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:1912.10756 · SciPost Physics

Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy

Saeed S. Jahromi, Román Orús, Didier Poilblanc, Frédéric Mila

Published Dec 29, 2020• 12 citations
arXivHTMLPDF

Abstract

We study the zero-temperature phase diagram of the spin-1/2 Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical lattice-nematic phase that breaks rotational symmetry in real space through a first-order quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.

DOI
10.21468/scipostphys.9.6.092

Related papers

Stability of the spin- 12 kagome ground state with breathing anisotropy

Cécile Repellin, Yin-Chen He, Frank Pollmann

We numerically study the spin-$\frac{1}{2}$ breathing kagome lattice. In this variation of the kagome Heisenberg antiferromagnet, the spins belonging to upward and downward facing triangles have different coupling strengths. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that the kagome antiferromagnet spin liquid is extremely robust to this anisotropy. Materials featuring this anisotropy---and especially the recently studied vanadium compound $[{\mathrm{NH}}_{4}{]}_{2}[{\mathbf{C}}_{7}{\mathbf{H}}_{14}\mathbf{N}][{\mathbf{V}}_{7}{\mathbf{O}}_{6}{\mathbf{F}}_{18}]$ (DQVOF)---may thus be very good candidates to realize the much studied kagome spin liquid. Further, we closely examine the limit of strong breathing anisotropy and find indications of a transition to a nematic phase.

arXiv:1706.10105•Physical review. B./Physical review. B•Nov 14, 2017•25 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

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

Yasir Iqbal, Didier Poilblanc, Ronny Thomale +1 more

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., ${J}_{▿}\ensuremath{\ll}{J}_{▵}$.

arXiv:1712.04579•Physical review. B./Physical review. B•Mar 13, 2018•40 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

Spin- S kagome quantum antiferromagnets in a field with tensor networks

Thibaut Picot, Marc Ziegler, Román Orús +1 more

Spin-$S$ Heisenberg quantum antiferromagnets on the kagome lattice offer, when placed in a magnetic field, a fantastic playground to observe exotic phases of matter with (magnetic analogs of) superfluid, charge, bond, or nematic orders, or a coexistence of several of the latter. In this context, we have obtained the (zero-temperature) phase diagrams up to $S=2$ directly in the thermodynamic limit owing to infinite projected entangled pair states, a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau versus field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semiclassical, as the plateaus at the $\frac{1}{3}\mathrm{th},\left(1\ensuremath{-}\frac{2}{9S}\right)\mathrm{th}$, and $\left(1\ensuremath{-}\frac{1}{9S}\right)\mathrm{th}$ of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-$\frac{1}{2}$ $\frac{1}{9}$ plateau exhibiting a coexistence of charge and bond orders. Upon restoration of the spin rotation $U(1)$ symmetry, a finite compressibility appears, although lattice symmetry breaking persists. For integer spin values we also identify spin gapped phases at low enough fields, such as the $S=2$ (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.

arXiv:1508.07189•Physical review. B./Physical review. B•Feb 19, 2016•109 citations

Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice

Shenghan Jiang, Panjin Kim, Jung Hoon Han +1 more

The properties of ground state of spin- \frac{1}{2} 1 2 kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and Z_2 Z 2 topological order leads to different types of Z_2 Z 2 spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a U(1) U ( 1 ) Dirac spin liquid rather than a Z_2 Z 2 spin liquid.

arXiv:1610.02024•SciPost Physics•Jul 9, 2019•38 citations
Spin-12\frac{1}{2}21​ kagome Heisenberg antiferromagnet with strong breathing anisotropy
We study the zero-temperature phase diagram of the spin-1/2 Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical lattice-nematic phase that breaks rotational symmetry in real space through a first-order quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.
We numerically study the spin-12\frac{1}{2}21​ breathing kagome lattice. In this variation of the kagome Heisenberg antiferromagnet, the spins belonging to upward and downward facing triangles have different coupling strengths. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that the kagome antiferromagnet spin liquid is extremely robust to this anisotropy. Materials featuring this anisotropy---and especially the recently studied vanadium compound [NH4]2[C7H14N][V7O6F18][{\mathrm{NH}}_{4}{]}_{2}[{\mathbf{C}}_{7}{\mathbf{H}}_{14}\mathbf{N}][{\mathbf{V}}_{7}{\mathbf{O}}_{6}{\mathbf{F}}_{18}][NH4​]2​[C7​H14​N][V7​O6​F18​] (DQVOF)---may thus be very good candidates to realize the much studied kagome spin liquid. Further, we closely examine the limit of strong breathing anisotropy and find indications of a transition to a nematic phase.
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.
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., ${J}_{▿}\ensuremath{\ll}{J}_{▵}$.
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.
Spin-SSS Heisenberg quantum antiferromagnets on the kagome lattice offer, when placed in a magnetic field, a fantastic playground to observe exotic phases of matter with (magnetic analogs of) superfluid, charge, bond, or nematic orders, or a coexistence of several of the latter. In this context, we have obtained the (zero-temperature) phase diagrams up to S=2S=2S=2 directly in the thermodynamic limit owing to infinite projected entangled pair states, a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau versus field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semiclassical, as the plateaus at the $\frac{1}{3}\mathrm{th},\left(1\ensuremath{-}\frac{2}{9S}\right)\mathrm{th}$, and $\left(1\ensuremath{-}\frac{1}{9S}\right)\mathrm{th}$ of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-12\frac{1}{2}21​ 19\frac{1}{9}91​ plateau exhibiting a coexistence of charge and bond orders. Upon restoration of the spin rotation U(1)U(1)U(1) symmetry, a finite compressibility appears, although lattice symmetry breaking persists. For integer spin values we also identify spin gapped phases at low enough fields, such as the S=2S=2S=2 (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.
Competing Spin Liquid Phases in the S=12\frac{1}{2}21​ Heisenberg Model on the Kagome Lattice
The properties of ground state of spin- \frac{1}{2} 1 2 kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and Z_2 Z 2 topological order leads to different types of Z_2 Z 2 spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a U(1) U ( 1 ) Dirac spin liquid rather than a Z_2 Z 2 spin liquid.