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

Scaling of the von Neumann entropy in a two-electron system near the ionization threshold

Omar Osenda, Pablo Serra

The critical behavior of entanglement near a quantum phase transition has been studied intensely over the past few years. Few-body quantum systems show critical behavior near the ionization point. We investigate the scaling properties of the von Neumann entropy for an atomiclike system near the ionization threshold. Using finite size scaling methods we calculate the critical charge and the critical exponent associated to the von Neumann entropy. The parallelism between the behavior of entanglement near a quantum phase transition and the behavior of the von Neumann entropy in a critical few-body quantum system is analyzed.The critical behavior of entanglement near a quantum phase transition has been studied intensely over the past few years. Few-body quantum systems show critical behavior near the ionization point. We investigate the scaling properties of the von Neumann entropy for an atomiclike system near the ionization threshold. Using finite size scaling methods we calculate the critical charge and the critical exponent associated to the von Neumann entropy. The parallelism between the behavior of entanglement near a quantum phase transition and the behavior of the von Neumann entropy in a critical few-body quantum system is analyzed.

Physical Review AApr 30, 200759 citations

Dynamic scaling hypothesis at the phase transition point

L. Wojtczak, B. Mrygoń

physica status solidi (b)Sep 1, 19762 citations

A Detailed View of Quantum Phase Transitions

ScienceJan 28, 20000 citations

Universality and Scaling Properties of Correlation Functions Near a Quantum Phase Transition

Rouhollah Jafari

In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of correlation functions with respect to the parameter that drives the quantum phase transitions, exhibit logarithmic divergence and finite size scaling the same as entanglement. In other words the non-analytic and finite size scaling behaviors of entanglement is not its intrinsic properties and inherit from the non-analytic and scaling behaviors of correlation functions and surveying at least the nearest neighbor correlation functions could specify the scaling and divergence properties of entanglement. However we show that the correlation functions could capture the quantum critical point without pre-assumed order parameters even for the cases where the two-body entanglement is absent.In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of correlation functions with respect to the parameter that drives the quantum phase transitions, exhibit logarithmic divergence and finite size scaling the same as entanglement. In other words the non-analytic and finite size scaling behaviors of entanglement is not its intrinsic properties and inherit from the non-analytic and scaling behaviors of correlation functions and surveying at least the nearest neighbor correlation functions could specify the scaling and divergence properties of entanglement. However we show that the correlation functions could capture the quantum critical point without pre-assumed order parameters even for the cases where the two-body entanglement is absent.

arXiv:1101.2354Jan 12, 20111 citation

{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.