The properties and experimental identification of quantum spin liquids (QSLs) remain an important topic with many fundamental questions. Here, we explore the dynamics of a single charge dopant (hole) in a $t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}$ model on a square lattice, which realizes a gapless ${\mathbb{Z}}_{2}$ QSL at half filling. Using a field theory approach based on the parton construction, which includes an infinite number of scatterings between the low-energy quasiparticle excitations of the QSL via a self-consistent Born approximation, we calculate both the equilibrium and nonequilibrium properties of the hole for weak and strong interactions. Quasiparticle branches as well as stringlike excitations of the holon are identified, and we furthermore explore the time-dependent spreading of a hole throughout the QSL after it has been injected at a given lattice site. The final ballistic expansion speed is shown to exhibit a nonmonotonic behavior as a quantum phase transition between an antiferromagnetic and the QSL phase is crossed, which is caused by a qualitative change in the fundamental kinematics of the interactions between the hole and the surrounding spins. Our results demonstrate how charge dopants can be used as a quantum probe for QSLs and are directly relevant to optical lattice experiments with single site resolution.
The properties and experimental identification of quantum spin liquids (QSLs) remain an important topic with many fundamental questions. Here, we explore the dynamics of a single charge dopant (hole) in a t\ensuremath−J1\ensuremath−J2 model on a square lattice, which realizes a gapless Z2 QSL at half filling. Using a field theory approach based on the parton construction, which includes an infinite number of scatterings between the low-energy quasiparticle excitations of the QSL via a self-consistent Born approximation, we calculate both the equilibrium and nonequilibrium properties of the hole for weak and strong interactions. Quasiparticle branches as well as stringlike excitations of the holon are identified, and we furthermore explore the time-dependent spreading of a hole throughout the QSL after it has been injected at a given lattice site. The final ballistic expansion speed is shown to exhibit a nonmonotonic behavior as a quantum phase transition between an antiferromagnetic and the QSL phase is crossed, which is caused by a qualitative change in the fundamental kinematics of the interactions between the hole and the surrounding spins. Our results demonstrate how charge dopants can be used as a quantum probe for QSLs and are directly relevant to optical lattice experiments with single site resolution.
The dynamics of charge carriers in lattices of quantum spins is a long standing and fundamental problem. Recently, a new generation of quantum simulation experiments based on atoms in optical lattices has emerged that gives unprecedented insights into the detailed spatial and temporal dynamics of this problem, which compliments earlier results from condensed matter experiments. Focusing on observables accessible in these new experiments, we explore here the equilibrium as well as nonequilibrium dynamics of a mobile hole in two coupled antiferromagnetic spin lattices. Using a self-consistent Born approximation, we calculate the spectral properties of the hole in the bilayer and extract the energy bands of the quasiparticles, corresponding to magnetic polarons that are either symmetric or antisymmetric under layer exchange. These two kinds of polarons are degenerate at certain momenta due to the antiferromagnetic symmetry, and we, furthermore, examine how the momentum of the ground-state polaron depends on the interlayer coupling strength. The long time dynamics of a hole initially created in one layer is shown to be characterized by oscillations between the two layers with a frequency given by the energy difference between the symmetric and the antisymmetric polaron. We finally demonstrate that the expansion velocity of a hole initially created at a given lattice site is governed by the ballistic motion of polarons for long times, and that it increases as a quantum phase transition to a disordered state is approached. While our linear spin wave theory does not include interlayer dimer correlations important close to the phase transition, this speedup is a physically robust prediction as it reflects the decreasing energy cost of hopping when the magnetic order decreases.
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 Z 2 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.
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.
Whereas a quantum spin liquid (QSL) phase has been identified in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on a triangular lattice via numerical calculations, debate persists about whether or not such a QSL is gapped or gapless with contradictory conclusions from different techniques. Moreover, information about excitations and dynamics is crucial for the experimental detection of such a phase. In this paper, we use exact diagonalization to characterize signatures of a QSL phase on the triangular lattice through the dynamical spin structure factor $\mathcal{S}(q,\ensuremath{\omega})$ and Raman susceptibility $\ensuremath{\chi}(\ensuremath{\omega})$. We find that spectra for the QSL phase show distinct features compared to those of neighboring phases; and both the Raman spectra and spin structure factor show gapped behavior in the QSL phase. Interestingly, there is a prominent excitation mode in the Raman A2 channel, indicating a strong subleading tendency toward a chiral spin liquid phase.
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.
The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1, and those between next-nearest-neighbor sites, J2. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region 0.4<J2/J1≤0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4<J2/J1≤0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5<J2/J1≤0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation ⟨S(0)S(r)⟩∝1/rz+η at a long distance r appears to increase from z+η∼1 at J2/J1∼0.4 toward the continuous transition to the VBC phase at J1/J1∼0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.