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Spin-Charge Bound States and Emerging Fermions in a Quantum Spin Liquid

Jens H. Nyhegn1,*, Kristian Knakkergaard Nielsen2,3, Leon Balents4,5,6, and Georg M. Bruun1

  • *Contact author: jensnyhegn@phys.au.dk
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PRX Quantum 6, 040347 – Published 26 November, 2025

DOI: https://doi.org/10.1103/w23h-dhrk

Abstract

The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended t-J model where the background spins form a Z2 quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid.

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Popular Summary

Entanglement lies at the heart of quantum mechanics and fuels the promise of next-generation technologies. Among the most entangled states of matter are quantum spin liquids, whose quantum nature makes them evade magnetic order even at zero temperature. In this work, we challenge a common paradigm that the elementary particles in spin liquids entirely lose their individual character, dissolving into collective quantum correlations. Our findings refine this picture and offer a potential explanation for puzzling experimental observations in high-temperature superconductors.

It is widely believed that spin liquids exhibit fractionalization, where an electron’s spin and charge degrees of freedom decouple and propagate essentially independently through the material. This phenomenon, if observed, would provide a strong signature for spin liquids. By systematically deriving a microscopic theory from first principles, we show that this fractionalization can break down: spin and charge can instead form bound states. These bound states behave as emergent particles with novel internal symmetries.

These findings not only deepen our understanding of spin liquids but also provide valuable guidance for interpreting angle-resolved photoemission spectroscopy measurements. Moreover, we show how cold-atom experiments in optical lattices offer a promising route to directly observe these unexpected bound states. Our theory also opens up new pathways for exploring high-temperature superconductivity as arising from a quantum spin liquid.

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PRX Quantum 6, 040347– Published 26 November, 2025
  • Received 8 July 2025
  • Revised 16 July 2025
  • Accepted 24 October 2025
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