Probing universal phase diagram of dimensional crossover with an atomic quantum simulator

TL;DR

This study uses an atomic quantum simulator with tunable anisotropy and temperature to explore a universal phase diagram of dimensional crossover, revealing distinct quantum and thermal regimes and their universality classes.

Contribution

It introduces a versatile atomic quantum simulator capable of continuous control over anisotropy and temperature to systematically study dimensional crossover phenomena.

Findings

Identification of regimes from quantum three to zero dimensions at low temperatures.

Observation of a thermal regime emerging between quantum zero and integer dimensions with increasing temperature.

Discovery of four universality classes for quantum-to-thermal transitions and a fifth class involving crossing low-dimensional quantum regimes.

Abstract

Dimensionality is a fundamental concept in physics, which plays a hidden but crucial role in various domains, including condensed matter physics, relativity and string theory, statistical physics, etc. In quantum physics, reducing dimensionality usually enhances fluctuations and leads to novel properties. Owing to these effects, quantum simulators in which dimensionality can be controlled have emerged as a new area of interest. However, such a platform has only been studied in specific regimes and a universal phase diagram is lacking. Here, we produce an interacting atomic quantum simulator with continuous tunability of anisotropy and temperature, and probe the universal phase diagram of dimensional crossover. At low temperatures, we identify the regimes from quantum three to zero dimensions. By increasing temperature, we observe the non-trivial emergence of a thermal regime situated between the quantum zero and integer dimensions. We show that the quantum-to thermal transition falls into four different universality classes depending on the dimensionality. Surprisingly, we also detect a fifth type where the high-dimensional quantum system can reach the thermal phase by crossing a low-dimensional quantum regime. Our results provide a crucial foundation for understanding the projective condensed matter structures in unconventional dimensions.