Resonant spin-changing collisions in spinor fermi gases

The compensation of quadratic Zeeman effect and trap energy in high-spin fermions is shown to lead to resonances in the spin-changing collisions that are typically absent in spinor condensates and spin-1/2 fermions. We study these resonances in lattice fermions, showing that they permit the targeting of a particular spin-changing channel while suppressing the rest and the creation of magnetically insensitive superpositions of many-body states with entangled spin and trap degrees of freedom. Finally, the intersite tunneling may lead to a quantum phase transition described by a quantum Ising model.     

A New Way of Bosonic Structure of Fermions

We propose a new approach to construct fermions in terms of usual bosons. The operator and normal product forms of the bosonic structure of fermions are obtained, and the extension of the method to many degrees of freedom and field theory is also given.     

Monte Carlo integration for lattice gauge theories with fermions

A Monte Carlo procedure is constructed for lattice gauge theories with fermions by replacing integration over fermion degrees of freedom in the path integral by conventional integration over effective boson degrees of freedom. The method is applied to gauge theories over two discrete subgroups of SU(2).     

Renormalization by continuous unitary transformations: one-dimensional spinless fermions

A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the Hamiltonian which stays hermitian throughout the renormalization flow, whereby any frequency dependence is avoided. The approach is illustrated in detail for a model of spinless fermions with nearest neighbour repulsion in one dimension. Even though the fermionic degrees of freedom do not provide an easy starting point in one dimension favorable results are obtained which agree well with the exact findings based on Bethe ansatz. Received 21 August 2002 / Received in final form 29 October 2002 Published online 31 December 2002     

THE SOLUTIONS FOR j3 SYSTEM FROM SHELL MODEL AND GENERATOR COORDINATE METHOD

The solutions for the problem of 3 particles moving in a single-j shell are given from the shell model and the generator coordiuate method (GCM) respectively. After taking all possible contractions of fermions as well as bosons, GCM can produce the same exact solution as the shell model. So it is quite reasonable to expect that GCM is an effective theory in treating coupling between boson and fermion degrees of freedom in nuclei microscopically.     

Gravitational fermion production in inflationary cosmology

We revisit the gravitational production of massive Dirac fermions in inflationary cosmology with a focus on clarifying the analytic computation of the particle number density in both the large and the small mass regimes. For the case in which the masses of the gravitationally produced fermions are small compared to the Hubble expansion rate at the end of inflation, we obtain a universal result for the number density that is nearly independent of the details of the inflationary model. The result is identical to the case of conformally coupled scalars up to an overall multiplicative factor of order unity for reasons other than just counting the fermionic degrees of freedom.     

Plasma oscillations in a one-dimensional many-fermion system

Following the Shevchik technique, a model Hamiltonian of collective oscillations (plasmons) in a one-dimensional system of complete degenerate fermions is obtained in terms of the Tomonaga boson operators. This Hamiltonian is diagonalized by means of the Mattis and Lieb canonical transformation and the plasma frequency is derived. The equation-of-motion method is applied in the RPA in order to include the coupling between the collective and individual degrees of freedom. The generalization to finite temperatures is performed and connection with the Tomonaga model is discussed.     

Quantum molecular dynamics study of the Su-Schrieffer-Heeger model

A quantum molecular dynamics technique is presented to compute the static and dynamic properties of a system of fermions coupled to classical degrees of freedom. The method is employed to investigate the properties of the Su-Schrieffer-Heeger model, an electron-phonon model which is often used to describe the electronic properties of conjugated polymers. The Su-Schrieffer-Heeger model is shown to exhibit a metal-insulator transition away from half-filling. In the metallic phase the electron transport is collective and shows the features characteristic of Fröhlich conductivity. Our simulation data for the optical absorption at room-temperature are in good agreement with experiment.     

Entanglement in the second quantization formalism

We study properties of entangled systems in the (mainly non-relativistic) second quantization formalism. This is then applied to interacting and non-interacting bosons and fermions and the differences between the two are discussed. We present a general formalism to show how entanglement changes with the change of modes of the system. This is illustrated with examples such as the Bose condensation and the Unruh effect. It is then shown that a non-interacting collection of fermions at zero temperature can be entangled in spin, providing that their distances do not exceed the inverse Fermi wavenumber. Beyond this distance all bipartite entanglement vanishes, although classical correlations still persist. We compute the entanglement of formation as well as the mutual information for two spin-correlated electrons as a function of their distance. The analogous, non-interacting collection of bosons displays no entanglement in the internal degrees of freedom. We show how to generalize our analysis of the entanglement in the internal degrees of freedom to an arbitrary number of particles.     

Topological characterization of quantum phase transitions in a spin-1/2 model

We have introduced a novel Majorana representation of S=1/2 spins using the Jordan-Wigner transformation and have shown that a generalized spin model of Kitaev defined on a brick-wall lattice is equivalent to a model of noninteracting Majorana fermions with Z2 gauge fields without redundant degrees of freedom. The quantum phase transitions of the system at zero temperature are found to be of topological type and can be characterized by nonlocal string order parameters (SOP). In appropriate dual representations, these SOP become local order parameters and the basic concept of Landau theory of continuous phase transition can be applied.     

Physics of the Schwinger model

The Coulomb gas of massless fermions (Schwinger model) is solved in a one-dimensional space of finite lengthL using the boson representation of fermions. Special attention is paid to boundary effects and global degrees of freedom. It is shown that the mean current is not conserved, but oscillates. The theory is constructed in all charge sectors. The Wightman functions are calculated and the limitL is discussed.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Bosonization rules in dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure.     

Phase diagram of interacting composite fermions in the bilayer nu=2/3 quantum hall effect

We study the phase diagram of composite fermions (CFs) in the presence of spin and pseudospin degrees of freedom in the bilayer nu=2/3 quantum Hall (QH) state. Activation studies elucidate the existence of three different QH states with two different types of hysteresis in the magnetotransport. While a noninteracting CF model provides a qualitative account of the phase diagram, the observed renormalization of tunneling gap and a non-QH state at high densities are not explained in the noninteracting CF model, and are suggested to be manifestations of interactions between CFs.     

Quantized Grassmann variables and unified theories

The color and flavor degrees of freedom are described in terms of Fermi oscillators (quantized Grassmann variables). The unified theories constructed in this way are vector-like. The fundamental fermions come out to be classified in the spinorial representations of the orthogonal groups.     

Pre-formed superconducting and quadrupolar fluctuations and heavy electron mass in an exactly solvable model

We present the Bethe ansatz solution for the two-channel non-magnetic hybridization impurity model of electrons with spin and orbital degrees of freedom. It is shown that a small concentration of such impurities enhances the effective mass of electrons. A large concentration of impurities results in a pre-formation of superconducting and quadrupolar-order fluctuations and in the co-existence of them for some range of parameters.Received: 26 June 2003, Published online: 11 August 2003PACS: 75.30.Mb Valence fluctuation, Kondo lattice, and heavy-fermion phenomena - 71.27.+a Strongly correlated electron systems; heavy fermions     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

Dual boson approach to collective excitations in correlated fermionic systems

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in the so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to an extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to “bare” RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.     

Lattice models with N=2 supersymmetry

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q+/- yield the Hamiltonian H=(Q(+),Q(-)) on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers; the Hamiltonian of our simplest model contains a hopping term and a repulsive potential. We analyze these models using conformal field theory, the Bethe ansatz, and cohomology. The simplest model provides a manifestly supersymmetric lattice regulator for the supersymmetric point of the massless (1+1)-dimensional Thirring (Luttinger) model. Generalizations include a quantum monomer-dimer model on a two-leg ladder.     

Spontaneous symmetry breakings in Z2 gauge theories for doped quantum dimer and eight-vertex models

Behavior of doped fermions in Z₂ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z₂ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.