We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the noninteracting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but nonzero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency $\ensuremath{\omega}$ and temperature T is determined by the scaling variable $\ensuremath{\omega}{/T}^{p}$ (where p is the exponent for the temperature dependence of the inelastic scattering rate) and not by $\ensuremath{\omega}/T,$ as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent p and the thermal exponent ${z}_{T}$ in terms of the scaling dimension $\ensuremath{-}\ensuremath{\alpha}<0$ of the interaction strength and the dynamical exponent z (which has the value $z=2),$ obtaining $p=1+2\ensuremath{\alpha}/z$ and ${z}_{T}=2/p.$ We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the noninteracting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but nonzero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency $\ensuremath{\omega}$ and temperature T is determined by the scaling variable $\ensuremath{\omega}{/T}^{p}$ (where p is the exponent for the temperature dependence of the inelastic scattering rate) and not by $\ensuremath{\omega}/T,$ as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent p and the thermal exponent ${z}_{T}$ in terms of the scaling dimension $\ensuremath{-}\ensuremath{\alpha}<0$ of the interaction strength and the dynamical exponent z (which has the value $z=2),$ obtaining $p=1+2\ensuremath{\alpha}/z$ and ${z}_{T}=2/p.$

arXiv:cond-mat/9906454Physical review. B, Condensed matterMar 15, 200051 citations

Interaction effects on quantum Hall transitions: Dynamical scaling laws and superuniversality

Prashant Kumar, P. A. Nosov, S. Raghu

We study the role of electron-electron interactions near integer and abelian fractional quantum Hall (QH) transitions using composite fermion (CF) representations. Interaction effects are encapsulated in CF theories as gauge fluctuations. Without gauge fluctuations, the CF system realizes a `dual' representation of the noninteracting QH transition. With gauge fluctuations, the system is governed by a gauged nonlinear sigma model (NLSM) with a $\ensuremath{\theta}\phantom{\rule{0.28em}{0ex}}\mathrm{term}$. While the transition is described by a strong-coupling fixed point of the NLSM, we are nevertheless able to deduce two of its properties. With $1/r$ interactions, (1) the transition has a dynamical exponent $z=1$ , and (2) all transitions are ``superuniversal'': fractional and integer QH transitions are in the same universality class. With short-range interactions, $z=2$ and the fate of superuniversality remains unclear.We study the role of electron-electron interactions near integer and abelian fractional quantum Hall (QH) transitions using composite fermion (CF) representations. Interaction effects are encapsulated in CF theories as gauge fluctuations. Without gauge fluctuations, the CF system realizes a `dual' representation of the noninteracting QH transition. With gauge fluctuations, the system is governed by a gauged nonlinear sigma model (NLSM) with a $\ensuremath{\theta}\phantom{\rule{0.28em}{0ex}}\mathrm{term}$. While the transition is described by a strong-coupling fixed point of the NLSM, we are nevertheless able to deduce two of its properties. With $1/r$ interactions, (1) the transition has a dynamical exponent $z=1$, and (2) all transitions are ``superuniversal'': fractional and integer QH transitions are in the same universality class. With short-range interactions, $z=2$ and the fate of superuniversality remains unclear.

arXiv:2006.11862Physical Review ResearchAug 24, 202211 citations

Edge-state critical behavior of the integer quantum Hall transition

Martin Puschmann, Philipp Cain, Michael Schreiber +1 more

arXiv:2004.01611The European Physical Journal Special TopicsApr 7, 20213 citations

Effects of Electron-Electron Interactions on the Integer Quantum Hall Transitions

D. H. Lee, Ziqiang Wang

We study the effects of the electron-electron interaction on the critical properties of the plateau transitions in the integer quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be $\ensuremath{-}0.66\ifmmode\pm\else\textpm\fi{}0.04$. Thus the noninteracting fixed point (characterized $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ and $\ensuremath{\nu}\ensuremath{\approx}2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ( $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ , $\ensuremath{\nu}\ensuremath{\approx}2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.We study the effects of the electron-electron interaction on the critical properties of the plateau transitions in the integer quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be $\ensuremath{-}0.66\ifmmode\pm\else\textpm\fi{}0.04$. Thus the noninteracting fixed point (characterized $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ and $\ensuremath{\nu}\ensuremath{\approx}2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ( $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, $\ensuremath{\nu}\ensuremath{\approx}2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.

arXiv:cond-mat/9511022Physical Review LettersMay 20, 199683 citations

{z}_{T}

in terms of the scaling dimension $\ensuremath{-}\ensuremath{\alpha}<0$ of the interaction strength and the dynamical exponent z (which has the value

z=2),

obtaining $p=1+2\ensuremath{\alpha}/z$ and

{z}_{T}=2/p.

1/r

interactions, (1) the transition has a dynamical exponent

z=1

, and (2) all transitions are ``superuniversal'': fractional and integer QH transitions are in the same universality class. With short-range interactions,

z=2

and the fate of superuniversality remains unclear.

z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

and $\ensuremath{\nu}\ensuremath{\approx}2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point (

z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

, $\ensuremath{\nu}\ensuremath{\approx}2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.