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Physical review. B, Condensed matter

Charged excitations of the chiral spin liquid

Z. Zou, R. B. Laughlin

Published Sep 1, 1990• 26 citations
Publisher

Abstract

We propose specific wave functions for the charged, spinless excitations hypothesized to exist in chiral spin liquids and show, in the context of the t-J Hamiltonian, that their variational energy and mobility are superior to those of ordinary holes. We find that these quantities limit to finite values as the amount of chirality in the ground state diminishes to zero, but that the statistics become abruptly ill defined in this limit.

DOI
10.1103/physrevb.42.4073

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We propose specific wave functions for the charged, spinless excitations hypothesized to exist in chiral spin liquids and show, in the context of the t-J Hamiltonian, that their variational energy and mobility are superior to those of ordinary holes. We find that these quantities limit to finite values as the amount of chirality in the ground state diminishes to zero, but that the statistics become abruptly ill defined in this limit.
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.
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.
Our previous work on the isolated charge excitations, holons, of the chiral-spin-liquid state is generalized to include a macroscopic number of holons. We propose a specific class of wave functions for multiholon excitations exhibiting 1/2-fractional statistics. The fractional statistics are demonstrated by means of analytic continuation methods, numerical calculations, and U(1) gauge-theory techniques. A Chern-Simons term is derived in a long-wavelength effective action for the holons. The exactness of the fractional statistics follows from the quantization of the coefficient of the Chern-Simons term. This particular class of wave functions seems energetically favorable for the t-J Hamiltonian in the small-doping limit for physical J/t, while in the large-doping limit the stability of these states requires large J/t. An upper bound for the ground-state energy of the t-J Hamiltonian within the fractional-statistics basis set is obtained.
The parton approach for quantum spin liquids gives a transparent description of low-energy elementary excitations, e.g., spinons and emergent gauge-field fluctuations. The latter ones are directly coupled to the hopping/pairing of spinons. By using the fermionic representation of the U(1)U(1)U(1) Dirac state on the kagome lattice and variational Monte Carlo techniques to include the Gutzwiller projection, we analyze the effect of modifying the gauge fields in the spinon kinematics. In particular, we construct low-energy monopole excitations, which are shown to be gapless in the thermodynamic limit. States with a finite number of monopoles or with a finite density of them are also considered, with different patterns of the gauge fluxes. We show that these chiral states are not stabilized in the Heisenberg model with nearest-neighbor superexchange couplings, and the Dirac state corresponds to the lowest-energy ansatz within this family of variational wave functions. Our results support the idea that spinons with a gapless conical spectrum coexist with gapless monopole excitations, even for the spin-1/2 case.
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.