Dynamic and quantum phase transitions in low-dimensional highly correlated systems

Kazuo Ueda, 上田 和夫

Dragana Popović

This chapter focuses on studies of the critical behavior of conductivity in two-dimensional electron systems (2DES) with different amounts and types of disorder as well as different ranges of Coulomb interactions, in order to identify possible universality classes of the 2D metal-insulator transition (MIT). It discusses the manifestations of glassiness in both low- and high-disorder samples. The chapter examines the critical region near the 2D MIT in particular on describing conductivity measurements that have demonstrated dynamical scaling, the main signature of the MIT as a quantum phase transition. It also focuses on experiments that probe the nature of the insulating state, as well as charge dynamics across the MIT, in both high- and low-disorder 2DESs. There is substantial evidence that in many materials near the MIT both strong electronic correlations and disorder play an important role, and thus their competition is expected to lead to glassy behavior of electrons, in analogy with other frustrated systems.

Can Shao, Hantao Lu, Xiao Zhang +3 more

By employing an unbiased numerical method, we investigate the ultrafast dynamics of the correlated systmes in one and two dimensions. For the extended Hubbard model on a periodic chain, the high-harmonic generation (HHG) of system close to the quantum critical point (QCP) is more intense than HHG in the neighboring two gapped phases, i.e., charge-density-wave and spin-density-wave states, especially in low-frequencies. The reason can be attributed to that the system in QCP is more sensitive to the external field and there are more optical-allowed excited states available to furnish photon-absorbing channels for this nonlinear processes. This feature provides a possibility of detecting the quantum phase transition by means of high-harmonic spectroscopy. We also expect to generate stronger HHG by irradiating materials with parameter settings close to QCP. In addition, we find that the even- or odd-order components of HHG can be used to distinguish the topologically ordered phases from locally ordered ones in a two-dimensional interacting Haldane model.

Ákos Rapp

Longhua Jiang

Farid Madani, Maxime Denis, Pascal Szriftgiser +3 more

Phase transitions are prevalent throughout physics, spanning thermal phenomena like water boiling to magnetic transitions in solids. They encompass cosmological phase transitions in the early universe and the transition into a quark-gluon plasma in high-energy collisions. Quantum phase transitions, particularly intriguing, occur at temperatures near absolute zero and are driven by quantum fluctuations rather than thermal ones. The strength of the fluctuations is very sensitive to the dimensionality of the physical systems, which determines the existence and nature of phase transitions. Low-dimensional systems often exhibit suppression of phase transitions, while high-dimensional systems tend to exhibit mean-field-like behavior. The localization-delocalization Anderson transition stands out among quantum phase transitions, as it is thought to retain its non-mean-field character across all dimensions. This work marks the first observation and characterization of the Anderson transition in four dimensions using ultracold atoms as a quantum simulator with synthetic dimensions. We characterize the universal dynamics in the vicinity of the phase transition. We measure the critical exponents describing the scale-invariant properties of the critical dynamics, which are shown to obey Wegner's scaling law. Our work is the first experimental demonstration that the Anderson transition is not mean-field in dimension four.