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

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

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

Exact Momentum Distribution of a Fermi Gas in One Dimension

We introduce an exactly solvable model of a fermi gas in one dimension and compute the momentum distribution exactly. This is based on a generalisation of the ideas of bosonization in one dimension. It is shown that in the RPA limit(the ultra-high density limit) the answers we get are the exact answers for a homogeneous fermi gas interacting via a two-body repulsive coulomb interaction. Furthermore, the solution may be obtained exactly for arbitrary functional forms of the interaction, so long as it is purely repulsive. No linearization of the bare fermion dispersion is required. We find that for the interaction considered, the fermi surface is intact for weak repulsion and is destroyed only for sufficiently strong repulsion. Comparison with other models like the supersymmetric t-J model with inverse square interactions is made.Comment: RevTex, 5 pages, no figures., modified following ref. comments, more detailed explanations, resutls same, one new ref. adde

Exact Dynamical Structure Factor of a Bose Liquid

Based on ideas introduced in a previous preprint cond-mat/9701206 we propose an exactly solvable model of bosons interacting amongst themselves via a Van-der Waal-like repulsive interaction, and compute both the filling fraction and the dynamical structure factor exactly. The novelty of this approach involves introducing, analogous to Fermi sea (or surface) displacements, Bose fields that in this case, correspond to fluctuations of the Bose condensate. The exact dynamical structure factor has a coherent part that corresponds to the Bogoliubov spectrum and an incoherent part that is a result of correlations.Comment: RevTex, 6 pages, no figures, replaced previously empty fil

A.C. Conductivity of a Disordered Metal

The degenerate free Fermi gas coupled to a random potential is used to compute a.c. conductivity in various dimensions. We first formally diagonalise the hamiltonian using an appropriate basis that is a functional of the disorder potential. Then we compute the a.c. conductivity at zero temperature using the Kubo formula. This a.c. conductivity is a functional of the disordered potential. The wavefunction of extended states is written as exponential of the logarithm. We use the cumulant expansion to compute the disordered averaged a.c. conductivity for Gaussian disorder. The formula is valid if a certain linearization approximation is valid in the long-wavelength limit.Comment: 22 pages, no figs., Plain LaTe

Myopic Bosonization

As the title suggests, this is an attempt at bosonizing fermions in any number of dimensions without paying attention to the fact that the Fermi surface is an extended object. One is tempted to introduce the density fluctuation and its conjugate and recast the interacting problem in terms of these canonical Bose fields. However, we find that the attempt is short-sighted figuratively as well for the same reason. But surprisingly, this flaw, which manifests itself as an inconsistency between Menikoff-Sharp's construction of the kinetic energy operator in terms of currents and densities, and our ansatz for this operator, is nevertheless able to reproduce(although reluctantly) many salient features of the free theory. Buoyed by this success, we solve the interacting problem and compute the full propagator.Comment: 3 pages RevTe

Momentum Distribution of the Hubbard Model

Using the recently perfected sea-boson method, we compute the momentum distribution of the one-band Hubbard model in one and two spatial dimensions. We compute the asymptotic features of the momentum distribution explicitly away from half filling for weak coupling in one and two dimensions. While the results are not exact by any means, they provide the exact asymptotics, namely they are able to reproduce the exponents obtained by Shulz in one dimension obtained using Bethe ansatz. The corresponding results in more than one dimension are therefore as believeable.Comment: 12 pages, LaTex, 2d case revised, new formula for field operato