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Physical review. B, Condensed matter

Hole propagator of the chiral spin liquid

R. B. Laughlin

Published Jan 1, 1992• 7 citations
Publisher

Abstract

The properties of a class of wave functions describing charged spinless excitations of the Kalmeyer-Laughlin spin-liquid state are studied within the context of the t-J model and the case made that they are legitimate elementary excitations of such a state. Using these wave functions and those previously proposed for the neutral spin-1/2 excitations, a variational calculation of the hole propagator is performed. The spectral density at a given momentum is found to be a broad continuum with resonant structures that move as the momentum is varied, and to be consistent with exact-diagonalization studies.

DOI
10.1103/physrevb.45.400

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arXiv:cond-mat/9307055•Jul 27, 1993•0 citations
The properties of a class of wave functions describing charged spinless excitations of the Kalmeyer-Laughlin spin-liquid state are studied within the context of the t-J model and the case made that they are legitimate elementary excitations of such a state. Using these wave functions and those previously proposed for the neutral spin-1/2 excitations, a variational calculation of the hole propagator is performed. The spectral density at a given momentum is found to be a broad continuum with resonant structures that move as the momentum is varied, and to be consistent with exact-diagonalization studies.
It is shown that one of the class of variational spin-liquid wave functions recently derived by Wen, Wilczek, and Zee [Phys. Rev. B 39, 11413 (1989)] is identical to the fractional-quantum-Hall analog state proposed by Kalmeyer and Laughlin [Phys. Rev. Lett. 59, 2095 (1987); Phys. Rev. B 39, 11 879 (1989)] and Laughlin [Ann. Phys. (N.Y.) 191, 163 (1989)], and that the neutral spin-1/2 excitations of the two states are also the same. The 1/2 fractional statistics obeyed by these particles is demonstrated explicitly. The spin-spin correlation function and quasiparticle profile for the Wen-Wilczek-Zee states are calculated both numerically and by a hypernetted-chain procedure. Both are consistent with the idea that spontaneous breaking of time-reversal symmetry is an essential feature of any spin state lacking magnetic order. A version of this state for a three-dimensional spin system is reported and shown to have similar properties. A case is made that the neutral spin-1/2 excitations of the three-dimensional spin liquid behave like anisotropic monopoles.
A Hamiltonian is introduced for which the spin-12 quantum liquid wavefunction proposed by Kalmeyer and Laughlin is the exact ground state. An explicit proof is given that this state is a doubly degenerate spin singlet. The excitation spectrum of the Hamiltonian is calculated variationally and a case is made for the presence of an energy gap. The spin-1 collective mode, calculated in the single-mode approximation, is shown to have a large energy that is minimized at the Brillouin zone corner. The spin-0 collective mode behaves similarly but has a lower overall energy. Wavefunctions for the neutral spin-12 excitations are shown to form an exact spin doublet. The energy of a pair of such excitations increases or decreases logarithmically with separation depending on the total spin. When widely separated, the excitations possess an internal 2-fold degree of freedom, a Brillouin zone that is half the linear dimension of the full zone, and a mass comparable to that of the collective modes.
We explore with exact diagonalization the propagation of a single hole in four magnetic phases of the $t\text{\ensuremath{-}}J$-like Kitaev-Heisenberg model on a honeycomb lattice: the N\'eel antiferromagnetic, stripe, zigzag, and Kitaev spin-liquid phases. We find coherent propagation of spin-polaron quasiparticles in the antiferromagnetic phase by a mechanism similar to that in the $t\text{\ensuremath{-}}J$ model for high-Tc{T}_{c}Tc​ cuprates. In the stripe and zigzag phases clear quasiparticles features appear in spectral functions of those propagators where holes are created and annihilated on one sublattice, while they remain largely hidden in those spectral functions that correspond to photoemission experiments. As the most surprising result, we find a totally incoherent spectral weight distribution for the spectral function of a hole moving in the Kitaev spin-liquid phase in the strong-coupling regime $t\ensuremath{\gg}J$ relevant for iridates. At intermediate coupling the finite systems calculation reveals a well-defined quasiparticle at the $\ensuremath{\Gamma}$ point; however, we find that the gapless spin excitations wipe out quasiparticles at finite momenta. Also for this more subtle case we conclude that in the thermodynamic limit the lightly doped Kitaev liquid phase does not support quasiparticle states in the neighborhood of $\ensuremath{\Gamma}$, and therefore yields a non-Fermi liquid, contrary to earlier suggestions based on slave-boson studies. These observations are supported by the presented study of the dynamic spin-structure factor in the Kitaev spin liquid regime.
Recent years have seen the discovery of a chiral spin liquid state - a bosonic analogue of a fractional Quantum Hall state first put forward by Kalmeyer and Laughlin in 1987 - in several deformations of the Heisenberg model on the Kagome lattice. Here, we apply state-of-the-art numerical techniques to one such model, where breaking of the time-reversal symmetry drives the system into the chiral phase. Our methods allow us to obtain explicit matrix-product state representations of the low-lying excitations of the chiral spin liquid state, including the topologically non-trivial semionic excitation. We characterize these excitations and study their energetics as the model is tuned towards a topological phase transition.
We study Gutzwiller-projected variational wavefunctions for charged, spinless holon excitations in chiral spin liquids. We find that these states describe anyons, with a statistical phase ΦsΦ_sΦs​ that is continuously adjustable between 000 and π/2π/2π/2, depending on a variational parameter. The statistical flux attached to each holon is localized to within a lattice constant. By diagonalizing the effective Hamiltonian for charge motion in our variational basis we obtain a two-holon pair state. This two-holon state has large overlap with a two-hole state whose relative wavefunction has ddd-wave symmetry and breaks time-reversal and parity.