Quantum spin liquids (QSLs) are long-range entangled phases of frustrated magnets exhibiting fractionalised spin excitations. In two dimensions, there is limited analytical understanding of their excitation spectra beyond parton mean-field theories, which fail to capture many features of the finite frequency dynamical response. We use a self-consistent mean-field theory combined with the random phase approximation (RPA) for the
J1-
J2 Heisenberg model on the triangular lattice to describe the strong spinon-spinon interactions of the U(1) Dirac QSL. We obtain quantitative results for the dynamical spin structure factor and phase diagram compatible with comprehensive numerical efforts. We show the continuum response at the Brillouin zone corners is described by a spinon-exciton hybridised with monopole gauge excitations. We further show that the transition from the QSL to 120-degree coplanar order is in the QED
3 O(3)-GN universality class. We extend the method to chiral QSLs and XXZ anisotropy, and discuss its broad range of applicability to other models and for describing inelastic neutron scattering experiments in KYbSe
2.
Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed.
It is widely believed that the
U(1) spin liquid with a large spinon Fermi surface (SFS state) can be realized in the spin-$\frac{1}{2}\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{4}$ model on the triangular lattice, when the ring exchange coupling
J4 is sufficiently strong to suppress the ${120}^{\ensuremath{\circ}}$ magnetic ordered state. This belief is supported by many variational studies on this model and seems to be consistent with the observations on the organic spin liquid materials such as $\ensuremath{\kappa}$-(BEDT-
TTF)2Cu2(CN)3 and
EtMe3Sb[Pd(dmit)2]2, which are systems close to their Mott transition and thus have large
J4. Here we show through systematic variational search that such a state is never favored in the ${J}_{1}\text{\ensuremath{-}}{J}_{4}$ model on the triangular lattice. Instead, a state with broken spatial symmetry is favored in the most probable parameter regime for the SFS state and has an energy much lower than that of the SFS state and other proposed variational states. More specifically, we find that for ${J}_{4}\ensuremath{\ge}0.09{J}_{1}$, the model favors a valence bond solid state with a $4\ifmmode\times\else\texttimes\fi{}6$ period in its local spin correlation pattern and has a variational energy that is about
5 lower than that of the SFS state. This state is separated from the $\ensuremath{\pi}$-flux state for ${J}_{4}\ensuremath{\le}0.045{J}_{1}$ by an intermediate symmetry-breaking phase with a zigzag pattern in its local spin correlation. We find that the variational phase diagram we got is in qualitative agreement with that obtained from exact diagonalization on a $6\ifmmode\times\else\texttimes\fi{}6$ cluster.
A quantum spin liquid (QSL) is an exotic state of matter characterized by quantum entanglement and the absence of any broken symmetry. A long-standing open problem, which is a key for fundamental understanding the mysterious QSL states, is how the quantum fluctuations respond to randomness due to quenched disorder. Transition metal dichalcogenide 1T-TaS
2 is a candidate material that hosts a QSL ground state with spin-1/2 on the two-dimensional perfect triangular lattice. Here, we performed systematic studies of low-temperature heat capacity and thermal conductivity on pure, Se-substituted and electron irradiated crystals of 1T-TaS
2. In pure 1T-TaS
2, the linear temperature term of the heat capacity
γT and the finite residual linear term of the thermal conductivity in the zero-temperature limit
κ0/T≡κ/T(T→0) are clearly resolved, consistent with the presence of gapless spinons with a Fermi surface. Moreover, while the strong magnetic field slightly enhances
κ0/T, it strongly suppresses
γ. These unusual contrasting responses to magnetic field imply the coexistence of two types of gapless excitations with itinerant and localized characters. Introduction of additional weak random exchange disorder in 1T-Ta(S
1−xSe
x)
2 leads to vanishing of
κ0/T, indicating that the itinerant gapless excitations are sensitive to the disorder. On the other hand, in both pure and Se-substituted systems, the magnetic contribution of the heat capacity obeys a universal scaling relation, which is consistent with a theory that assumes the presence of localized orphan spins forming random singlets. Electron irradiation in pure 1T-TaS
2 largely enhances
γ and changes the scaling function dramatically, suggesting a possible new state of spin liquid.
We investigate the spin-
21 nearest-neighbor Heisenberg model with the four-site ring-exchange
J4 and chiral interaction ${J}_{\ensuremath{\chi}}$ on the triangular lattice by using the variational Monte Carlo method. The
J4 term induces the quadratic band touching (QBT) quantum spin liquid (QSL) with only a
d+id spinon pairing (without hopping term), the nodal
d-wave QSL and
U(1) QSL with a finite spinon Fermi surface progressively. The effect of the chiral interaction ${J}_{\ensuremath{\chi}}$ can enrich the phase diagram with two interesting chiral QSLs (topological orders) with the same quantized Chern number
C=21 and ground-state degeneracy GSD = 2, namely the
U(1) chiral spin liquid (CSL) and
Z2d+id-wave QSL. The nodal
d-wave QSL is fragile and will turn to the
Z2d+id QSL with any finite ${J}_{\ensuremath{\chi}}$ within our numerical calculation. However, in the process from QBT to the
Z2d+id QSL with the increase of ${J}_{\ensuremath{\chi}}$, an exotic crossover region is found. In this region, the previous QBT state acquires a small hopping term so that it opens a small gap at the band touching points, and leads to an energy minimum which is energetically more favorable compared to another competitive local minimum from the
Z2d+id QSL. We dub this state as the proximate QBT QSL and it gives way to the
Z2d+id QSL eventually. Therefore, the cooperation of the
J4 and ${J}_{\ensuremath{\chi}}$ terms favors mostly the
Z2d+id-wave QSL, so that this phase occupies the largest region in the phase diagram.
We study the transverse dynamical spin susceptibility of the two-dimensional U(1) spinon Fermi-surface spin liquid in a small applied Zeeman field. We show that both short-range interactions, present in a generic Fermi liquid, as well as gauge fluctuations, characteristic of the U(1) spin liquid, qualitatively change the result based on the frequently assumed noninteracting spinon approximation. The short-range part of the interaction lead to a collective ``spinon spin wave'' mode, which splits off from the two-spinon continuum at a small momentum and disperses downward. Gauge fluctuations renormalize the susceptibility, providing nonzero power-law weight in the region outside the spinon continuum and giving the spin wave a finite lifetime, which scales as momentum squared. We also study the effect of Dzyaloshinskii-Moriya anisotropy on the zero momentum susceptibility, which is measured in electron spin resonance (ESR), and obtain a resonance linewidth linear in temperature and varying as
B2/3 with magnetic field
B at low temperatures. Our results form the basis for a theory of inelastic neutron scattering, ESR, and resonant inelastic x-ray scattering studies of this quantum spin-liquid state.