arXiv subjects

Girish S. Setlur

Publications and source records attributed to Girish S. Setlur.

At least 37 records · Page 2Linked to original sources

arXiv2004

A Novel Non-Fermi Liquid Ground State in One Dimension

We propose a new non-Fermi liquid ground state in one dimension that is not of the Luttinger type. It is the ground state of fermions interacting via a long range repulsive interaction in real space of the form $ V(x) = e^2/|x| $. We characterise it by computing the momentum distribution which is perfectly flat near the Fermi points signalling a radical departure from Luttinger liquid theory(and Fermi liquid theory). The dispersion of elementary excitations is found to be sublinear but gapless of the form $ v {} |q| {}[ Log[2k_{F}/|q| ]^{1/2} $. We also compute the conductance of a mesoscopic wire made of such objects and contrast it from the answer we obtain for a Luttinger wire.

cond-mat.mes-hall↗

arXiv2004

Quantum Hydrodynamics of Fermi Fluids

It is shown that gauge theories with fermions are most naturally studied via a polar decomposition of the field variable. This is the fermionic analog of the preprint cond-mat/0210673. The hope is that these two put together will enable the treatment of neutral nonrelativisitc matter composed of electrons and nuclei in a nonperturbative manner with nuclei and electrons treated on an equal footing. We recast the electron-phonon (superconductivity) problem in the hydrodynamic language and indicate how it is solved. In particular we focus on the a.c. conductivity.

cond-mat.supr-con↗

arXiv2004

U(1) Gauge Theory as Quantum Hydrodynamics

It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The path integral approach is used to compute the partition function. When gauge fields are included, the constraint brought about by gauge invariance simply means an appropriate linear combination of the gradients of the phase variable and the gauge field is invariant. No gauge fixing is needed in this approach that is closest to the spirit of the gauge principle. We derive an exact formula for the condensate fraction and in case it is zero, an exact formula for the anomalous exponent. We also derive a formula for the vortex strength which involves computing radiation corrections.

cond-mat.other↗

arXiv2004

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.

cond-mat.str-el↗

arXiv2003

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.

cond-mat.str-el↗

arXiv2003

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.

cond-mat.str-el↗

arXiv2003

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.

cond-mat.str-el↗

arXiv2003

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.

cond-mat.str-el↗

arXiv2001

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.

cond-mat↗

arXiv2001

Calculus of Sea-Displacement Operators

Sea-Displacement Operators for fermions are defined in terms of the Fermi fields in a one-component Fermi system. The main conclusions of this article fully corroborate the conjectures made in our earlier works and provide a mathematically rigorous foundations for these works. These ideas are generalised to electron-hole systems where we are able to explore clearly the nature of exciton-exciton interactions. We find that exciton-exciton interactions in an ideal model of GaAs are not adequately treated as simply of the two-body type; rather, the interactions are mediated by the exchange of other bosons that are present in the system. These bosons are identified explicitly and the exciton Green function is calculated. This excercise is also intended to be a precursor to a systematic nonperturbative treatment of gauge theories.

cond-mat↗

arXiv2000

Bosonization Rules for Electron-Hole Systems - II

Here we write down and prove closed commutation rules for Fermi bilinears in a two-component Fermi system in terms of the relevant sea-bosons. We show how the commutation rules come out correctly within the RPA-approximation as do the zero temperature correlation functions. We write down hamiltonains of nonrelativistic interacting electron-hole systems and point out several attractive features such as the natural roles excitons play in this language. We then use this language to derive a set of equations analogous to the Semiconductor Bloch Equations in the presence of phonons and with external fields such as those present in pump-probe experiments. We solve these equations using parameters of interesting and topical materials such as GaN and compare with some recent experimental data.

cond-mat↗

arXiv2000

Improved Theory of Single-Particle Properties Using Sea-bosons

In this article, we combine the ideas introduced by us earlier in various proportions to arrive at a simple and yet powerful means of studying single-particle properties of homogeneous Fermi systems in detail without making assumptions regarding the validity or otherwise of Fermi-liquid theory. Novelties include the exact forms of the momentum distribution and spectral functions in the intermediate density regime and a dielectric function that is sensitive to significant qualitative changes in single-particle properties. This time, care is taken to include the particle-hole mode by interpreting the sum over modes as a weighted sum with the dynamical structure factor appearing as the weight.

cond-mat↗

arXiv1999

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).

cond-mat↗

arXiv1998

Corrections to the RPA Dielectric Function Induced by Fluctuations in the Momentum Distribution

In this article, we introduce a new dielectric function that is different even from the generalised RPA, first introduced in cond-mat/9810043, in that it pays attention to fluctuations in the momentum distribution. We argued that this is important when the momentum distribution is very nonideal. This new dielectric function reduces to the generalised RPA when the number-fluctuations are small, and the generalised RPA in turn reduces to the traditional RPA dielectric function when the momentum distribution is close to ideal.

cond-mat↗

arXiv1998

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.

cond-mat↗

arXiv1998

Exact Single-Particle Green Functions of Fermi Systems Without Using Bosonization or Are Hartree-Fock and Random Phase Approximations 'Controlled Approximations' ?

In this article, we revisit the question of the validity of Hartree-Fock and random-phase approximations. We show that there is a connection between the two and while the RPA as it is known in much of the physics literature is of limited validity, there is a generalised sense in which the random phase approximation is of much wider applicability including to systems that do not possess Fermi surfaces. The main conclusion is that the Hartree-Fock approximation is a mean-field idea applied to the density operator, and the random-phase approximation is a mean-field idea applied to the number operator. The generalised RPA is used to compute single-particle properties such as momentum distribution and spectral functions. It is found that we have to go beyond the generalised RPA and include fluctuations in the momentum distribution in order to recover a nonzero imaginary part of the one-particle self energy, which is also explicitly computed, all this in any number of spatial dimensions and no bosonization is needed.

cond-mat.str-el↗

arXiv1998

Computing Number Fluctuations

Here we try and delienate the properties of the function that corresponds to fluctuations in the momentum distribution. The quantity denoted by $ N(k,k^{'}) $ is quite an interesting object. It satisfies various elegant sum rules and is also quite singular in some respects. All these properties are brought out and a formal connection is found between this object and the momentum distribution of the interacting and non-interacting many-fermion systems. This exercise is quite general in that it does not refer to any particular hamiltonian. It is also quite useful since in an earlier preprint(cond-mat/9810043) we showed how to compute the spectral function and single-particle lifetime of homogeneous Fermi systems where the only undetermined quantity was this function $ N(k,k^{'}) $.

cond-mat↗

arXiv1998

Energy Levels of Multielectron Atoms using the Sea-boson Method

In this article, we study an antithesis of the homogeneous Fermi system (jellium model) namely a single multielectron atom using the sea-boson approach. This system in addition to having a small number of electrons(finite system) is also extremely inhomogeneous. This means that the plane-wave basis is ill-suited to study this system, instead we use a basis consisting of the eigenfunctions of an electron interacting with the nucleus situated at the origin (ideal atom). We compute the energy levels of this system and polarizabilities and compare with the results of other approaches such as Hartree-Fock and pseudopotentials for the former and aysmptotic wavefunctions for the latter and with experiments.

physics.atom-ph↗