Quantum spin liquids (QSLs) are magnetic phases that evade long-range order down to the lowest temperatures due to strong quantum fluctuations. Their lack of conventional order parameters, however, makes experimental identification challenging. In this work, we investigate how distinct QSL phases affect phonon dynamics through spinon-phonon coupling. By computing the phonon self-energy, we show that the phonon spectrum remains unrenormalized by spinon interactions, while sound attenuation and phonon thermal conductivity exhibit distinct signatures of the underlying QSL phase. These response functions therefore provide experimentally accessible fingerprints for distinguishing different QSL backgrounds. Remarkably, we find that a chiral QSL coupled to phonons does not generate a phonon thermal Hall effect despite explicitly breaking time-reversal symmetry. Our results establish phonon transport as a potential probe for identifying and characterizing quantum spin liquids.
Spinon-Induced Phonon Dynamics in Chiral and π-Flux Quantum Spin Liquids
Quantum spin liquids (QSLs) are magnetic phases that evade long-range order down to the lowest temperatures due to strong quantum fluctuations. Their lack of conventional order parameters, however, makes experimental identification challenging. In this work, we investigate how distinct QSL phases affect phonon dynamics through spinon-phonon coupling. By computing the phonon self-energy, we show that the phonon spectrum remains unrenormalized by spinon interactions, while sound attenuation and phonon thermal conductivity exhibit distinct signatures of the underlying QSL phase. These response functions therefore provide experimentally accessible fingerprints for distinguishing different QSL backgrounds. Remarkably, we find that a chiral QSL coupled to phonons does not generate a phonon thermal Hall effect despite explicitly breaking time-reversal symmetry. Our results establish phonon transport as a potential probe for identifying and characterizing quantum spin liquids.
Abstract Quantum spin liquid (QSL) has become an exciting topic in interacting spin systems that do not order magnetically down to the lowest experimentally accessible temperature; however, conclusive experimental evidence remains lacking. Motivated by the recent surge of theoretical and experimental interest in a half-filled Hubbard model on the triangular lattice, where chiral QSL can be stabilized, we investigate the electromagnetic signature of the chiral QSL to aid experimental detection. We systematically studied the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL based on parton mean-field theory and unbiased density-matrix renormalization group calculations. We then calculated both longitudinal and transverse optical conductivities below the Mott gap. We also conduct quantum field theory analysis to unravel the connection between spinon excitation and emergent and physical gauge fields. Our results show that the chiral QSL phase has a clear electromagnetic response even in a Mott insulator regime, which can facilitate the experimental detection of this long-sought-after phase.
Motivated by a search for experimental probes to access the physics of fractionalized excitations called spinons in spin liquids, we study the interaction of spinons with lattice vibrations. We consider the case of algebraic spin liquid, when spinons have fermionic statistics and a Dirac-like dispersion. We establish the general procedure for deriving spinon-phonon interactions, which is based on symmetry considerations. The procedure is illustrated for four different algebraic spin liquids: $\ensuremath{\pi}$-flux and staggered-flux phases on a square lattice, $\ensuremath{\pi}$-flux phase on a kagome lattice, and zero-flux phase on a honeycomb lattice. Although the low-energy description is similar for all these phases, different underlying symmetry groups lead to a distinct form of spinon-phonon interaction Hamiltonian. The explicit form of the spinon-phonon interaction is used to estimate the attenuation of ultrasound in an algebraic spin liquid. The prospects of the sound attenuation as a probe of spinons are discussed.
Quantum spin liquids (QSLs) host emergent, fractionalized fermionic excitations that are charge-neutral. Identifying clear experimental signatures of these excitations remains a central challenge in the field of strongly correlated systems, as they do not couple to conventional electromagnetic probes. Here, we propose lattice strain as a powerful and tunable probe: Mechanical deformation of the lattice generates large pseudomagnetic fields, inducing pseudo-Landau levels that serve as distinctive spectroscopic signatures of these excitations. Using the Kitaev model on the honeycomb lattice, we show that distinct QSL phases exhibit strikingly different strain responses. The semimetallic Kitaev spin liquid and the gapped chiral spin liquid display pronounced Landau quantization and a diamagnetic-like response to strain, whereas the Majorana metal phase shows a paramagnetic-like response without forming Landau levels. These contrasting behaviors provide a direct route to experimentally identifying and distinguishing QSL phases hosting fractionalized excitations. We further outline how local resonant ultrasound spectroscopy can detect the strain-induced resonances associated with these responses, offering a practical pathway towards identifying fractionalized excitations in candidate materials.
The search for exotic states of matter continues to be a central theme in condensed matter physics. Among these, quantum spin liquids (QSLs) represent a profound challenge and opportunity, characterized by long-range entanglement and fractionalized excitations without conventional magnetic order even at absolute zero temperature. Frustrated quantum magnets are prime candidates for hosting such states, where competing interactions prevent classical ground states. This paper reports the theoretical and experimental signatures that would lead to the discovery of a chiral bosonic liquid (CBL) in a novel frustrated quantum magnet. A CBL is a particularly elusive type of QSL characterized by elementary excitations that behave as bosons and exhibit a distinct chirality, manifesting as a non-zero thermal Hall effect in the absence of a magnetic field. We outline a comprehensive strategy involving advanced material synthesis, precise low-temperature thermodynamic measurements, inelastic neutron scattering, and numerical simulations to identify the unique fingerprints of this novel state. Key indicators include a gapless or nearly gapless excitation spectrum, a specific heat scaling characteristic of bosonic excitations, and, most critically, a quantized or near-quantized thermal Hall conductivity directly reflecting the chiral nature of the bosonic fractional excitations. The implications of this discovery extend to fundamental understanding of quantum entanglement, topological states of matter, and potential applications in robust quantum information processing.
Candidate materials for the Kitaev spin liquid generically have residual interactions beyond the Kitaev coupling. It therefore becomes necessary to understand how signatures of the quantum spin liquid, e.g., fractionalization of the spin excitations, are affected by the presence of these interactions. Recently it was shown that phonon dynamics is an indirect but effective probe to study fractionalized excitations in the Kitaev spin liquid. Ultrasound experiments can measure sound attenuation, which should show characteristic temperature and angular dependence of the sound-attenuation coefficient if the scattering of phonons happens predominantly on Majorana fermions. So far the computation of the sound attenuation was only done in the pure spin-phonon coupled Kitaev model, without taking into account residual interactions. In order to understand experimental signatures, here we present a mean-field study of the sound attenuation in the generalized $J\text{\ensuremath{-}}K\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}$ model, which is relevant to candidate materials. Our findings show that as long as the system is in the spin liquid phase, characteristic features of the sound attenuation remain observable even in the presence of residual interactions.
Frustrated magnetism provides a rich platform for realizing exotic quantum phases in condensed matter systems. Among these, quantum spin liquids (QSLs) are a particularly intriguing class of states that exhibit no magnetic ordering and preserve all symmetries down to zero temperature. Just as conventional magnets can be thought of as spin crystals,QSLs represent their liquid analogs. This thesis explores two broad types of QSLs in two-dimensional magnets, with a focus on their dynamic properties and the nature of transitions from conventional magnetic states into QSL phases. QSLs are topological phases that host fractionalized excitations known as spinons. In these states, mobile spinons are coupled to an emergent gauge field, forming a highly entangled phase of matter. The first part of this thesis focuses on Dirac spin liquids (DSLs), a class of QSLs where spinons exhibit a gapless Dirac dispersion. To study the dynamicsof these spin liquids beyond leading-order mean-field theory, we develop a novel large-N fermionic limit of gapless spinons. In this limit, all gauge excitations are suppressed, and the leading-order corrections instead arise from order parameter fluctuations, which may condense and drive transitions into symmetry-broken phases from the parent DSL. Incorporating random phase approximation (RPA) corrections to the spin susceptibility, we find that sharp, spin-wave–like modes are recovered in the excitation spectrum. This methodology successfully captures characteristic features of the dynamics near phase transitions and in weakly symmetry-broken phases proximate to a DSL. We apply this approach to microscopic models, including the J1-J2 XXZ model on the triangular lattice and the J1-J3 XXZ model on the honeycomb lattice. These models closely represent a wide range of frustrated materials, such as triangular and honeycomb cobaltates and triangular ytterbium compounds. Our theoretical predictions show excellent agreement with experimentally measured inelastic neutron scattering spectra from these materials. Gapless spinons can also sometimes become gapped through chiral symmetry breaking, leading to the formation of a chiral spin liquid (CSL). The CSL is an archetypal bosonic realization of a fractional quantum Hall (FQH) state at half-filling, and has been proposed as a time-reversal–breaking ground state in a variety of frustrated spin models. The second part of this thesis addresses the intriguing possibility of realizing a CSL through the "melting" of a chiral spin crystal—a conventional magnet with non-coplanar ordering. Such a transition offers a physically appealing analogue to the melting of a Wigner crystal into a fermionic FQH liquid. Focusing on the kagome lattice, where chiral interactions are knownto stabilize a CSL ground state, we study the effects of additional long-range Heisenberg interactions and demonstrate a phase transition into a non-coplanar octahedral magnetic order. To describe the universal class of transition between a CSL and a non-coplanar anti-ferromagnetic order, we then develop a novel Chern-Simons–matter field theory framework, constrained by symmetry principles and symmetry fractionalization patterns. This thesis thus provides new insights into the dynamical signatures and phase transitions of quantum spin liquids, offering a bridge between theoretical models and experimental observations in frustrated magnetic systems.