Numerical studies on novel critical phenomena in low-dimensional electron systems due to randomness and strong correlation

Nobuhiro Sue, Yuhei Natsume, 須江 信洋 +1 more

Masuo Suzuki

Yuto Ashida

Quantum critical phenomena originate from collective behavior of strongly correlated particles and lie at the heart of universal low-energy properties in many-body systems. The strong correlation between quantum particles is particularly prominent in a low-dimensional system. In the first part of this Chapter, we identify what types of measurements are relevant to one-dimensional low-energy properties and address how they qualitatively alter the underlying quantum critical behavior. In the second part, we study how the measurement backaction influences on quantum phase transitions in higher dimensions by focusing on the Bose-Hubbard model. For all the theoretical considerations, we discuss possible experimental implementations in ultracold atomic gases.

Maryam Pirgholi, M. N. Najafi, V. Adami

We investigate self-organized criticality in a two-dimensional electron gas (2DEG) by introducing a lattice-based model that incorporates electron-electron interactions through the concept of coherence length. Our numerical simulations demonstrate that in the strongly interacting regime, the system exhibits a distinct set of universal critical exponents, markedly different from those observed in the weakly interacting limit. This dichotomy aligns with experimental findings on the metal-insulator transition in 2DEGs, where high-interaction strength (low carrier density) leads to qualitatively different behavior. The analysis includes scaling of the average electron density with temperature, the power spectral density, and the statistics of electronic avalanches, including avalanche size distributions and autocorrelation functions. In all cases the extracted exponents differ significantly between the weak and strong interaction regimes, highlighting the emergence of two universality classes governed by interaction strength. These results underscore the critical role of electron correlations in the self-organized behavior of low-dimensional electronic systems.

Yasuhiro Hatsugai

Steven Allan Kivelson

The 2012 Gordon Conference on Correlated Electron Systems will present cutting-edge research on emergent properties arising from strong electronic correlations. While we expect the discussion at the meeting to be wide-ranging, given the breadth of the title subject matter, we have chosen several topics to be the particular focus of the talks. These are New Developments in Single and Bilayer Graphene, Topological States of Matter, including Topological Insulators and Spin Liquids, the Interplay Between Magnetism and Unconventional Superconductivity, and Quantum Critical Phenomena in Metallic Systems. We also plan to have shorter sessions on Systems Far From Equilibrium, Low Dimensional Electron Fluids, and New Directions (which will primarily focus on new experimental methodologies and their interpretation).