Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9307055

Holons in Chiral Spin-Liquids: Statistics and Pairing

D. M. Deaven, Daniel S. Rokhsar, Barbieri, A.

Published Jul 27, 1993• 0 citations
arXivHTMLPDF

Abstract

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 $Φ_s$ that is continuously adjustable between $0$ and $π/2$, 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 $d$-wave symmetry and breaks time-reversal and parity.

DOI
10.48550/arxiv.cond-mat/9307055

Related papers

Variational wavefunctions for ideal anyon gas: superfluid and skyrmion Hall crystal

Ya-Hui Zhang

The ground state of an ideal gas of anyons with statistical angle $θ\in(0,π)$ is a long-standing open problem, with renewed interest from the recent observations of fractional Chern insulators. In this work we construct variational wavefunctions that build in the exact anyon statistics and combine theory-guided composite-boson, composite-fermion and parton wavefunctions with neural-network correlations on the sphere. For spinless and SU(2) semions we confirm the paired anyon superfluid, well below the best crystal states. At $θ=π/3$ liquids and crystals are closer in energy for the spinless case. For $θ=π/3$ anyons with SU(3) flavor, we find two candidates. One is a skyrmion Hall crystal, in which the anyons form an integer quantum Hall state in the effective magnetic field from the spin texture. The other is a chiral color superconductor of six-anyon clusters, the color-flavor-locked pairing descendant of a holon metal with SU(3) color gauge symmetry and SU(3) flavor symmetry; its wavefunction is a hyperdeterminant rather than a product of parton determinants. Within our variational ansatz the color superconductor has better energy than both crystals and the color-flavor locked phases with U(1)$^2$ and Z$_3$ gauge groups. For twisted MoTe$_2$ this suggests that the reentrant integer quantum anomalous Hall phase is the skyrmion Hall crystal of the doped anyons, and that the observed superconductivity may be the color superconductor, which can undergo a transition to an $f+if$ BCS superconductor with a jump of the chiral central charge by 3.

arXiv:2610.40657•Oct 29, 2026•0 citations

Macroscopically doped chiral-spin-liquid state

Z. Zou, J. L. Levy, R. B. Laughlin

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.

Physical review. B, Condensed matter•Jan 1, 1992•14 citations

Charged excitations of the chiral spin liquid

Z. Zou, R. B. Laughlin

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.

Physical review. B, Condensed matter•Sep 1, 1990•26 citations

Pairing in doped spin liquids: Anyon versusd-wave superconductivity

Daniel S. Rokhsar

Using a simple variational ansatz, we estimate the pair wave function of a superconductor obtained by doping a Mott insulator with short-range antiferromagnetic spin correlations. The pairing symmetry is generically d wave. The so-called ``anyon superconductors'' are related to traditional BCS states with d-wave order parameters that break parity and time-reversal invariance. The transition between a tetragonal normal metal and a superconductor of this type generically proceeds through an intermediate phase with either superconducting order or broken time reversal, but not both.

Physical Review Letters•Jan 25, 1993•76 citations

Nature of chiral spin liquids on the kagome lattice

Alexander Wietek, Antoine Sterdyniak, Andreas Martin Läuchli

We investigate the stability and the nature of the chiral spin liquids which were recently uncovered in extended Heisenberg models on the kagome lattice. Using a Gutzwiller projected wave function approach, i.e., a parton construction, we obtain large overlaps with ground states of these extended Heisenberg models. We further suggest that the appearance of the chiral spin liquid in the time-reversal invariant case is linked to a classical transition line between two magnetically ordered phases.

arXiv:1503.03389•Physical Review B•Sep 14, 2015•91 citations

Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice

Chunxiao Liu, Leon Balents, Yasir Iqbal

Abstract We present a systematic classification and variational study of chiral quantum spin liquids on the pyrochlore lattice based on fermionic parton constructions. Focusing on chiral U ( 1 ) and Z 2 spin-liquid Ansätze , we characterize their symmetry properties, flux structures, and low-energy spinon spectra within a projective symmetry group framework, and incorporate gauge fluctuations through Gutzwiller-projected wave functions studied by variational Monte Carlo. From the equal-time spin structure factor, we develop correlation-based diagnostics that distinguish gauge-dominated Coulomb phases from states with substantial matter-field and short-range contributions. Distinct chiral flux sectors, though close in energy, exhibit markedly different degrees of emergent U ( 1 ) gauge-field dominance, reflected in the geometry and contrast of pinch-point singularities. Although these states are not competitive ground states of the nearest-neighbor Heisenberg model, they define a physically meaningful family of proximate chiral phases relevant to extended pyrochlore Hamiltonians.

arXiv:2604.11880•Reports on Progress in Physics•Jul 1, 2026•0 citations
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.
The ground state of an ideal gas of anyons with statistical angle θ∈(0,π)θ\in(0,π)θ∈(0,π) is a long-standing open problem, with renewed interest from the recent observations of fractional Chern insulators. In this work we construct variational wavefunctions that build in the exact anyon statistics and combine theory-guided composite-boson, composite-fermion and parton wavefunctions with neural-network correlations on the sphere. For spinless and SU(2) semions we confirm the paired anyon superfluid, well below the best crystal states. At θ=π/3θ=π/3θ=π/3 liquids and crystals are closer in energy for the spinless case. For θ=π/3θ=π/3θ=π/3 anyons with SU(3) flavor, we find two candidates. One is a skyrmion Hall crystal, in which the anyons form an integer quantum Hall state in the effective magnetic field from the spin texture. The other is a chiral color superconductor of six-anyon clusters, the color-flavor-locked pairing descendant of a holon metal with SU(3) color gauge symmetry and SU(3) flavor symmetry; its wavefunction is a hyperdeterminant rather than a product of parton determinants. Within our variational ansatz the color superconductor has better energy than both crystals and the color-flavor locked phases with U(1)2^22 and Z3_33​ gauge groups. For twisted MoTe2_22​ this suggests that the reentrant integer quantum anomalous Hall phase is the skyrmion Hall crystal of the doped anyons, and that the observed superconductivity may be the color superconductor, which can undergo a transition to an f+iff+iff+if BCS superconductor with a jump of the chiral central charge by 3.
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.
Using a simple variational ansatz, we estimate the pair wave function of a superconductor obtained by doping a Mott insulator with short-range antiferromagnetic spin correlations. The pairing symmetry is generically d wave. The so-called ``anyon superconductors'' are related to traditional BCS states with d-wave order parameters that break parity and time-reversal invariance. The transition between a tetragonal normal metal and a superconductor of this type generically proceeds through an intermediate phase with either superconducting order or broken time reversal, but not both.
Abstract We present a systematic classification and variational study of chiral quantum spin liquids on the pyrochlore lattice based on fermionic parton constructions. Focusing on chiral U ( 1 ) and Z 2 spin-liquid Ansätze , we characterize their symmetry properties, flux structures, and low-energy spinon spectra within a projective symmetry group framework, and incorporate gauge fluctuations through Gutzwiller-projected wave functions studied by variational Monte Carlo. From the equal-time spin structure factor, we develop correlation-based diagnostics that distinguish gauge-dominated Coulomb phases from states with substantial matter-field and short-range contributions. Distinct chiral flux sectors, though close in energy, exhibit markedly different degrees of emergent U ( 1 ) gauge-field dominance, reflected in the geometry and contrast of pinch-point singularities. Although these states are not competitive ground states of the nearest-neighbor Heisenberg model, they define a physically meaningful family of proximate chiral phases relevant to extended pyrochlore Hamiltonians.