Absence of crystalling ordering in quantum systems of one dimension

Б. И. Садовников, Elena M. Sorokina

Biao Huang, Ying-Hai Wu, W. Vincent Liu

Time crystals, a phase showing spontaneous breaking of time-translation symmetry, has been an intriguing subject for systems far away from equilibrium. Recent experiments found such a phase in both the presence and the absence of localization, while in theories localization by disorder is usually assumed a priori. In this work, we point out that time crystals can generally exist in systems without disorder. A series of clean quasi-one-dimensional models under Floquet driving are proposed to demonstrate this unexpected result in principle. Robust time crystalline orders are found in the strongly interacting regime along with the emergent integrals of motion in the dynamical system, which can be characterized by level statistics and the out-of-time-ordered correlators. We propose two cold atom experimental schemes to realize the clean Floquet time crystals, one by making use of dipolar gases and another by synthetic dimensions.

Zeki Zeybek, Peter Schmelcher, Rick Mukherjee

Quantum fluctuations in frustrated systems can lead to the emergence of complex many-body phases. However, the role of quantum fluctuations in frustration-free lattices is less explored and could provide an interesting avenue for exploring new physics, and perhaps is easier to realize compared to frustrated lattice systems. Using Rydberg atoms with tunable interactions as a platform, we leverage strong van der Waals interactions and obtain a constrained model in one dimension with nonlocal fluctuations given by dipolar interactions alongside local fluctuations. The combined effect of such processes leads to intrinsically quantum-ordered Rydberg crystals through the order-by-disorder mechanism. Finite-size analyses indicate that combined fluctuations drive the transition from disordered to ordered phases, contrary to the expected direction. We provide a theoretical description to understand the physics of order-by-disorder in one-dimensional systems, which are typically seen only in higher dimensions.

S. M. Girvin

Canio Noce

We investigate the possibility of long range orbital order in low- dimensional systems. The study is performed within a two-orbital Hubbard model by means of the Bogoliubov's inequality. We show that, in one- and two-dimensions, and when a narrow conduction band is concerned, this model does not exhibit orbital order at any filling and any finite temperature.

Hanoch Gutfreund, W. A. Little