2 and V 2 1 4 toward the chiral limit.

Supersymmetry and bosonization in three dimensions

We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the bosonization of free massive fermions and show that, under certain conditions on the masses, this model displays a supersymmetric-like invariance in the low energy regime. We construct the purely fermionic expression for the supercurrent and the non-linear supersymmetry transformation laws. We argue that the supersymmetry is absent in the limit of massless fermions where the bosonized theory is non-local.

De Haas-van Alphen oscillations in the high-field state of the Anderson lattice

A strong coupling spin fluctuation theory of the Anderson lattice in a high magnetic field has recently been extended to include Landau levels. Oscillations in the minority spin self-energy as a function of the inverse field arise from majority spin Landau levels passing through the Fermi level. In the heavy fermion limit of strong mass enhancement these oscillations lead to significant modifications in the standard theory of the de Haas-van Alphen effect. The effect on the spin moment as well as on the diamagnetic moment is analysed. An attempt is made to relate the present work to unusual results of the de Haas-van Alphen measurements in the high-field state of CeRu 2Si 2.

Series expansions for the massive Schwinger model in Hamiltonian lattice theory

It is shown that detailed and accurate information about the mass spectrum of the massive Schwinger model can be obtained using the technique of strong-coupling series expansions. Extended strong-coupling series for the energy eigenvalues are calculated, and extrapolated to the continuum limit by means of integrated differential approximants, which are matched onto a weak-coupling expansion. The numerical estimates are compared with exact results, and with finite-lattice results calculated for an equivalent lattice spin model with long-range interactions. Both the heavy fermion and the light fermion limits of the model are explored in some detail.

A possible scaling region of chiral fermions on a lattice

We present the details of analyzing an SU L (2) ⊗ U R (1) chiral theory with multifermion couplings on a lattice. The existence of a possible scaling region in the phase space of multifermion couplings for defining the continuum limit of chiral fermions is advocated. In this scaling region, no spontaneous symmetry breaking occurs; the “spectator” fermion ψ R ( x) is a free mode and decoupled; doublers are decoupled as massive Dirac fermions consistently with the SU L (2) ⊗ U R (1) chiral symmetry, whereas the normal mode of ψ L i ( x) is plausibly speculated to be chiral in the continuum limit. This is not in agreement with the general belief of the definite failure of theories so constructed.

On the three-dimensional reductions of the Bethe - Salpeter equation and their one-body limits (two-boson and boson - fermion cases)

We transform the Bethe - Salpeter equation for the two-boson and for the boson - fermion systems into equivalent Salpeter or Sazdjian equations, with a three-dimensional (3D) potential directly computable from a series of reducible and irreducible Feynman graphs. We compute the various one-body limits (in the boson - fermion case we compute the heavy boson and the heavy fermion limits). To be definite, we work in the QED framework, but we also consider the scalar bosons exchanges in the two-boson case.

The Maxwell-Boltzmann behavior of a quon gas

A model gas of quons whose operators obey the minimally deformed commutators a ia j † − qa j †a i = δ ij (−1 ≤ q ≤ 1) is studied in two dimensions. While interpolating between the boson limit ( q → 1) and the fermion limit ( q → −1), the gas behaves like a Maxwell-Boltzmann gas when q = 0 at any temperature.

Energy spectra of three anyons in a harmonic well

A procedure is proposed to diagonalize the Hamiltonian of three anyons in a harmonic potential. The energy spectra have been obtained as a function of the statistical parameter. Some regularities have been observed as the system evolves from the boson to the fermion limits.

Pairing instabilities induced by residual statistical interactions

AbstractAt two space dimensions we consider small changes in quantum statistics around the bosonic and fermionic limits. An anyon gas near the Bose statistics becomes unstable towards pair condensation at arbitrarily small statistical parameter in front of the Aharonov‐Bohm interaction. The self‐consistency problem within the Cooper scattering channel is solved analytically by taking into account the full momentum dependence of the singular two‐particle vertex. The pairing, whose amplitude and critical temperature we calculate in mean‐field approximation, has d‐wave symmetry unlike the p‐wave BCS‐type pairing instability for anyons near the Fermi point. The connection to paired‐boson (holon) superconductivity is pointed out.

Statistical screening in aP, T-invariant model

It is shown that in theP, T-invariant model with the mixed Chern-Simons term the interaction of charge carriers leads to effective changing of their statistics, which depends on distance between them. In particular, in the limit of large distances fermions effectively turn into bosons.