Frustrated quantum magnets are a central theme in condensed matter physics due to the richness of their phase diagrams. They support a panoply of phases including various ordered states and topological phases. Yet, this problem has defied a solution for a long time due to the lack of controlled approximations which make it difficult to distinguish between competing phases. Here we report the discovery of a special quantum macroscopically degenerate point in the XXZ model on the spin-1/2 kagome quantum antiferromagnet for the ratio of Ising to antiferromagnetic transverse coupling J_{z}/J=-1/2. This point is proximate to many competing phases explaining the source of the complexity of the phase diagram. We identify five phases near this point including both spin-liquid and broken-symmetry phases and give evidence that the kagome Heisenberg antiferromagnet is close to a transition between two phases.
Frustrated quantum magnets are a central theme in condensed matter physics due to the richness of their phase diagrams. They support a panoply of phases including various ordered states and topological phases. Yet, this problem has defied a solution for a long time due to the lack of controlled approximations which make it difficult to distinguish between competing phases. Here we report the discovery of a special quantum macroscopically degenerate point in the XXZ model on the spin-1/2 kagome quantum antiferromagnet for the ratio of Ising to antiferromagnetic transverse coupling J_{z}/J=-1/2. This point is proximate to many competing phases explaining the source of the complexity of the phase diagram. We identify five phases near this point including both spin-liquid and broken-symmetry phases and give evidence that the kagome Heisenberg antiferromagnet is close to a transition between two phases.
Exactly solvable models play a special role in condensed matter physics, serving as secure theoretical starting points for investigation of new phenomena. Changlani et al. [Phys. Rev. Lett. 120, 117202 (2018)] have discovered a limit of the XXZ model for S=21 spins on the kagome lattice, which is not only exactly solvable, but features a huge degeneracy of exact ground states corresponding to solutions of a three-coloring problem. This special point of the model was proposed as a parent for multiple phases in the wider phase diagram, including quantum spin liquids. Here, we show that the construction of Changlani et al. can be extended to more general forms of anisotropic exchange interaction, finding a line of parameter space in an XYZ model which maintains both the macroscopic degeneracy and the three-coloring structure of solutions. We show that the ground states along this line are partially ordered, in the sense that infinite-range correlations of some spin components coexist with a macroscopic number of undetermined degrees of freedom. We therefore propose the exactly solvable limit of the XYZ model on corner-sharing triangle-based lattices as a tractable starting point for discovery of quantum spin systems which mix ordered and spin-liquid-like properties.
We analyze the antiferromagnetic spin-1/2 XXZ model on the kagome lattice at finite external magnetic field with the help of a non-perturbative zero-temperature renormalization group (RG) technique. The exact nature of the ground and excited state properties (e.g. gapped or gapless spectrum etc) of this system are still debated. Approximate methods have typically been adopted towards understanding the low-energy spectrum. Following the work of Kumar et al (2014 Phys. Rev. B 90 174409), we use a Jordan–Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbor interactions. While the work of Kumar et al was confined mostly to the plateau at 1/3-filling (magnetization per site) in the XY regime, we analyze the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel–Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a SU (2)-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar et al . We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.
The phase diagram of the XXZ spin-1 quantum magnet on the kagome lattice is studied for all cases where the z-component nearest-neighbor spin interaction Jz is antiferromagnetic. Besides Jz and the nearest-neighbor in-plane spin interaction Jxy, the system is also parametrized by an on-site anisotropic term D(Sz)2. In the zero magnetic field case, the six previously introduced phases, found using various methods, are the nondegenerate gapped photon phase, which breaks no space symmetry or spin symmetry; the sixfold degenerate phase with plaquette order, which breaks both time-reversal symmetry and translational symmetry; the ``superfluid'' (ferromagnetic) phase with an in-plane global U(1) symmetry broken when Jxy<0; the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ order when Jxy>0; the nematic phase when D<0 and large; and a phase with resonating dimers on each hexagon. We obtain all of these phases and partial information about their quantum phase transitions in a single framework by studying condensation of defects in the sixfold plaquette phases. The transition between nematic phase and the sixfold degenerate plaquette phase is potentially an unconventional second-order critical point. In the case of a nonzero magnetic field along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$, another ordered phase with translation symmetry broken is opened up in the nematic phase. Due to the breaking of time-reversal symmetry by the field, a supersolid phase emerges between the sixfold plaquette order and the superfluid phase. This phase diagram might be accessible in nickel compounds, organic compound $m\text{\ensuremath{-}}\mathrm{MPYNN}∙\mathrm{B}{\mathrm{F}}_{4}$, or optical lattices of atoms with three degenerate states on every site.
We study the ground-state phase diagram of the spin-1/2 antiferromagnetic Heisenberg model on the square-kagome lattice using infinite projected entangled-pair states (iPEPS). By systematically varying the ratio of exchange couplings on triangular and square plaquettes, we establish a complete quantum phase diagram in the thermodynamic limit. In the intermediate-coupling regime, we identify four distinct nonmagnetic phases that are unambiguously characterized as valence-bond crystals (VBCs) by their symmetry-inequivalent patterns of strong and weak spin-spin correlations. These include a plaquette crossed-dimer VBC, a loop-six VBC stabilized around the isotropic point, a generalized pinwheel VBC with reduced rotational symmetry, and a decorated loop-six VBC proximate to ferrimagnetic order. We determine the phase boundaries using a combination of bond-resolved correlation functions, entanglement entropy, and magnetization. For transitions not accompanied by sharp entanglement signatures, we extract the spin gap from finite-field simulations, allowing us to distinguish gapped and gapless VBC phases. At larger coupling ratios, the system undergoes transitions into imperfect and perfect ferrimagnetic states. Our results resolve long-standing ambiguities in the square-kagome Heisenberg model and provide a quantitatively reliable reference for future theoretical and experimental studies of frustrated quantum magnets.
Abstract The nature of the ground state for the S = 1/2 Kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state is a chiral spin liquid. Combining the density matrix renormalization group method with analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region of the phase diagram. We characterize the nature of the ground state by computing energy derivatives, revealing the ground-state degeneracy arising from the spontaneous breaking of the time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a 3×3 3 × 3 magnetically ordered phase and two valence-bond crystal phases.
Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-1/2XXZ model for ${J}_{z}/J=\ensuremath{-}1/2$ on the kagome lattice [H. J. Changlani et al. Phys. Rev. Lett. 120, 117202 (2018)]---a result that holds for arbitrary magnetization---we develop an exact mapping between its exact ''quantum three-coloring'' wave functions and the characteristic localized and topological magnons. This map, involving ''resonating two-color loops,'' is developed to represent exact many-body ground state wave functions for special high magnetizations. Using this map we show that these exact ground state solutions are valid for any ${J}_{z}/J\ensuremath{\ge}\ensuremath{-}1/2$. This demonstrates the equivalence of the ground-state wave function of the Ising, Heisenberg, and XY regimes all the way to the ${J}_{z}/J=\ensuremath{-}1/2$ point for these high magnetization sectors. In the hardcore bosonic language, this means that a certain class of exact many-body solutions, previously argued to hold for purely repulsive interactions $({J}_{z}\ensuremath{\ge}0)$, actually hold for attractive interactions as well, up to a critical interaction strength. For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. Based on the calculation of the ground state energy and measurement of order parameters, we provide evidence for a lack of any qualitative change in the ground state on finite clusters in the Ising $({J}_{z}\ensuremath{\gg}J)$, Heisenberg (Jz=J), and XY(Jz=0) regimes, continuing adiabatically to the vicinity of the macroscopically degenerate ${J}_{z}/J=\ensuremath{-}1/2$ point. These findings offer a framework for recent results in the literature and also suggest that the ${J}_{z}/J=\ensuremath{-}1/2$ point is an unconventional quantum critical point whose vicinity may contain the key to resolving the spin-1/2 kagome problem.