arXiv subjects

M. Voropaev

Publications and source records attributed to M. Voropaev.

2 recordsLinked to original sources

arXiv2002

The $θ$ vacuum reveals itself as the fundamental theory of the quantum Hall effect. I. Confronting controversies

The $θ$ dependence of the Grassmannian $U(m+n)/U(m)\times U(n)$ non-linear $σ$ model is reexamined. This general theory provides an important laboratory for studying the quantum Hall effect, in the special limit $m=n=0$ (replica limit). We discover however that the quantum Hall effect is in fact independent of this limit and exists as a generic topological feature of the theory for all non-negative values of $m$ and $n$. The results are in concflict with many of the historical ideas and expectations on the basis of the large $N$ expansion of the $CP^{N-1}$ or $SU(N)/U(N-1)$ model

cond-mat.mes-hall↗

arXiv2000

The large N theory exactly reveals the quantum Hall effect and theta-renormalization

We revisit the $θ$ dependence in $CP^{N-1}$ model with large $N$. We study the consequences of a recently discovered new ingredient of the instanton vacuum, i.e. the massless chiral edge excitations. Contrary to the previous believes, our results demonstrate that the large $N$ expansion displays all the fundamental features of the quantum Hall effect. This includes the {\em robust} quantization of the Hall conductance, as well as the appearance of massless bulk excitations at $θ= π$. We conclude that the quantum Hall effect is a generic feature of the instanton vacuum, i.e. for any number of field components and not just for the theory in the replica limit alone.

cond-mat.mes-hall↗