Fermionic Space Research Articles

Bulk and edge excitations of aν=1Hall ferromagnet

We focus on the collective dynamics of the fermions in a $\ensuremath{\nu}=1$ quantum-Hall droplet. Specifically, we look at the quantum Hall ferromagnet. In this system, the electron spins are ordered in the ground state due to the exchange part of the Coulomb interaction and the Pauli exclusion principle. The low-energy excitations are ferromagnetic magnons. In order to obtain an effective Lagrangian for these magnons, we introduce bosonic collective coordinates in the Hilbert space of many-fermion systems. These collective coordinates describe a part of the fermionic Hilbert space. Using this technique, we interpret the magnons as bosonic collective excitations in the Hilbert space of the many-electron Hall system. Furthermore, by considering a Hall droplet of finite extent, we also obtain the effective Lagrangian governing the spin collective excitations at the edge of the sample.

Toward a unified algebraic understanding of concepts of particle and collective motions in fermion many-body systems

Toward a unified algebraic understanding of physical concepts of the so-called particle and collective motions, a new theory for unified description of both the motions is proposed with the use of time-dependent Hartree-Fock theory on a circle S1. The theory simply and clearly elucidates a collective motion induced by a TD mean-field potential. It also describes symmetry breaking of fermion systems and successive occurrence of the collective motion due to recovery of the symmetry. The theoretical frame asserts that the Fock space of finite-dimensional fermions has an algebraic structure to be embedded into that of infinite-dimensional fermions.

BULK AND EDGE EXCITATIONS IN A ν=1 QUANTUM HALL FERROMAGNET

In this article, we shall focus on the collective dynamics of the fermions in a ν=1 quantum Hall droplet. Specifically, we propose to look at the quantum Hall ferromagnet. In this system, the electron spins are ordered in the ground state due to the exchange part of the Coulomb interaction and the Pauli exclusion principle. The low energy excitations are ferromagnetic magnons. To provide a means for describing these magnons, we shall discuss a method of introducing collective coordinates in the Hilbert space of many-fermion systems. These collective coordinates are bosonic in nature. They map a part of the fermionic Hilbert space into a bosonic Hilbert space. Using this technique, we shall interpret the magnons as bosonic collective excitations in the Hilbert space of the many-electron Hall system. By considering a Hall droplet of finite extent, we shall also obtain the effective Lagrangian governing the spin collective excitations at the edge of the sample.

A new proposal to solve the time-dependent infinite- U Anderson model applied to ion–surface scattering processes

The interaction between delocalized conduction band states and localized states on an atom site is well described by an Anderson Hamiltonian. The time dependence of this Hamiltonian comes from the trajectory dependence of the parameters in processes where there are atoms moving near a surface (scattering and emission processes). Interesting many-body effects are expected due to the large Coulomb repulsion in the atom site. In this work the time-dependent Keldysh Green functions defined in a mixed space of fermions and bosons with the constraint of a total number Q=1, are calculated by using the equation of motion method. The dynamical equations obtained in this form allow to calculate the charge state of the moving atom, and in the stationary limit they reproduce a spectral density of states with properties in an excellent agreement with exact results.

Holographic renormalization group with fermions and form fields

We find the Holographic Renormalization Group equations for the holographic duals of generic gravity theories coupled to form fields and spin-1/2 fermions. Using Hamilton-Jacobi theory we discuss the structure of Ward identities, anomalies, and the recursive equations for determining the divergent terms of the generating functional. In particular, the Ward identity associated to diffeomorphism invariance contains an anomalous contribution that, however, can be solved either by a suitable counter term or by imposing a condition on the boundary fields. Consistency conditions for the existence of the dual arise, if one requires that a Callan-Symanzik type equation follows from the Hamiltonian constraint. Under mild assumptions we are able to find a class of solutions to the constraint equations. The structure of the fermionic phase space and constraints is treated extensively for any dimension and signature.

DYNAMICAL HAMILTONIAN FOR PREASSIGNED TIME-EVOLUTION OF FERMIONIC SQUEEZING

We derive the general form of dynamical Hamiltonian generating the preassigned time-evolution of multimode fermionic squeezing. The fermionic squeezing is a quantum-mechanical image in fermionic Hilbert space corresponding to an orthogonal transformation in pseudo-classical Grassmann number space. The derivation is mainly based on the orthogonal properties of the transformation matrices. It is shown that some new fermionic operator realization of SO (2n) group and some new Hamiltonians can be obtained via this approach.

Fermionic random transverse-field Ising spin chain

The interplay of spin and charge fluctuations in the random transverse-field Ising spin chain on the fermionic space is investigated. The finite chemical potential, which controls the charge fluctuations, leads to the appearance of the quantum critical region in the phase diagram where the magnetic correlations are quenched by nonmagnetic sites. Regions of nonmonotonous temperature dependence of spin-spin correlation length appear at nonzero $\mu$. The results on the one-fermion density of states of the model are discussed.

Functional Representations for Fock Superalgebras

The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite-dimensional superspaces, and construct super-analogs of the classical function spaces with a reproducing kernel — including the Bargmann–Fock representation — and of the Wiener–Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein–Uhlenbeck semigroup on the Fock space.

TWO-PARAMETER DIFFERENTIAL CALCULUS ON THE h-EXTERIOR PLANE

We construct a two-parameter covariant differential calculus on the quantum h-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.

Fermionic q-Fock space and braided geometry

We write the fermionic q-Fock space representation of Uq(sln) as an infinite extended braided tensor product of finite-dimensional fermionic Uq(sln)-quantum planes or exterior algebras. Using braided geometrical techniques developed for such quantum exterior algebras, we provide a new R-matrix approach to the Kashiwara–Miwa–Stern action of the Heisenberg algebra on the q-fermionic Fock space, obtaining the action in detail for the lowest nontrivial case [b2, b−2]=2((1−q−4n)/(1−q−4)).

Interacting fluctuations and the two-loop order parameters of the strong-coupling negative- U Hubbard model

The effective field theory that describes the interaction of fluctuations of the attractive Hubbard model in the strong-coupling limit is formulated and applied to obtain the two-loop results for the order parameters of the model at low temperatures and in the leading singularities near two dimensions. Starting from a Grassmann functional integral representation of the strong-coupling model on the restricted fermionic Hilbert space, which corresponds to the anisotropic spin- 1 2 Heisenberg quantum antiferromagnet, we derive the effective field theory up to fifth order in the bosonic fluctuation fields. The loop corrections of the order parameters for superconductivity and charge ordering and of the chemical potential are evaluated including both the singular planar phase fluctuations and the out-of-plane fluctuations, which become soft at half band-filling. The results are in agreement with the scaling behaviour expected from the corresponding XY and Heisenberg limits of the O( n) non-linear σ-model.

AN ALGEBRAIC FORMULATION OF LEVEL ONE WESS-ZUMINO-WITTEN MODELS

The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras. It is shown that the representation theory of the underlying even CAR algebras reproduces precisely the sectors of the chiral algebra. This fact allows to develop a theory of local von Neumann algebras on the punctured circle, fitting nicely in the Doplicher-Haag-Roberts framework. The relevant localized endomorphisms which generate the charged sectors are explicitly constructed by means of Bogoliubov transformations. Using CAR theory, the fusion rules in terms of sector equivalence classes are proven.

Boson-fermion mapping and dynamical supersymmetry in fermion models

We show that a dynamical supersymmetry can appear in a purely fermionic system. This “supersymmetry without bosons” is constructed by application of a recently introduced boson-fermion Dyson mapping from a fermion space to a space comprised of collective bosons and ideal fermions. In some algebraic fermion models of nuclear structure, particular Hamiltonians may lead to collective spectra of even and odd nuclei that can be unified using the dynamical supersymmetry concept with Pauli correlations exactly taken into account.

QUANTUM DEFORMATION OF igl(n) ALGEBRA ON QUANTUM SPACE

We study quantum deformed gl(n) and igl(n) algebras on a quantum space discussing multi-parametric extension. We realize elements of deformed gl(n) and igl(n) algebras by a quantum fermionic space. We investigate a map between deformed igl(2) algebras of our basis and other basis.

Auxiliary fermion linearization

We present a novel mean-field-like scheme for -spin fermions on a lattice in arbitrary dimension, generalizing the fermionic linearization approach. It describes the interaction of each lattice site with its neighbours by means of auxiliary fermions, living on the same site, dynamically coupled with the physical ones. This leads to a single-site picture in an enlarged 16-dimensional space given by the tensor square of the fermionic single-site Hilbert space. The general approach is applied to the extended Hubbard Hamiltonian and to the ferromagnetic Heisenberg model. The spectrum and the self-consistency equations can be determined in a straightforward way thanks to the factorization of the linearized dynamical algebra in u(n) components with n = 4 at most. The self-consistency is formulated as a fixed-point problem for a map in the space of coupling constants.

Microscopic Foundations of the Interacting Boson Model from the Shell-Model Point of View

The validity of the essential ingredients of the microscopic formulation of the interacting boson model: (i) truncation of the shell-model or fermion space and (ii) the procedures for mapping the truncated fermion space on to the boson space, is tested over various (spherical, deformed and transitional) regions both in the simplistic single j-shell, identical boson sys­ tems and the more realistic multi j-shell, proton-neutron systems depending on the feasibility of such calculations. In the situations where the truncation and mapping procedures fail to reproduce the exact shell-model results, it is demonstrated that renormalization and higher order mapping procedures cure the associated problems, respectively and provide excellent agreements. In addition, a Hamiltonian of the interacting boson-fermion model which is relevant for a study of odd mass nuclei is derived for a single j-shell case in the shell-model framework, which yields results identical to those in the shell-model for the monopole pairing interaction.

Shape transitions in even Mo and Sm isotopes: Study in a new microscopic interacting boson model scheme

A simple dynamic procedure, based on the deformed Hartree-Fock solution of a nucleus, is presented to construct the IBM operators in microscopic basis. The parameters of these operators are evaluated by establishing a Marumori mapping from the truncated shell model space onto the boson space. The transitions from spherical to axial-rotor shape observed in the low-lying levels ofeven96–108Mo and146–154Sm isotopes are reproduced qualitatively by applying this procedure with a fixed set of fermion input parameters to each chain. Variation of a few parameters in fermion space leads to quantitative agreement.

Negative-energy spinors and the Fock space of lattice fermions at finite chemical potential

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial ``energy'' in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.

Relation between the Boson Expansion Theory and the Boson-Fermion Expansion Theory

The relation between the hermitian type boson expansion theory and the boson-fermion expansion theory recently proposed as the alternative to it is discussed. It is shown that the apparent difference between some of the expansion coefficients in both theories is due to arbitrariness about the definition of the collective state in the fermion space and that one can remove the difference by the appropriate unitary transformation.

Relation between the Boson Expansion Theory and the Boson-Fermion Expansion Theory

The relation between the hermitian type boson expansion theory and the boson-fermion expansion theory recently proposed as the alternative to it is discussed. It is shown that the apparent difference between some of the expansion coefficients in both theories is due to arbitrariness about the definition of the collective state in the fermion space and that one can remove the difference by the appropriate unitary transformation.