Lowest Landau level theory of the bosonic Jain states
Abstract
Quantum Hall systems offer the most familiar setting where strong interparticle interactions combine with the topology of single particle states to yield novel phenomena. Despite our mature understanding of these systems, an open challenge has been to to develop a microscopic theory capturing both their universal and nonuniversal properties, when the Hamiltonian is restricted to the noncommutative space of the lowest Landau level. Here we develop such a theory for the Jain sequence of bosonic fractional quantum Hall states at fillings $\nu={p\over p+1}$. Building on a lowest Landau level description of a parent composite fermi liquid at $\nu = 1$, we describe how to dope the system to reach the Jain states. Upon doping, the composite fermions fill noncommutative generalizations of Landau levels, and the Jain states correspond to integer composite fermion filling. Using this approach, we obtain an approximate expression for the bosonic Jain sequence gaps with no reference to any longwavelength approximation. Furthermore, we show that the universal properties, such as Hall conductivity, are encoded in an effective noncommutative ChernSimons theory, which is obtained on integrating out the composite fermions. This theory has the same topological content as the familiar Abelian ChernSimons theory on commutative space.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.03700
 Bibcode:
 2021arXiv211003700G
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 40 pages, 1 figure, and 2 appendices