Sea-Boson Theory of Landau Fermi Liquids, Luttinger Liquids and Wigner Crystals

It is shown how Luttinger liquids may be studied using sea-bosons. The main advantage of the sea-boson method is its ability to provide information about short-wavelength physics in addition to the asymptotics and is naturally generalisable to more than one dimension. In this article, we solve the Luttinger model and the Calogero-Sutherland model, the latter in the weak-coupling limit. The anomalous exponent we obtain in the former case is identical to the one obtained by Mattis and Lieb. We also apply this method to solve the two-dimensional analog of the Luttinger model and show that the system is a Landau Fermi liquid. Then we solve the model of spinless fermions in one-dimension with long-range (gauge) interactions and map the Wigner crystal phase of the system.Comment: 19 pages, RevTeX, 3 eps figs, final published versio

Sea-Boson Analysis of the Infinite-U Hubbard Model

By expanding the projection operator in powers of the density fluctuations, we conjecture a hamiltonian purely quadratic in the sea-bosons that reproduces the right spin and charge velocities and exponent for the $U = \infty$ case in one dimension known from the work of Schulz. Then we argue that by simply promoting wavenumbers to wave vectors we are able to study the two dimensional case. We find that the quasiparticle residue takes a value $Z_{F} = 0.79$ close to half-filling where it is the smallest. This is in exact agreement with the prediction by Castro-Neto and Fradkin nearly ten years ago. We also compute the magnetic suceptibility and find that it diverges close to half-filling consistent with Nagakoka's theorem.Comment: 7 pages (revtex), radically revise

Expressing Products of Fermi Fields in terms of Fermi Sea Displacements

An attempt is made to generalise the ideas introduced by Haldane and others regarding Bosonizing the Fermi surface. The present attempt involves introduction of Bose fields that correspond to displacements of the Fermi sea rather than just the Fermi surface. This enables the study of short wavelength fluctuations of the Fermi surface and hence the dispersion of single particle excitations with high energy. The number conserving product of two Fermi fields is represented as a simple combination of these Bose fields. It is shown that most(!) commutation rules involving these number conserving products are reproduced exactly, as are the dynamical correlation functions of the free theory. Also the work of Sharp, Menikoff and Goldin has shown that the field operator may be viewed as a unitary representation of the current algebra. An explicit realisation of this unitary representation is given in terms of canonical conjugate of the density operator.Comment: Plain Tex, 27 pages, lots of algebra, "all commutation rules" replaced by "most commutation rules" are recovered exactl

Towards a Hydrodynamic Theory of Infinite Neutral Nonrelativistic Matter

We recast the problem of infinite neutral nonrelativistic matter interacting via U(1) gauge fields in the hydrodynamic language. We treat the nuclei as being spinless bosons for simplicity(for example in He4). We write down the formal action in terms of a full set of independent gauge invariant hydrodynamic variables. The claim is that the results of this theory are nonperturbative and nuclei and electrons are treated on an equal footing.Comment: 4 page

Xray-Edge Spectra From Sea-Bosons-I

The well-studied phenomenon of X-ray edge singularities is revisited using the sea-boson approach that has recently been placed on a rigorous footing. We are able to reproduce the well-known result namely, Mahan's power law divergences. Unlike the work of Schotte and Schotte, no linearization of the bare fermion dispersion is needed, which, by their own admission, is a source of some difficulty. Our approach also brings out some differences between the different dimensions which is not present in their work. Finally, our work also allows for easy generalization to potentials more realistic than the simple delta-function used commonly in the literature.Comment: 8 pages, regular LaTeX, one inbuilt fi

Why Self-Consistent Diagrammatic Perturbation Theory is `just' Perturbation Theory

In this short write-up we argue that self-consistent diagrammatic perturbation theory(i.e. Feynman diagrams) for the one-particle Green function is unable to capture some important qualitative features no matter how self-consistently the Green functions are obtained. This write-up is intended to highlight the short-comings of perturbation theory and also tout the advantages of the sea-boson technique(hep-th/9706006).Comment: 3 pages, RevTe

Momentum Distribution of a Weakly Coupled Fermi Gas

We apply the sea-boson method to compute the momentum distribution of a spinless continuum Fermi gas in two space dimensions with short-range repulsive interactions. We find that the ground state of the system is a Landau Fermi liquid($0 < Z_{F} < 1$). We also apply this method to study the one-dimensional system when the interactions are long-ranged gauge interactions. We map the Wigner crystal phase of this system.Comment: 5 pages, plain LaTe

Quenched Disorder From Sea-Bosons

The degenerate Fermi gas coupled to a random potential is used to study metal-insulator transitions in various dimensions. We first recast the problem in the sea-boson language that allows for an easy evaluation of important physical attributes. We evaluate the dynamical number-number correlation function and from this compute the a.c. conductivity. We find that the d.c. conductivity vanishes in one and two dimensions. For a hamiltonian that forbids scattering of an electron from within the Fermi surface to another state within the Fermi surface we find that there is no metal-insulator transition in three dimensions either.Comment: 8 pages, Plain LaTe

Hydrodynamic Formulation of the Hubbard Model

In this article, we show how to recast the Hubbard model in one dimension in a hydrodynamic language and use the path integral approach to compute the one-particle Green function. We compare with the Bethe ansatz results of Schulz and find exact agreement with the formulas for spin and charge velocities and anomalous exponent in weak coupling regime. These methods may be naturally generalized to more than one dimension by simply promoting wavenumbers to wavevectors.Comment: 7 pages, no fig

Weak value amplification of atomic cat states

We show the utility of the weak value amplification to observe the quantum interference between two close lying atomic coherent states in a post-selected atomic cat state, produced in a system of $N$ identical two-level atoms weakly interacting with a single photon field. Through the observation of the negative parts of the Wigner distribution of the post-selected atomic cat state, we find that the post-selected atomic cat state becomes more nonclassical when the post-selected polarization state of the single photon field tends toward becoming orthogonal to its pre-selected state. We show that the small phase shift in the post-selected atomic cat state can be amplified via measuring the peak shift of its phase distribution when the post-selected state of the single photon field is nearly orthogonal to its pre-selected state. We find that the amplification factor of 15 [5] can be obtained for a sample of 10 [100] atoms. This effectively provides us with a method to discriminate two close lying states on the Bloch sphere. We discuss possible experimental implementation of the scheme, and conclude with a discussion of the Fisher information.Comment: 16 pages, 8 figure