Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

High Temperature Fermi Statistics from Majorana Fermions in an Insulating Magnet

Yi‐Ping Wang, Gavin B. Osterhoudt, Yao Tian, Paula Lampen-Kelley, Arnab Banerjee, Thomas Goldstein, Jun Yan, Johannes Knolle, Joji Nasu, Yukitoshi Motome, S. E. Nagler, David G. Mandrus, Kenneth S. Burch

Published Sep 20, 2018• 2 citations
OpenAlex

Abstract

A key characteristic of quantum spin liquids(QSL) is the presence of fractional excitations related to their entanglement properties, yet experimental verification of their statistics is missing. For example, in the potential Kitaev spin liquid, RuCl3 experiments uncovered signs of fractional particles, though not their Fermi statistics. Here we employ Raman scattering to reveal the true nature of the magnetic excitations, using improved experimental methods and analysis to remove the influence of laser heating and thermal fluctuations. Via the energy loss and gain spectra, we extract the energy and temperature dependence of the Raman susceptibility to prove RuCl3's magnetic response is given by pair creation of fermionic excitations. Furthermore, by comparing with quantum Monte Carlo (QMC) results for the exact Kitaev limit, we are able to discern the energy and temperature range where additional interaction terms are important. Our results open new directions in QSL research by providing a new way to investigate fractional excitations and the importance of terms causing spinon confinement.

Related papers

Direct Evidence for Fermi Statistics from Proximity to the Kitaev Spin Liquid in RuCl3

Yi‐Ping Wang, Gavin B. Osterhoudt, Yao Tian +12 more

A key characteristic of quantum spin liquids(QSL) is the presence of fractional excitations related to their entanglement properties, yet experimental verification of their statistics is missing. For example, in the potential Kitaev spin liquid, RuCl3 experiments uncovered signs of fractional particles, though not their Fermi statistics. Here we employ Raman scattering to reveal the true nature of the magnetic excitations, using improved experimental methods and analysis to remove the influence of laser heating and thermal fluctuations. Via the energy loss and gain spectra, we extract the energy and temperature dependence of the Raman susceptibility to prove RuCl3's magnetic response is given by pair creation of fermionic excitations. Furthermore, by comparing with quantum Monte Carlo (QMC) results for the exact Kitaev limit, we are able to discern the energy and temperature range where additional interaction terms are important. Our results open new directions in QSL research by providing a new way to investigate fractional excitations and the importance of terms causing spinon confinement.

arXiv:1809.07782•Sep 20, 2018•3 citations

The range of non-Kitaev terms and fractional particles in α-RuCl3

Yiping Wang, Gavin B. Osterhoudt, Yao Tian +12 more

Abstract Significant efforts have focused on the magnetic excitations of relativistic Mott insulators, predicted to realize the Kitaev quantum spin liquid (QSL). This exactly solvable model involves a highly entangled state resulting from bond-dependent Ising interactions that produce excitations which are non-local in terms of spin flips. A key challenge in real materials is identifying the relative size of the non-Kitaev terms and their role in the emergence or suppression of fractional excitations. Here, we identify the energy and temperature boundaries of non-Kitaev interactions by direct comparison of the Raman susceptibility of α -RuCl 3 with quantum Monte Carlo (QMC) results for the Kitaev QSL. Moreover, we further confirm the fractional nature of the magnetic excitations, which is given by creating a pair of fermionic quasiparticles. Interestingly, this fermionic response remains valid in the non-Kitaev range. Our results and focus on the use of the Raman susceptibility provide a stringent new test for future theoretical and experimental studies of QSLs.

arXiv:2003.09274•npj Quantum Materials•Mar 4, 2020•60 citations

Probing signatures of fractionalization in the candidate quantum spin liquid Cu2IrO3 via anomalous Raman scattering

Srishti Pal, Arnab Seth, Piyush Sakrikar +5 more

Long-range entanglement in quantum spin liquids (QSLs) leads to novel low-energy excitations with fractionalized quantum numbers and (in two dimensions) statistics. Experimental detection and manipulation of these excitations present a challenge particularly in view of diverse candidate magnets. A promising probe of fractionalization is their coupling to phonons. Here, we present Raman scattering results for the $S=1/2$ honeycomb iridate ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$, a candidate Kitaev QSL with fractionalized Majorana fermions and Ising flux excitations. We observe anomalous low-temperature frequency shift and linewidth broadening of the Raman intensities in addition to a broad magnetic continuum, both of which, as we derive, are naturally attributed to the phonon decaying into itinerant Majoranas. The dynamic Raman susceptibility marks a crossover from the QSL to a thermal paramagnet at $\ensuremath{\sim}120$ K. The phonon anomalies below this temperature demonstrate a strong phonon-Majorana coupling. These results provide evidence of spin fractionalization in ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$.

arXiv:2011.00606•Physical review. B./Physical review. B•Nov 17, 2021•23 citations

Magnetic field induced phenomena in Kitaev spin liquids

Shi Feng, Nandini Trivedi

Quantum spin liquids (QSLs) host a variety of fractionalized particles. In Kitaev's paradigmatic honeycomb model a spin-fractionalizes intoflux due to emergentgauge field and matter Majorana fermions. Although these excitations have well-defined dynamics in the integrable limit, their direct experimental identification is notoriously challenging: realistic materials inevitably host additional symmetry-allowed interactions that break integrability and hybridize gauge and matter sectors, while magnetic fields, which are often required to suppress competing order and stabilize a putative QSL regime, further entangle the responses of different fractionalized quasiparticles and may even drive the system into field-induced spin-liquid phases that are not adiabatically connected to the integrable limit. A prominent example is the quantum Majorana metal, in which the distinct dynamics of fractionalized Majorana fermions can become directly visible in scattering. This review highlights recent progress on these related questions: in which field-stabilized QSL regimes and nearby emergent phases, and under what conditions, can the response of a specific fractionalized quasiparticle be isolated and positively understood, thereby clarifying the existence and the experimental scope of putative spin liquids? We review the progress on these questions across Abelian, non-Abelian, and emergent quantum phases under magnetic field that are not perturbatively connected to the integrable limit. We connect these field-induced dynamical phenomena to concrete experimental observables, relevant for neutron scattering, resonant inelastic x-ray scattering, and pump-probe spectroscopy, techniques that are capable of identifying the nature of different magnetic-field-induced phases and resolving specific types of fractionalized particles, including Majoranas andfluxes.

arXiv:2601.14496•Reports on Progress in Physics•Oct 1, 2026•0 citations

Optical observation of fermionic partons in Kitaev spin balls

Shoji Yamamoto, Taku Kimura

Abstract We demonstrate a Kitaev spin liquid in a polyhedral cluster and propose detecting its fractional excitations—Majorana spinons—by magnetic Raman scattering. While little polarization dependence of the Raman spectra at sufficiently low temperatures is usual with quantum spin liquids, the present observations are primarily of geometric origin. The Raman scattering intensity peaks melt with increasing temperature, to be more precise, with increasing number of background gauge-flux excitations.

Journal of Physics Conference Series•May 1, 2019•2 citations

Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field

Peng Rao, Roderich Moessner, Johannes Knolle

Motivated by the appearance of Majorana fermions in a broad range of correlated and topological electronic systems, we develop a general method to compute the dynamical response of interacting Majorana fermions in the random-phase approximation (RPA). This can be applied self-consistently on top of Majorana mean-field theory backgrounds, thereby in particular providing a powerful tool to analyze behavior in the vicinity of (various heavily studied) exactly soluble models. Prime examples are quantum spin liquids (QSL) with emergent Majorana excitations, with the celebrated exact solution of Kitaev. We employ the RPA to study in considerable detail phase structure and dynamics of the extended Kitaev honeycomb K J Γ model, with and without an applied field. First, we benchmark our method with Kitaev's exactly soluble model, finding a remarkable agreement. The interactions between Majorana fermions even turn out to mimic the effect of local Z 2 flux excitations, which we explain analytically. Second, we show how small non-Kitaev couplings J and Γ induce Majorana bound states, resulting in sharp features in the dynamical structure factor in the presence of fractionalization: such “spinon excitons” naturally appear, and can coexist and interact with the broad Majorana continuum. Third, for increasing couplings or field, our theory predicts instabilities of the Kitaev QSL (KQSL) triggered by the condensation of the sharp modes. From the high-symmetry momenta of the condensation we can deduce which magnetically ordered phases surround the KQSL, in good agreement with previous finite-size numerics. We discuss implications for experiments and the broad range of applicability of our method to other QSL and Majorana systems.

arXiv:2503.10330•Physical review. B./Physical review. B•Jul 14, 2025•7 citations
A key characteristic of quantum spin liquids(QSL) is the presence of fractional excitations related to their entanglement properties, yet experimental verification of their statistics is missing. For example, in the potential Kitaev spin liquid, RuCl3 experiments uncovered signs of fractional particles, though not their Fermi statistics. Here we employ Raman scattering to reveal the true nature of the magnetic excitations, using improved experimental methods and analysis to remove the influence of laser heating and thermal fluctuations. Via the energy loss and gain spectra, we extract the energy and temperature dependence of the Raman susceptibility to prove RuCl3's magnetic response is given by pair creation of fermionic excitations. Furthermore, by comparing with quantum Monte Carlo (QMC) results for the exact Kitaev limit, we are able to discern the energy and temperature range where additional interaction terms are important. Our results open new directions in QSL research by providing a new way to investigate fractional excitations and the importance of terms causing spinon confinement.
A key characteristic of quantum spin liquids(QSL) is the presence of fractional excitations related to their entanglement properties, yet experimental verification of their statistics is missing. For example, in the potential Kitaev spin liquid, RuCl3 experiments uncovered signs of fractional particles, though not their Fermi statistics. Here we employ Raman scattering to reveal the true nature of the magnetic excitations, using improved experimental methods and analysis to remove the influence of laser heating and thermal fluctuations. Via the energy loss and gain spectra, we extract the energy and temperature dependence of the Raman susceptibility to prove RuCl3's magnetic response is given by pair creation of fermionic excitations. Furthermore, by comparing with quantum Monte Carlo (QMC) results for the exact Kitaev limit, we are able to discern the energy and temperature range where additional interaction terms are important. Our results open new directions in QSL research by providing a new way to investigate fractional excitations and the importance of terms causing spinon confinement.
Abstract Significant efforts have focused on the magnetic excitations of relativistic Mott insulators, predicted to realize the Kitaev quantum spin liquid (QSL). This exactly solvable model involves a highly entangled state resulting from bond-dependent Ising interactions that produce excitations which are non-local in terms of spin flips. A key challenge in real materials is identifying the relative size of the non-Kitaev terms and their role in the emergence or suppression of fractional excitations. Here, we identify the energy and temperature boundaries of non-Kitaev interactions by direct comparison of the Raman susceptibility of α -RuCl 3 with quantum Monte Carlo (QMC) results for the Kitaev QSL. Moreover, we further confirm the fractional nature of the magnetic excitations, which is given by creating a pair of fermionic quasiparticles. Interestingly, this fermionic response remains valid in the non-Kitaev range. Our results and focus on the use of the Raman susceptibility provide a stringent new test for future theoretical and experimental studies of QSLs.
Long-range entanglement in quantum spin liquids (QSLs) leads to novel low-energy excitations with fractionalized quantum numbers and (in two dimensions) statistics. Experimental detection and manipulation of these excitations present a challenge particularly in view of diverse candidate magnets. A promising probe of fractionalization is their coupling to phonons. Here, we present Raman scattering results for the S=1/2S=1/2S=1/2 honeycomb iridate Cu2IrO3{\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}Cu2​IrO3​, a candidate Kitaev QSL with fractionalized Majorana fermions and Ising flux excitations. We observe anomalous low-temperature frequency shift and linewidth broadening of the Raman intensities in addition to a broad magnetic continuum, both of which, as we derive, are naturally attributed to the phonon decaying into itinerant Majoranas. The dynamic Raman susceptibility marks a crossover from the QSL to a thermal paramagnet at $\ensuremath{\sim}120$ K. The phonon anomalies below this temperature demonstrate a strong phonon-Majorana coupling. These results provide evidence of spin fractionalization in Cu2IrO3{\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}Cu2​IrO3​.
Quantum spin liquids (QSLs) host a variety of fractionalized particles. In Kitaev's paradigmatic honeycomb model a spin-fractionalizes intoflux due to emergentgauge field and matter Majorana fermions. Although these excitations have well-defined dynamics in the integrable limit, their direct experimental identification is notoriously challenging: realistic materials inevitably host additional symmetry-allowed interactions that break integrability and hybridize gauge and matter sectors, while magnetic fields, which are often required to suppress competing order and stabilize a putative QSL regime, further entangle the responses of different fractionalized quasiparticles and may even drive the system into field-induced spin-liquid phases that are not adiabatically connected to the integrable limit. A prominent example is the quantum Majorana metal, in which the distinct dynamics of fractionalized Majorana fermions can become directly visible in scattering. This review highlights recent progress on these related questions: in which field-stabilized QSL regimes and nearby emergent phases, and under what conditions, can the response of a specific fractionalized quasiparticle be isolated and positively understood, thereby clarifying the existence and the experimental scope of putative spin liquids? We review the progress on these questions across Abelian, non-Abelian, and emergent quantum phases under magnetic field that are not perturbatively connected to the integrable limit. We connect these field-induced dynamical phenomena to concrete experimental observables, relevant for neutron scattering, resonant inelastic x-ray scattering, and pump-probe spectroscopy, techniques that are capable of identifying the nature of different magnetic-field-induced phases and resolving specific types of fractionalized particles, including Majoranas andfluxes.
Abstract We demonstrate a Kitaev spin liquid in a polyhedral cluster and propose detecting its fractional excitations—Majorana spinons—by magnetic Raman scattering. While little polarization dependence of the Raman spectra at sufficiently low temperatures is usual with quantum spin liquids, the present observations are primarily of geometric origin. The Raman scattering intensity peaks melt with increasing temperature, to be more precise, with increasing number of background gauge-flux excitations.
Motivated by the appearance of Majorana fermions in a broad range of correlated and topological electronic systems, we develop a general method to compute the dynamical response of interacting Majorana fermions in the random-phase approximation (RPA). This can be applied self-consistently on top of Majorana mean-field theory backgrounds, thereby in particular providing a powerful tool to analyze behavior in the vicinity of (various heavily studied) exactly soluble models. Prime examples are quantum spin liquids (QSL) with emergent Majorana excitations, with the celebrated exact solution of Kitaev. We employ the RPA to study in considerable detail phase structure and dynamics of the extended Kitaev honeycomb K J Γ model, with and without an applied field. First, we benchmark our method with Kitaev's exactly soluble model, finding a remarkable agreement. The interactions between Majorana fermions even turn out to mimic the effect of local Z 2 flux excitations, which we explain analytically. Second, we show how small non-Kitaev couplings J and Γ induce Majorana bound states, resulting in sharp features in the dynamical structure factor in the presence of fractionalization: such “spinon excitons” naturally appear, and can coexist and interact with the broad Majorana continuum. Third, for increasing couplings or field, our theory predicts instabilities of the Kitaev QSL (KQSL) triggered by the condensation of the sharp modes. From the high-symmetry momenta of the condensation we can deduce which magnetically ordered phases surround the KQSL, in good agreement with previous finite-size numerics. We discuss implications for experiments and the broad range of applicability of our method to other QSL and Majorana systems.