Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice (1902.10934v3)

Abstract: Higher-rank generalisations of electrodynamics have recently attracted considerable attention because of their ability to host "fracton" excitations, with connections to both quantum stabilizer codes and holography. However, the search for higher-rank gauge theories in experiment has been greatly hindered by the lack of materially-relevant microscopic models. Here we show how a spin liquid described by rank-2 $U(1)$ gauge theory can arise in a magnet on the breathing pyrochlore lattice. We identify Yb-based breathing pyrochlores as candidate systems, and make explicit predictions for how the rank-2 $U(1)$ spin liquid would manifest itself in experiment.

Study of Rank-2 U(1) Spin Liquid in Breathing Pyrochlore Lattice

This paper explores the theoretical foundations and predictions for the realization of a rank-2 U(1) spin liquid in a magnetically frustrated system, specifically on the breathing pyrochlore lattice. The paper explores the complex mechanisms that underpin the emergence of higher-rank gauge theories, a topic that has garnered interest due to its connections to emergent phenomena like fracton order, gravity analogies, and long-range topological order.

Background and Motivation

The paper sets out to bridge the gap in existing literature, which predominantly discusses conventional U(1) gauge theories on the standard pyrochlore lattice and their spin phenomena, such as quantum spin ice. The authors aim to extend this framework to higher-rank gauge theories that link to novel topological states such as fracton orders. These states, characterized by constrained mobility of excitations, offer pathways to exploring connections to elasticity theories, particularly through self-dual and dual descriptions.

Model and Theoretical Framework

The researchers propose a microscopic model of a frustrated magnet on a breathing pyrochlore lattice. This lattice comprises two types of tetrahedra of different sizes, A and B, and interactions are defined by the Heisenberg antiferromagnetic (HAF) model with Dzyaloshinskii-Moriya (DM) perturbations. Utilizing classical Monte Carlo (MC) simulations, they confirm that fluctuations within this system can indeed describe a tensor field adherent to the constraints of a rank-2 U(1) gauge theory.

A distinctive aspect of their findings is the identification of four-fold pinch points (4FPP), key in distinguishing this higher-rank spin liquid from its lower-order counterparts. These points manifest in singular correlation functions, adding new dimensions to the conventional pinch points observed in standard spin ice.

Key Results and Implications

The paper presents compelling evidence that Yb-based breathing pyrochlores serve as potential candidates for hosting R2-U1 states. This is substantiated by parameter calculations aligned with experimental data, notably in materials like Ba3Yb2Zn5O11. The authors emphasize that the unique scattering signatures, such as the visibility of 4FPP in polarized neutron studies, provide an experimental haLLMark for validating these theoretical predictions.

Theoretical considerations highlight that despite the classical nature of the paper, quantum tunneling effects akin to those observed in quantum spin ice may complement these findings at lower temperature regimes, hinting at intricate quantum effects deserving of further exploration.

Conclusions and Future Directions

This paper contributes significantly to the understanding and potential realization of high-rank gauge theories in condensed matter systems by offering a structured approach to identifying candidate materials and setting a pathway for experimental validation. The findings hold potential applications not only in the quest for understanding emergent higher-dimensional gauge theories but also in the practical utilization of fracton-like behaviors in materials science.

Future investigations could explore the quantum dynamics of these models, exploring the extent to which coherent gauge fluctuations and emergent photon-like excitations alter the low-temperature phases. Additionally, addressing the interplay between classical stability induced by entropy and quantum coherence will be vital in establishing a more integrated framework for the theoretical predictions laid out in this research.