Shimul Akhanjee

Spin-charge separation in a strongly correlated spin-polarized chain

We combine the first-quantized path-integral formalism and bosonization to develop a phenomenological theory for spin-charge-coupled dynamics in one-dimensional (1D) ferromagnetic systems with strong interparticle repulsion, at low temperatures. We assume an effective spin-charge separation and retain the standard Luttinger-liquid plasmon branch, which is explicitly coupled to a ferromagnetic spin-wave texture with a quadratic dispersion. The dynamic spin structure severely suppresses the plasmon peak in the single-particle propagator, in both fermionic and bosonic systems. Our analysis provides an effective theory for the new universality class of 1D ferromagnetic systems, capturing both the trapped spin and propagating spin-wave regimes of the long-time behavior.

Spherical spin-glass-Coulomb-gas duality: solution beyond mean-field theory.

We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé τ{IV}[n] function in the n→0 limit. The large-N thermodynamics exactly recovers that of Kosterlitz, Thouless, and Jones [Phys. Rev. Lett. 36, 1217 (1976)10.1103/PhysRevLett.36.1217]. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.

Quasiparticle excitations in Bose-Fermi mixtures

We analyze the excitation spectrum of a three-dimensional Bose-Fermi mixture with tunable resonant interaction parameters and high hyperfine spin multiplets. We focus on a three-particle vertex describing fermionic and bosonic atoms which can scatter to create fermionic molecules or disassociate. For a single molecular level, in analogy to the single magnetic impurity problem we argue that the low-lying excitations of the mean-field theory are described by the Fermi-liquid picture with a quasiparticle weight and charge which is justified by a 1/N{sub {psi}}expansion, expected to be exact in the limit of infinite degeneracy (or very high fermionic spin) N{sub {psi}{yields}{infinity}}. Our emphasis is placed on the novel conditions for chemical equilibrium and how many-body chemical reactions renormalize the bosonic chemical potential, modifying condensation and superfluid-insulator transitions.

Disorder induced transition into a one-dimensional wigner glass.

The destruction of quasi-long-range crystalline order as a consequence of strong disorder effects is shown to accompany the strict localization of all classical plasma modes of one-dimensional Wigner crystals at T=0. We construct a phase diagram that relates the structural phase properties of Wigner crystals to a plasmon delocalization transition recently reported. Deep inside the strictly localized phase of the strong disorder regime, we observe glasslike behavior. However, well into the critical phase with a plasmon mobility edge, the system retains its crystalline composition. We predict that a transition between the two phases occurs at a critical value of the relative disorder strength. This transition has an experimental signature in the ac conductivity as a local maximum of the largest spectral amplitude as a function of the relative disorder strength.

Quantum phase coherence in non-Markovian and reaction-diffusive transport

We study quantum phase coherence and weak localization (WL) in disordered metals with restricted back-scattering and phenomenologically formulate a large class of unconventional transport mechanisms as modified diffusion processes not captured by the Boltzmann picture. Inspired by conductivity measurements in ferromagnetic films and semiconductors where anomalous power law corrections have been observed, we constrain memory dependent, self avoidance effects onto the quantum enhanced back-scattered trajectories, drastically altering the effect of weak localization in two dimensions (2D). Scale dependent corrections to the conductivity fail to localize the electrons in

Negative effective-mass transition and anomalous transport in power-law hopping bands

d \ge 2

Anderson transition of the plasma oscillations of one-dimensional disordered Wigner lattices

for sufficiently weak disorder. Additionally, we analyze quantum transport in reaction-diffusion systems governed by the Fishers equation and observe asymptotically similar delocalization in 2D. Such unconventional transport might be relevant to certain non-Fermi liquid or strongly correlated phases in 2D within the negative compressibility regime.

Exact longitudinal plasmon dispersion relations for one and two dimensional Wigner crystals

We study the stability of spinless Fermions with power law hopping

Statistical, collective, and critical phenomena of classical one-dimensional disordered Wigner lattices

H_{ij} \propto |i - j|^{-\alpha}

Statistical, Collective and Critical Phenomena of Classical 1D Disordered Wigner Lattices

. It is shown that at precisely