Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
arXiv:2309.13116 · doi:10.1103/PhysRevB.109.035162
Abstract
The Jordan-Wigner map in 2D is as an exact lattice regularization of the 2 pi-flux attachment to a hard-core boson (or spin-1/2) leading to a composite-fermion particle. When the spin-1/2 model obeys ice rules this map preserves locality, namely, local Rohkshar-Kivelson models of spins are mapped onto local models of Jordan-Wigner/composite-fermions. Using this composite-fermion dual representation of RK models, we construct spin-liquid states by projecting Slater determinants onto the subspaces of the ice rules. Interestingly, we find that these composite-fermions behave as ``dipolar" partons for which the projective implementations of symmetries are very different from standard ``point-like" partons. We construct interesting examples of composite-fermion liquid states that respect all microscopic symmetries of the RK model. In the six-vertex subspace, we constructed a time-reversal and particle-hole-invariant state featuring two massless Dirac nodes, which is a composite-fermion counterpart to the classic pi-flux state of Abrikosov-Schwinger fermions in the square lattice. This state is a good ground state candidate for a modified RK-like Hamiltonian of quantum spin-ice. In the dimer subspace, we construct a state fearturing a composite Fermi surface but with nesting instabilities towards ordered phases such as the columnar state. We have also analyzed the low energy emergent gauge structure. If one ignores confinement, the system would feature a U(1) x U(1) low energy gauge structure with two associated gapless photon modes, but with the composite fermion carrying gauge charge only for one photon and behaving as a gauge neutral dipole under the other. These states are examples of pseudo-scalar U(1) spin liquids where mirror and time-reversal symmetries act as particle-hole conjugations, and the emergent magnetic fields are even under such time-reversal or lattice mirror symmetries.
44 pages, 35 figures
References in corpus (23)
- Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
- A Duality Web in 2+1 Dimensions and Condensed Matter Physics
- U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
- On the stability of U(1) spin liquids in two dimensions
- Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
- Majorana Fermions, Exact Mappings between Classical and Topological Orders
- Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice
- SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice
- Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
- Scars from protected zero modes and beyond in quantum link and quantum dimer models
- Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice
- Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model
- Bootstrapping conformal QED
- Gutzwiller-projected states for the - Heisenberg model on the kagome lattice: achievements and pitfalls
- Origin of oscillatory structures in the magnetothermal conductivity of the putative Kitaev magnet -RuCl
- Oscillations in the magnetothermal conductivity of -RuCl: Evidence of transition anomalies
- Weak Ferromagnetic Exchange and Anomalous Specific Heat in ZnCu3(OH)6Cl2
- Topological spin ordering via Chern-Simons superconductivity
- Evidence for the first-order topological phase transition in a Kitaev spin liquid candidate -RuCl
- Height-conserving quantum dimer models
- Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models
- Solving the quantum dimer and six vertex models one electric field line at a time
- Crystalline phases at finite winding densities in a quantum link ladder