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arXiv:1706.10105 · Physical review. B./Physical review. B

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

Cécile Repellin, Yin-Chen He, Frank Pollmann

Published Nov 14, 2017• 25 citations
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Abstract

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.

DOI
10.1103/physrevb.96.205124

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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.
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.
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.
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagomé lattice using the density-matrix renormalization group (DMRG) method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commersurate antiferromangetic wavevectors. We obtain a spin triplet excitation gap ΔE(S=1)=0.055±0.005ΔE(S=1)=0.055\pm 0.005ΔE(S=1)=0.055±0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.
We perform a density-matrix renormalization group (DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16,000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of -0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation functions and finite topological entanglement gamma consistent with gamma=ld 2, ruling out gapless, chiral or non-topological spin liquids. At the same time, DMRG results provide strong evidence for a gapped topological Z2 spin liquid.