1. Quantum fermions on lattices

Projects:

1.1 Characterizing ground state from exact diagonalizations

  • Spinless fermion model -- a.k.a. "t-V" model: fermions of just one spin flavor hop on a square lattice, with a large (for simplicity, infinite) repulsive interaction between those on nearest-neighbor sites. This "poor man's Hubbard model" is comparatively tractable (numerically and analytically) and had interesting charged domain walls called stripes. (studied with Naigong Zhang, PhD '02)
  • Supersymmetric fermion model -- Paul Fendley has devised a similar model which -- for a special value of an added pair interaction -- is supersymmetric. We are trying to understand the phase diagram next to that special point, which Fendley conjectures to be multicritical. (With Dr. Stefanos Papanikolaou.)
  • Quantum renormalization group -- Siew-Ann Cheong (PhD '06) and I studied the density matrix for a block of sites in a ground state of (e.g.) a fermion model. The DM might be useful in guiding the truncation in a two-dimensional real-space renormalization (such as "contractor renormalization"). (Unfinished)
  • Correlation density matrix -- This is a way to discover what kind of correlations are dominant in a particular system; or to verify that a system has no hidden correlations. (with S-A Cheong, PhD 2006).

    • 1.2 Phenomenological modeling to describe of STM data from high-Tc cuprates

  • Quasiparticle echolocation -- The density of states (DOS) includes oscillations as a function of energy, the frequency of which is h/T, where T is the delay time for quasiparticles to echo off a nearby scatterer. In principle, this allows the locations of scatterers to be determined from measurements at a few sites nearby. (With Sumiran Pujari, grad).
  • Phonon couplings -- The DOS has features offset from the singular "coherence" peaks by a phonon energy. We are analytically studying the model in which BCS quasiparticles are given and the electron-phonon coupling is a perturbation (With Sumiran Pujari, grad).