184 research outputs found

### Mott Transition in the Hubbard model

In this article, I discuss W.Kohn's criterion for a metal insulator
transition, within the framework of a one band Hubbard model. This and related
ideas are applied to 1-dimensional Hubbard systems, and some intersting
miscellaneous results discussed. The Jordan Wigner transformation converting
the two species of fermions to two species of hardcore bosons is performed in
detail, and the ``extra phases'' arising from odd-even effects are explicitly
derived. Bosons are shown to prefer zero flux (i.e. diamagnetism), and the
corresponding ``happy fluxes'' for the fermions identified. A curious result
following from the interplay between orbital diamagnetism and spin polarization
is highlighted.
A ``spin-statistics'' like theorem, showing that the anticommutation
relations between fermions of opposite spin are crucial to obtain the SU(2)
invariance is pointed out.Comment: 15 page

### Spin-Ice and Other Frustrated Magnets on the Pyrochlore Lattice

The recent identification of the dysprosium titanate compound $Dy_2 Ti_2 O_7$
as a ``Spin-Ice'', i.e. the spin analog of regular entropic ice of Pauling, has
created considerable excitement. The ability to manipulate spins using magnetic
fields gives a unique advantage over regular ice in these systems, and has been
used to study the recovery of entropy. Predicted magnetization plateaus have
been observed, testing the underlying model consisting of a competition between
short ranged super exchange, and long ranged dipolar interactions between
spins. I discuss other compounds that are possibly spin ice like: $Ho_2 Ti_2
O_7$, and the two stannates $Ho_2 Sn_2 O_7$, $Dy_2 Sn_2 O_7$.Comment: 4 pages, Invited Contribution for Low Temperature Conference LT23,
August 20-27, Hiroshima JAPAN, to be published in Physica B & C (2003

### Theory of extreme correlations using canonical Fermions and path integrals

The t-J model is studied using a novel and rigorous mapping of the Gutzwiller
projected electrons, in terms of canonical electrons. The mapping has
considerable similarity to the Dyson-Maleev transformation relating spin
operators to canonical Bosons. This representation gives rise to a non
Hermitean quantum theory, characterized by minimal redundancies. A path
integral representation of the canonical theory is given. Using it, the salient
results of the extremely correlated Fermi liquid (ECFL) theory, including the
previously found Schwinger equations of motion, are easily rederived. Further a
transparent physical interpretation of the previously introduced auxiliary
Greens functions and the caparison factor is obtained.
The low energy electron spectral function in this theory with a strong
intrinsic asymmetry, is summarized in terms of a few expansion coefficients.
These include an important emergent energy scale $\Delta_0$ that shrinks to
zero on approaching the insulating state, thereby making it difficult to access
the underlying low energy Fermi liquid behavior. The scaled low frequency ECFL
spectral function is related simply to the Fano line shape. The resulting
energy dispersion (EDC or MDC) is a hybrid of a massive and a massless Dirac
spectrum $E^*_Q\sim \gamma\, Q- \sqrt{\Gamma_0^2 + Q^2}$, where the vanishing
of $Q$, a momentum like variable, locates the kink. Therefore the quasiparticle
velocity interpolates between $(\gamma \mp 1)$ over a width $\Gamma_0$ on the
two sides of $Q=0$. The resulting kink strongly resembles a prominent low
energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate
materials. We also propose novel ways of analyzing the ARPES data to isolate
the predicted asymmetry between particle and hole excitations.Comment: 27 pages, 1 Figure, Updated figure and discussion of the "kink"
featur

### $Sr Cu_2 (BO_3)_2$: A Unique Mott Hubbard Insulator

We discuss the recently discovered system $Sr Cu_2 (BO_3)_2$, a realization
of an exactly solvable model proposed two decades earlier. We propose its
interpretation as a Mott Hubbard insulator. The possible superconducting phase
arising from doping is explored, and its nature as well as its importance for
testing the RVB theory of superconductivity are discussed.Comment: 18 pages,7 figures, Based on Invited Talk at 16th Nishinomiya Yukawa
memorial symposium, Nov 13-14, Nishinomiya. To appear in Progress in
Theoretical Physics, Suppliment 145(2002

### Majorana Fermion Representation For An Antiferromagnetic Spin-1/2 Chain

We study the 1-dimensional Heisenberg antiferromagnet with s=1/2 using a
Majorana representation of the s=1/2 spins. A simple Hartree-Fock approximation
of the resulting model gives a bilinear fermionic description of the model.
This description is rotationally invariant and gives power-law correlations in
the ``ground state'' in a natural fashion. The excitations are a two-parameter
family of particles, which are spin-1 objects. These are contrasted to the
``spinon'' spectrum, and the technical aspects of the representation are
discussed, including the problem of redundant states.Comment: 24 pages in LaTeX, no figures; some clarifications/additions have
been made following the referee's comments; to appear in Phys. Rev.

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