Critical behaviors in low dimensional quantum systems

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.

Masuo Suzuki

Yusuke Tomita

At low temperatures, the two-dimensional continuous-spin systems exhibit large correlation lengths. Some of them show the Berezinskii-Kosterlitz-Thouless-like transitions, and some others show pseudocritical behaviors for which correlation lengths are extremely large but finite. To distinguish pseudo and genuine critical behaviors, it is important to understand the nature of spin-spin correlations and topological defects at low temperatures in continuous-spin systems. In this paper, I develop a finite-size scaling analysis which is suitable for distinguishing the critical behavior and its applications to the two-dimensional XY, Heisenberg, and RP(2) models.

Giovanni Battimelli, Giovanni Ciccotti, Pietro Greco

Tôru Sakai

Demetris Nicolaides

In ferromagnets with low critical temperatures, dipolar interactions are the reason for the reduction of the critical dimension above which mean-field behavior prevails. Specifically, it is shown that a three-dimensional uniaxial system with dipole–dipole interactions falls into the universality class of a four-dimensional strictly short-range system, whose behavior is mean field with subtle logarithmic corrections which reflect the nonmean-field behavior that sets in fully below four space dimensions.