arXiv subjects

Jainendra K Jain

Publications and source records attributed to Jainendra K Jain.

3 recordsLinked to original sources

arXiv2021

An Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field

States of strongly interacting particles are of fundamental interest in physics, and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the standard practice of restricting to the lowest LL, introduce a model short-range interaction that is infinitely strong compared to the cyclotron energy. We demonstrate that this model lends itself to an exact solution for the ground as well as excited states at arbitrary filling factors $ν<1/2p$ and produces a fractional quantum Hall effect at fractions of the form $ν=n/(2pn+ 1)$, where n and p are integers. The fractional quantum Hall states of our model share many topological properties with the corresponding Coulomb ground states in the lowest Landau level, such as the edge physics and the fractional charge of the excitations.

cond-mat.str-el↗

arXiv2018

Search for exact local Hamiltonians for general fractional quantum Hall states

We report on our systematic attempts at finding local interactions for which the lowest-Landau-level projected composite-fermion wave functions are the unique zero energy ground states. For this purpose, we study in detail the simplest non-trivial system beyond the Laughlin states, namely bosons at filling $ν=\frac{2}{3}$ and identify local constraints among clusters of particles in the ground state. By explicit calculation, we show that no Hamiltonian up to (and including) four particle interactions produces this state as the exact ground state, and speculate that this remains true even when interaction terms involving greater number of particles are included. Surprisingly, we can identify an interaction, which imposes an energetic penalty for a specific entangled configuration of four particles with relative angular momentum of $6\hbar$, that produces a unique zero energy solution (as we have confirmed for up to 12 particles). This state, referred to as the $λ$-state, is not identical to the projected composite-fermion state, but the following facts suggest that the two might be topologically equivalent: the two sates have a high overlap; they have the same root partition; the quantum numbers for their neutral excitations are identical; and the quantum numbers for the quasiparticle excitations also match. On the quasihole side, we find that even though the quantum numbers of the lowest energy states agree with the prediction from the composite-fermion theory, these states are not separated from the others by a clearly identifiable gap. This prevents us from making a conclusive claim regarding the topological equivalence of the $λ$ state and the composite-fermion state. Our study illustrates how new candidate states can be identified from constraining selected many particle configurations and it would be interesting to pursue their topological classification.

cond-mat.str-el↗

arXiv2013

Tripartite Composite Fermion States

The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction $ν=2+\nicefrac{3}{5}$, and thereby also its hole conjugate at $2+\nicefrac{2}{5}$. We study a general class of "tripartite" composite fermion wave functions, which reduce to the Read-Rezayi ground state and quasiholes for appropriate quantum numbers, but also allow a construction of wave functions for quasiparticles and neutral excitations by analogy to the standard composite fermion theory. We present numerical evidence in finite systems that these trial wave functions capture well the low energy physics of a 4-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at $2+\nicefrac{3}{5}$, and find reasonably good agreement. The ground state as well as several excited states of the 4-body interaction are seen to evolve adiabatically into the corresponding Coulomb states for N=15 particles. These results support the plausibility of the Read-Rezayi proposal for the $2+\nicefrac{2}{5}$ and $2+\nicefrac{3}{5}$ fractional quantum Hall effect. However, certain other proposals also remain viable, and further study of excitations and edge states will be necessary for a decisive establishment of the physical mechanism of these fractional quantum Hall states.

cond-mat.str-el↗