Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases

Using the bosonization approach we study fermionic systems with a nonlinear dispersion relation in dimension d>2. We explicitly show how the band curvature gives rise to interaction terms in the bosonic version of the model. Although these terms are perturbatively irrelevant in relation to the Landau Fermi liquid fixed point, they become relevant perturbations when instabilities take place. Using a coherent state path integral technique we built up the effective action that governs the dynamics of the Fermi surface fluctuations. We consider the combined effect of fermionic interactions and band curvature on possible anisotropic phases triggered by negative Landau parameters. In particular we study in some detail the phase diagram for the isotropic/nematic/hexatic quantum phase transition.Comment: RevTeX4, 9 pages, 2 eps figures, Final version as appeared in Phys.Rev.

Role of disorder in half-filled high Landau levels

We study the effects of disorder on the quantum Hall stripe phases in half-filled high Landau levels using exact numerical diagonalization. We show that, in the presence of weak disorder, a compressible, striped charge density wave, becomes the true ground state. The projected electron density profile resembles that of a smectic liquid. With increasing disorder strength W, we find that there exists a critical value, W_c \sim 0.12 e^2/\epsilon l, where a transition/crossover to an isotropic phase with strong local electron density fluctuations takes place. The many-body density of states are qualitatively distinguishable in these two phases and help elucidate the nature of the transition.Comment: 4 pages, 4 figure

Quantum Field Theory Description of Tunneling in the Integer Quantum Hall Effect

We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the tunneling. It is shown that the phenomenon of fermion number fractionalization is expected to occur, either localized in conveniently modulated barriers or in the form of free excitations, once lattice effects are taken into account. This opens the experimental possibility of an observation of fractional charges with internal structure, close to the magnetic length scale. The coupling of the system to external gauge fields is performed, leading us to the exact quantization of the Hall conductivity at the interface. The field theory approach is well supported by a numerical diagonalization of the microscopic Hamiltonian.Comment: 34 pages, PUPT-1468. (3 figures available upon resquest to the authors at [email protected] or [email protected]

Three dimensional fermionic determinants, Chern-Simons and nonlinear field redefinitions

The three dimensional abelian fermionic determinant of a two component massive spinor in flat euclidean space-time is resetted to a pure Chern-Simons action through a nonlinear redefinition of the gauge field.Comment: 18 pages, latex2

Mean-field Phase Diagram of Two-Dimensional Electrons with Disorder in a Weak Magnetic Field

We study two-dimensional interacting electrons in a weak perpendicular magnetic field with the filling factor $\nu \gg 1$ and in the presence of a quenched disorder. In the framework of the Hartree-Fock approximation, we obtain the mean-field phase diagram for the partially filled highest Landau level. We find that the CDW state can exist if the Landau level broadening $1/2\tau$ does not exceed the critical value $1/2\tau_{c}=0.038\omega_{H}$. Our analysis of weak crystallization corrections to the mean-field results shows that these corrections are of the order of $(1/\nu)^{2/3}\ll 1$ and therefore can be neglected

Theory of the Quantum Hall Smectic Phase II: Microscopic Theory

We present a microscopic derivation of the hydrodynamic theory of the Quantum Hall smectic or stripe phase of a two-dimensional electron gas in a large magnetic field. The effective action of the low energy is derived here from a microscopic picture by integrating out high energy excitations with a scale of the order the cyclotron energy.The remaining low-energy theory can be expressed in terms of two canonically conjugate sets of degrees of freedom: the displacement field, that describes the fluctuations of the shapes of the stripes, and the local charge fluctuations on each stripe.Comment: 20 pages, RevTex, 3 figures, second part of cond-mat/0105448 New and improved Introduction. Final version as it will appear in Physical Review

Bosonic String and String Field Theory: a solution using Ultradistributions of Exponential Type

In this paper we show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way string and string field theories. A new Lagrangian for the closed string is obtained and shown to be equivalent to Nambu-Goto's Lagrangian. We also show that the string field is a linear superposition of UET of compact support CUET). We evaluate the propagator for the string field, and calculate the convolution of two of them.Comment: 30 page

Charge Density Wave-Assisted Tunneling Between Hall Edge States

We study the intra-planar tunneling between quantum Hall samples separated by a quasi one-dimensional barrier, induced through the interaction of edge degrees of freedom with the charge density waves of a Hall crystal defined in a parallel layer. A field theory formulation is set up in terms of bosonic (2+1)-dimensional excitations coupled to (1+1)-dimensional fermions. Parity symmetry is broken at the quantum level by the confinement of soliton-antisoliton pairs near the tunneling region. The usual Peierls argument allows to estimate the critical temperature $T_c$, so that for $T > T_c$ mass corrections due to longitudinal density fluctuations disappear from the edge spectrum. We compute the gap dependence upon the random global phase of the pinned charge density wave, as well as the effects of a voltage bias applied across the tunneling junction.Comment: Additional references + 1 figure + more detailed discussions. To be published in Phys. Rev.

Interacting Electrons on a Fluctuating String

We consider the problem of interacting electrons constrained to move on a fluctuating one-dimensional string. An effective low-energy theory for the electrons is derived by integrating out the string degrees of freedom to lowest order in the inverse of the string tension and mass density, which are assumed to be large. We obtain expressions for the tunneling density of states, the spectral function and the optical conductivity of the system. Possible connections with the phenomenology of the cuprate high temperature superconductors are discussed.Comment: 14 pages, 1 figur

Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem

We investigate the convergence properties of optimized perturbation theory, or linear $\delta$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature T_c for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for $T_c$ already at the first non-trivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.Comment: 38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev.