The nontriviality of quantum spin liquids (QSLs) typically manifests in the nonlocal observables that signify their existence; however, this fact actually casts a shadow on detecting QSLs with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating a dynamical signature of anyonic excitations and symmetry fractionalization in QSLs. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that, across the phase transitions from Z_{2} QSLs to different symmetry breaking phases, spin spectral functions can reveal the presence and condensation of emergent anyonic spinon and vison excitations, in particular, the translational symmetry fractionalization of the latter, which can be served as the dynamical signature of the seemingly ephemeral QSLs in spectroscopic techniques such as inelastic neutron or resonance (inelastic) x-ray scatterings.
The nontriviality of quantum spin liquids (QSLs) typically manifests in the nonlocal observables that signify their existence; however, this fact actually casts a shadow on detecting QSLs with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating a dynamical signature of anyonic excitations and symmetry fractionalization in QSLs. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that, across the phase transitions from Z_{2} QSLs to different symmetry breaking phases, spin spectral functions can reveal the presence and condensation of emergent anyonic spinon and vison excitations, in particular, the translational symmetry fractionalization of the latter, which can be served as the dynamical signature of the seemingly ephemeral QSLs in spectroscopic techniques such as inelastic neutron or resonance (inelastic) x-ray scatterings.
Quantum spin liquids (QSLs) host exotic fractionalized magnetic and gauge-field excitations whose microscopic origins and experimental verification remain frustratingly elusive. In the absence of static magnetic order, the spin excitation spectrum constitutes the crucial probe of QSL behavior, but its theoretical computation is a serious challenge. Here we employ state-of-the-art tensor-network methods to obtain the full dynamical spectral function of the J1-J2 kagome Heisenberg model and benchmark our results by tracking their evolution across the magnetically ordered and QSL phases. Reducing ∣J2∣/J1 causes increasingly strong spin-wave renormalization, flattening these modes then merging them into a continuum characteristic of deconfined spinons at all finite energies in the QSL. The low-energy continuum and the occurrence of gap closure at multiple high-symmetry points identify this gapless QSL as the U(1) Dirac spin liquid. These results establish a unified understanding of spin excitations in highly frustrated quantum magnets and provide clear spectral fingerprints for experimental detection in candidate kagome QSL materials.
Based on large-scale quantum Monte Carlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice spin-1/2 model, which is known to harbor an extended Z_{2} quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the Z_{2} quantum spin liquid regime. In the latter phase, we identify a gapped two-spinon continuum in the transverse scattering channel, which is faithfully modeled by an effective spinon tight-binding model. Within the longitudinal channel, we identify gapped vison excitations and exhibit indications for the translational symmetry fractionalization of the visons via an enhanced spectral periodicity.
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.
Abstract Among the quantum many-body models that host anyon excitation and topological orders, quantum dimer models (QDM) provide a suitable playground for studying the relation between single-anyon and multi-anyon continuum spectra. However, as the prototypical correlated system with local constraints, the generic solution of QDM at different lattice geometry and parameter regimes is still missing due to the lack of controlled methodologies. Here we obtain, via sweeping cluster quantum Monte Carlo algorithm, the excitation spectra in different phases of the triangular lattice QDM. Our results reveal the single vison excitations inside the Z2 quantum spin liquid (QSL) and its condensation towards the 12×12 12 × 12 valence bond solid (VBS), and demonstrate the translational symmetry fractionalization and emergent O(4) symmetry at the QSL-VBS transition. We find the single vison excitations, whose convolution qualitatively reproduces the dimer spectra, are not free but subject to interaction effects throughout the transition. The nature of the VBS with its O(4) order parameters are unearthed in full scope. Our approach opens the avenue for generic solution of the static and dynamic properties of QDMs and has relevance towards the realization and detection of fractional excitations in programmable quantum simulators.
The presence of multiple competing interactions in spin systems can lead to novel phases known as quantum spin liquids (QSLs). QSLs are disordered spin systems with long-range entanglement that realize the deconfined phase of emergent lattice gauge theories and host fractional excitations. A notable example of great experimental interest is quantum spin ice (QSI), a three-dimensional QSL that realizes an analog of quantum electrodynamics with emergent photons and interacting electric and magnetic charges. The current leading candidate materials for realizing QSI are dipolar-octupolar (DO) cerium-based pyrochlore compounds. These are believed to stabilize a U(1) QSL known as π-flux QSI, where translation symmetry acting on spinon excitations fractionalizes. In this thesis, we explore the physics of QSI, relying heavily on parton constructions, to make experimentally relevant predictions for DO materials. First, we explore the physics of symmetry fractionalization in QSI, whereby lattice symmetries are realized projectively when acting on fractional quasiparticles. Symmetry fractionalization is examined within the framework of gauge mean-field theory (GMFT), a parton construction designed explicitly for application to QSI. This study shows that the pyrochlore lattice space group strongly constrains possible symmetry fractionalization classes. It systematically explains how all space group transformations, beyond translation, fractionalize in π-flux QSI. Next, we apply this framework to DO materials and show how the equal-time structure factor predicted for π-flux QSI is consistent with recent energy-integrated inelastic neutron scattering experiments on certain candidate materials. We also predict that the dynamical spin structure factor of π-flux QSI is characterized by a broad continuum with three distinctive peaks of decreasing intensity that are approximately equally spaced. We argue that these peaks should be accessible with currently available experimental apparatus and offer a smoking-gun signature of π-flux QSI. We confirm those predictions by extending the exclusive boson representation and speculate on the thermodynamic behavior of cerium candidates. We close by commenting on recent experimental breakthroughs and possible future directions.
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.