We study the ground-state phase diagram of the spin-
1/2${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on the square lattice with an accurate bosonic resonating-valence-bond (RVB) wave function. In contrast to the RVB ansatz based on Schwinger fermions, the representation based on Schwinger bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime. In particular, a fully symmetric
Z2 spin liquid is stable between two antiferromagnetic phases; a continuous transition at
J2=0.4J1, when the Marshall sign rule begins to be essentially violated, and a first-order transition around
J2=0.6J1 are present. Most importantly, the triplet gap is found to have a nonmonotonic behavior, reaching a maximum around
J2=0.51J1, when the lowest spinon excitation moves from the $\ensuremath{\Gamma}$ to the
M point, i.e., $k=(\ensuremath{\pi},0)$.
We study a chiral spin liquid wave function defined as a Gutzwiller projected BCS state with a complex pairing function. After projection, spontaneous dimerization is found for any odd but finite number of chains, thus satisfying the Lieb-Schultz-Mattis theorem, whereas for an even number of chains there is no dimerization. The two-dimensional thermodynamic limit is consistently reached for a large number of chains since the dimer order parameter vanishes in this limit. This property clearly supports the possibility of a spin liquid ground state in two dimensions with a gap to all physical excitations and with no broken translation symmetry.
We consider an exchange model describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on the square lattice. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit, and is known to show a spin-Peierls-like dimerization in one dimension. In two dimensions we calculate energy gaps, susceptibilities, and correlation functions with a Green's function Monte Carlo method. We find a finite triplet and singlet gap, with no evidence of order of any kind. We conclude that the ground state is, most likely, a spin liquid of resonating valence bonds.
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.
The Gutzwiller projection produces a well-known ansatz for spin-liquid and quantum Hall ground-state wavefunctions that is amenable to numerical simulation, with the Laughlin wavefunction being the most celebrated example. A long-standing issue is the precise relation between the Gutzwiller projection and the closely related parton gauge theory. Here, we clarify this issue by providing a field-theoretic description of the Gutzwiller projection. In a path integral description, the universal physics of the projected state is described in terms of a gauge field supported on a temporal slab of vanishing width
ε→0 coupled to the bulk matter fields. We analytically derive the universal physics of various Gutzwiller projected states. Our construction is also applicable to discrete symmetries, and we use it to analyze various projected SPT states. Among our results, we show that the Gutzwiller projection is not a good ansatz for the long-distance properties of
U(1) Dirac spin liquids, spinon Fermi surface spin liquids or composite Fermi liquids, and that the Gutzwiller projection of a quantum spin Hall state has only quasi-long range order. In contrast, in examples where the gauge field is gapped, including Laughlin states,
Z2 spin liquids and Luttinger liquids, we show that the slab gauge theory from Gutzwiller projection reproduces the correct universal physics of the full parton gauge theory. We also present a generalization of our field theory that describes
G-intertwining defects, with application to self-duality defects of recent theoretical interest.