Localization-delocalization transitions in strongly correlated electron systems

Hideo Aoki

We study two examples of transport properties of electron systems in the vicinity of a critical point. The first example, a one-body problem, is the disorder-driven metal-insulator transition in the integer quantum Hall system. We have numerically examined the multifractality of the critical wavefunction, which is relevant to an anomalous diffusion of electrons. The second example, a many-body problem, is the paramagnetic-ferromagnetic transition in a strongly correlated clean electron system. We show that the proximity to ferromagnetism can give rise to a negative magnetoresistance. These exemplify how a criticality manifests itself in transport properties.

I. V. Sankar, Soma Mukhopadhyay, Ashok Chatterjee

Y. Yin

We present a low-energy effective theory to describe the localization-delocalization transition, which occurs for wave functions of electrons and holes injected individually by a voltage pulse with noninteger flux quantum. We find that the transition can be described by an effective scattering matrix in a truncated low-energy space, which is composed of two parts. The first part describes the infrared-divergence of the scattering matrix, while the second part represents the high-energy correlation. For short-tailed pulses which decay faster than Lorentzian, the scattering matrix exhibits solely an inverse linear divergence in the infrared limit. The divergence is responsible for the dynamical orthogonality catastrophe, which leads to electron-hole pairs with delocalized wave functions. In contrast, the high-energy correlation can be approximated by a constant term, which leads to electron-hole pairs with localized wave functions. Due to the competition between the two terms, the wave functions can undergo a localization-delocalization transition, which occurs for electrons and holes injected individually by the voltage pulse. As a consequence, the localization-delocalization transitions for all short-tailed pulses can be described by the same effective scattering matrix, suggesting that they belong to the same universality class. For pulses with longer tails, the scattering matrix can exhibit additional infrared-divergences. We show that a Lorentzian pulse gives rise to a logarithmic divergence, while a fractional-powered Lorentzian pulse gives rise to a power-law divergence. The additional divergence can lead to localization-delocalization transitions belonging to different universality classes. These results demonstrate the fine-tuning capabilities of the localization-delocalization transition in time-dependent quantum transport.

Rajdeep Sensarma, Abhisek Samanta, Ahana Chakraborty

Pavel V. Shevchenko

V. Dobrosavljević, A. A. Pastor, Branislav K. Nikolić

We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain the typical local density of states as an order parameter, thereby reproducing the essential features of a phase diagram of localization-delocalization quantum phase transition in the standard lattice models of the disordered electron problem. Due to the local character of our theory, it can easily be combined with dynamical mean-field approaches to strongly correlated electrons, thus opening an attractive avenue for a genuine non-perturbative treatment of the interplay of strong interactions and strong disorder.