Anomalous Suppression of Large-Scale Density Fluctuations in Classical and Quantum Spin Liquids

Academic Background

Classical spin liquids (CSLs) and quantum spin liquids (QSLs) are highly attractive research areas in condensed matter physics. CSLs are states of matter that do not exhibit long-range magnetic order and have extensive ground-state degeneracy. When quantum fluctuations are introduced, the dynamics between these classical ground states can give rise to QSLs, which are highly entangled quantum phases characterized by fractionalized excitations and topological order.

However, despite significant theoretical advancements in the study of QSLs, experimentally detecting Z2 QSLs remains challenging. Moreover, the structural properties of CSLs and QSLs, particularly their large-scale density fluctuations, have not been systematically studied. Therefore, this paper aims to uncover a hidden large-scale structural property of CSLs and QSLs known as hyperuniformity, i.e., the complete suppression of infinite-wavelength density fluctuations. Hyperuniformity not only aids in understanding the long-range correlations in these disordered states but also provides new tools for experimentally identifying QSLs.

Paper Source

This paper was co-authored by Duyu Chen, Rhine Samajdar, Yang Jiao, and Salvatore Torquato from the University of California, Santa Barbara, Princeton University, and Arizona State University. It was published in PNAS (Proceedings of the National Academy of Sciences) on February 7, 2025.

Research Content

Research Process

1. Hyperuniformity Study of Classical Spin Liquids

The researchers first investigated the structure of classical dimer coverings on the Kagome lattice. The Kagome lattice is a lattice structure with highly degenerate ground states, where dimer coverings under hard-core constraints (each vertex can be covered by only one dimer) form a classical dimer liquid. The research team generated perfect dimer coverings for different system sizes (n = 600, 2,400, 3,456, 5,400, 7,776, 9,600) using a simulated annealing algorithm and calculated their structure factor S(k) and local number variance σ²®.

2. Hyperuniformity Study of Quantum Spin Liquids

Subsequently, the researchers extended their investigation to the quantum counterparts of classical dimer coverings—quantum resonating valence bond (RVB) states—and studied their hyperuniformity. RVB states are quantum superpositions of dimer coverings and are considered manifestations of QSLs. The research team demonstrated that fixed-point RVB states remain perfectly hyperuniform while preserving all symmetries.

3. Impact of Quantum Fluctuations and Matter Fields

To better approximate experimental reality, the researchers further examined the effects of quantum fluctuations and matter fields on QSLs. They used the density matrix renormalization group (DMRG) algorithm to study the Hamiltonian of Rydberg atom arrays on the ruby lattice and generated the system’s ground-state wavefunction. By sampling this wavefunction, they obtained numerous monomer-dimer covering configurations and analyzed their hyperuniformity.

Key Results

1. Hyperuniformity of Classical Dimer Coverings

The study found that perfect dimer coverings on the Kagome lattice exhibit perfect disordered hyperuniformity, with the structure factor scaling as S(k) ∼ k⁶ at small wavenumber k. The local number variance σ²® increases linearly with r at large r, indicating these systems belong to class-I hyperuniform systems. Additionally, the dimer-dimer pair correlation function c® rapidly decays to zero, further supporting the existence of hyperuniformity.

2. Hyperuniformity of Quantum RVB States

The researchers proved that the hyperuniformity of perfect classical dimer coverings extends to quantum RVB states. Even in the presence of a finite density of spinons and visons, the QSL remains effectively hyperuniform as long as the dimer constraint is largely preserved.

3. Impact of Quantum Fluctuations

Despite quantum fluctuations causing the dimer filling fraction to deviate from the fixed value of ¹⁄₄, the QSL still exhibits effective hyperuniformity. By calculating the b/a ratio of the local number variance, the researchers distinguished the QSL from other phases, such as trivial disordered phases and ordered valence bond solid phases.

Conclusion and Significance

This paper is the first to reveal hyperuniformity in both classical and quantum spin liquids and demonstrates that hyperuniformity can serve as a powerful tool to distinguish spin liquids from other disordered and ordered quantum phases. The study deepens the understanding of density fluctuations in CSLs and QSLs and provides new methods for experimentally identifying QSLs.

Highlights

1. First discovery of hyperuniformity in classical and quantum spin liquids, revealing anomalous suppression of large-scale density fluctuations.
2. Development of metrics based on hyperuniformity to distinguish QSLs from other quantum phases, including trivial disordered phases and ordered valence bond solid phases.
3. Use of DMRG and simulated annealing algorithms to successfully handle large-scale quantum system simulations, providing new tools for studying strongly correlated quantum systems.

Additional Valuable Information

The results of this study provide important guidance for future experimental work, especially in identifying QSLs using single-site measurements and structural analysis. Furthermore, the proposed framework of hyperuniformity can be extended to other types of QSLs and quantum materials, broadening the scope of applications in this research field.