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:1712.04579 · Physical review. B./Physical review. B

Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet

Yasir Iqbal, Didier Poilblanc, Ronny Thomale, Federico Becca

Published Mar 13, 2018• 40 citations
arXivHTMLPDF

Abstract

The nature of the ground state of the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings ${J}_{▵}$ and ${J}_{▿}$ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the $\text{U}(1)$ Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped ${\mathbb{Z}}_{2}$ spin liquid. For several values of the ratio ${J}_{▿}/{J}_{▵}$, the size scaling of the energy gain due to the pairing fields and the variational parameters are reported. Our results show that the energy gain of the gapped spin liquid with respect to the gapless state either vanishes for large enough system size or scales to zero in the thermodynamic limit. Similarly, the optimized pairing amplitudes (responsible for opening the spin gap) are shown to vanish in the thermodynamic limit. Our outcome is corroborated by the application of one and two Lanczos steps to the gapless and gapped wave functions, for which no energy gain of the gapped state is detected when improving the quality of the variational states. Finally, we discuss the competition with the ``simplex'' ${\mathbb{Z}}_{2}$ resonating-valence-bond spin liquid, valence-bond crystal, and nematic states in the strongly anisotropic regime, i.e., ${J}_{▿}\ensuremath{\ll}{J}_{▵}$.

DOI
10.1103/physrevb.97.115127

Related papers

Variational Monte Carlo study of a gapless spin liquid in the spin- 12 XXZ antiferromagnetic model on the kagome lattice

Wen-Jun Hu, Shou-Shu Gong, Federico Becca +1 more

By using the variational Monte Carlo technique, we study the spin-$\frac{1}{2}$ XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice. A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids [with $U(1)$ or ${Z}_{2}$ symmetry] or magnetically ordered phases [with $\mathbf{q}=(0,0)$ or $\mathbf{q}=(4\ensuremath{\pi}/3,0)$]. We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from $U(1)$ to ${Z}_{2}$ within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the $U(1)$ Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing $S=2$ spin gap is obtained at the variational level, in the whole regime from the $XY$ to the Heisenberg model.

arXiv:1505.06276•Physical Review B•Nov 11, 2015•6 citations

Projected wave function study of Z 2 spin liquids on the kagome lattice for the spin- 1 2 quantum Heisenberg antiferromagnet

Yasir Iqbal, Federico Becca, Didier Poilblanc

Motivated by recent density-matrix renormalization group (DMRG) calculations [Yan, Huse, and White, Science 332, 1173 (2011)], which claimed that the ground state of the nearest-neighbor spin-$1/2$ Heisenberg antiferromagnet on the kagome lattice geometry is a fully gapped spin liquid with numerical signatures of ${\mathbb{Z}}_{2}$ gauge structure, and a further theoretical work [Lu, Ran, and Lee, Phys. Rev. B 83, 224413 (2011)], which gave a classification of all Schwinger-fermion mean-field fully symmetric ${\mathbb{Z}}_{2}$ spin liquids on the kagome lattice, we have thoroughly studied Gutzwiller-projected fermionic wave functions by using quantum variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. In particular, we investigated the energetics of all ${\mathbb{Z}}_{2}$ candidates (gapped and gapless) that lie in the neighborhood of the energetically competitive U(1) gapless spin liquids. By using a state-of-the-art optimization method, we were able to conclusively show that the U(1) Dirac state is remarkably stable with respect to all ${\mathbb{Z}}_{2}$ spin liquids in its neighborhood, and in particular for opening a gap toward the so-called ${\mathbb{Z}}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ state, which was conjectured to describe the ground state obtained by the DMRG method. Finally, we also considered the addition of a small second nearest-neighbor exchange coupling of both antiferromagnetic and ferromagnetic type, and obtained similar results, namely, a U(1) Dirac spin-liquid ground state.

arXiv:1105.0341•Physical Review B•Jul 20, 2011•172 citations

Gapless spin-liquid phase in the kagome spin- 12 Heisenberg antiferromagnet

Yasir Iqbal, Federico Becca, Sandro Sorella +1 more

We study the energy and the static spin structure factor of the ground state of the spin-$1/2$ quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) $U(1)$ Dirac spin liquid is competitive with previously proposed gapped (topological) ${\mathbb{Z}}_{2}$ spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site $E/J=\ensuremath{-}0.4365(2)$, which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.

arXiv:1209.1858•Physical Review B•Feb 14, 2013•331 citations

Gapped Z2 spin liquid in the breathing kagome Heisenberg antiferromagnet

Mohsin Iqbal, Didier Poilblanc, Norbert Schuch

We investigate the spin-1/2 Heisenberg antiferromagnet on a kagome lattice with breathing anisotropy (i.e., with weak and strong triangular units), constructing an improved simplex resonating valence bond (RVB) ansatz by successive applications (up to three times) of local quantum gates, which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting projected entangled pair state involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB provides very good variational energies at strong and even intermediate breathing anisotropy. We show that it carries ${\mathbb{Z}}_{2}$ topological order which does not fade away under the first few applications of the quantum gates, suggesting that the RVB topological spin liquid becomes a competing ground state candidate for the kagome antiferromagnet at large breathing anisotropy.

arXiv:1912.08284•Physical review. B./Physical review. B•Apr 28, 2020•12 citations

Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet

Yasir Iqbal, Didier Poilblanc, Federico Becca

We provide strong numerical evidence, using improved variational wave functions, for a ground state with vanishing spin gap in the spin-$1/2$ quantum Heisenberg model on the kagome lattice. Starting from the algebraic $U(1)$ Dirac spin liquid state proposed by Ran et al. [Phys. Rev. Lett. 98, 117205 (2007)] and iteratively applying a few Lanczos steps, we compute the lowest $S=2$ excitation constructed by exciting spinons close to the Dirac nodes. Our results are compatible with a vanishing spin gap in the thermodynamic limit and in consonance with a power-law decay of long distance spin-spin correlations in real space. The competition with a gapped (topological) spin liquid is discussed.

arXiv:1311.5038•Physical Review B•Jan 16, 2014•131 citations

Quantum spin liquid in a breathing kagome lattice

Robert Schaffer, Yejin Huh, Kyusung Hwang +1 more

Motivated by recent experiments on the vanadium oxyfluoride material DQVOF, we examine possible spin liquid phases on a breathing kagome lattice of $S=1/2$ spins. By performing a projective symmetry group analysis, we determine the possible phases for both fermionic and bosonic ${\mathbb{Z}}_{2}$ spin liquids on this lattice, and establish the correspondence between the two. The nature of the ground state of the Heisenberg model on the isotropic kagome lattice is a hotly debated topic, with both ${\mathbb{Z}}_{2}$ and U(1) spin liquids argued to be plausible ground states. Using variational Monte Carlo techniques, we show that a gapped ${\mathbb{Z}}_{2}$ spin liquid emerges as the clear ground state in the presence of this breathing anisotropy. Our results suggest that the breathing anisotropy helps to stabilize this spin liquid ground state, which may aid us in understanding the results of experiments and help to direct future numerical studies on these systems.

arXiv:1605.05322•Physical review. B./Physical review. B•Feb 8, 2017•49 citations
The nature of the ground state of the spin S=1/2S=1/2S=1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings J▵{J}_{▵}J▵​ and J▿{J}_{▿}J▿​ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1)\text{U}(1)U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped Z2{\mathbb{Z}}_{2}Z2​ spin liquid. For several values of the ratio J▿/J▵{J}_{▿}/{J}_{▵}J▿​/J▵​, the size scaling of the energy gain due to the pairing fields and the variational parameters are reported. Our results show that the energy gain of the gapped spin liquid with respect to the gapless state either vanishes for large enough system size or scales to zero in the thermodynamic limit. Similarly, the optimized pairing amplitudes (responsible for opening the spin gap) are shown to vanish in the thermodynamic limit. Our outcome is corroborated by the application of one and two Lanczos steps to the gapless and gapped wave functions, for which no energy gain of the gapped state is detected when improving the quality of the variational states. Finally, we discuss the competition with the ``simplex'' Z2{\mathbb{Z}}_{2}Z2​ resonating-valence-bond spin liquid, valence-bond crystal, and nematic states in the strongly anisotropic regime, i.e., J▿\ensuremath≪J▵{J}_{▿}\ensuremath{\ll}{J}_{▵}J▿​\ensuremath≪J▵​.
By using the variational Monte Carlo technique, we study the spin-12\frac{1}{2}21​ XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice. A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids [with U(1)U(1)U(1) or Z2{Z}_{2}Z2​ symmetry] or magnetically ordered phases [with q=(0,0)\mathbf{q}=(0,0)q=(0,0) or $\mathbf{q}=(4\ensuremath{\pi}/3,0)$]. We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from U(1)U(1)U(1) to Z2{Z}_{2}Z2​ within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the U(1)U(1)U(1) Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing S=2S=2S=2 spin gap is obtained at the variational level, in the whole regime from the XYXYXY to the Heisenberg model.
Motivated by recent density-matrix renormalization group (DMRG) calculations [Yan, Huse, and White, Science 332, 1173 (2011)], which claimed that the ground state of the nearest-neighbor spin-1/21/21/2 Heisenberg antiferromagnet on the kagome lattice geometry is a fully gapped spin liquid with numerical signatures of Z2{\mathbb{Z}}_{2}Z2​ gauge structure, and a further theoretical work [Lu, Ran, and Lee, Phys. Rev. B 83, 224413 (2011)], which gave a classification of all Schwinger-fermion mean-field fully symmetric Z2{\mathbb{Z}}_{2}Z2​ spin liquids on the kagome lattice, we have thoroughly studied Gutzwiller-projected fermionic wave functions by using quantum variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. In particular, we investigated the energetics of all Z2{\mathbb{Z}}_{2}Z2​ candidates (gapped and gapless) that lie in the neighborhood of the energetically competitive U(1) gapless spin liquids. By using a state-of-the-art optimization method, we were able to conclusively show that the U(1) Dirac state is remarkably stable with respect to all Z2{\mathbb{Z}}_{2}Z2​ spin liquids in its neighborhood, and in particular for opening a gap toward the so-called ${\mathbb{Z}}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ state, which was conjectured to describe the ground state obtained by the DMRG method. Finally, we also considered the addition of a small second nearest-neighbor exchange coupling of both antiferromagnetic and ferromagnetic type, and obtained similar results, namely, a U(1) Dirac spin-liquid ground state.
We study the energy and the static spin structure factor of the ground state of the spin-1/21/21/2 quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) U(1)U(1)U(1) Dirac spin liquid is competitive with previously proposed gapped (topological) Z2{\mathbb{Z}}_{2}Z2​ spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site $E/J=\ensuremath{-}0.4365(2)$, which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.
We investigate the spin-1/2 Heisenberg antiferromagnet on a kagome lattice with breathing anisotropy (i.e., with weak and strong triangular units), constructing an improved simplex resonating valence bond (RVB) ansatz by successive applications (up to three times) of local quantum gates, which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting projected entangled pair state involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB provides very good variational energies at strong and even intermediate breathing anisotropy. We show that it carries Z2{\mathbb{Z}}_{2}Z2​ topological order which does not fade away under the first few applications of the quantum gates, suggesting that the RVB topological spin liquid becomes a competing ground state candidate for the kagome antiferromagnet at large breathing anisotropy.
We provide strong numerical evidence, using improved variational wave functions, for a ground state with vanishing spin gap in the spin-1/21/21/2 quantum Heisenberg model on the kagome lattice. Starting from the algebraic U(1)U(1)U(1) Dirac spin liquid state proposed by Ran et al. [Phys. Rev. Lett. 98, 117205 (2007)] and iteratively applying a few Lanczos steps, we compute the lowest S=2S=2S=2 excitation constructed by exciting spinons close to the Dirac nodes. Our results are compatible with a vanishing spin gap in the thermodynamic limit and in consonance with a power-law decay of long distance spin-spin correlations in real space. The competition with a gapped (topological) spin liquid is discussed.
Motivated by recent experiments on the vanadium oxyfluoride material DQVOF, we examine possible spin liquid phases on a breathing kagome lattice of S=1/2S=1/2S=1/2 spins. By performing a projective symmetry group analysis, we determine the possible phases for both fermionic and bosonic Z2{\mathbb{Z}}_{2}Z2​ spin liquids on this lattice, and establish the correspondence between the two. The nature of the ground state of the Heisenberg model on the isotropic kagome lattice is a hotly debated topic, with both Z2{\mathbb{Z}}_{2}Z2​ and U(1) spin liquids argued to be plausible ground states. Using variational Monte Carlo techniques, we show that a gapped Z2{\mathbb{Z}}_{2}Z2​ spin liquid emerges as the clear ground state in the presence of this breathing anisotropy. Our results suggest that the breathing anisotropy helps to stabilize this spin liquid ground state, which may aid us in understanding the results of experiments and help to direct future numerical studies on these systems.