The Heisenberg antiferromagnet on the maple-leaf lattice has recently gathered a great deal of attention. Competition between three nonequivalent bond interactions results in various ground-state quantum phases, with the exact dimer-product singlet ground state being among them. The thermodynamic properties of this model are much less understood. We used high-temperature expansion up to the 18th order to study the thermodynamics of the S = 1 / 2 Heisenberg model on the uniform maple-leaf lattice with the ground state exhibiting a six-sublattice 120 ∘ long-range magnetic order. Padé approximants allow us to get reliable results up to the temperatures of about T ≈ 0.4 . To study thermodynamics for arbitrary temperatures, we made the interpolation using the entropy method. Based on the analysis of close Padé approximants, we find ground-state energy e 0 = − 0.53064 ... − 0.53023 in good agreement with numerical results. The specific heat c ( T ) has a typical maximum at rather low temperatures T ≈ 0.379 and the uniform susceptibility χ ( T ) at T ≈ 0.49 . We also estimate the value of χ ( T ) at zero temperature χ 0 ≈ 0.05 ... 0.06 . The ground-state order manifests itself in the divergence of the so-called generalized Wilson ratio.
The Heisenberg antiferromagnet on the maple-leaf lattice has recently gathered a great deal of attention. Competition between three nonequivalent bond interactions results in various ground-state quantum phases, with the exact dimer-product singlet ground state being among them. The thermodynamic properties of this model are much less understood. We used high-temperature expansion up to the 18th order to study the thermodynamics of the S = 1 / 2 Heisenberg model on the uniform maple-leaf lattice with the ground state exhibiting a six-sublattice 120 ∘ long-range magnetic order. Padé approximants allow us to get reliable results up to the temperatures of about T ≈ 0.4 . To study thermodynamics for arbitrary temperatures, we made the interpolation using the entropy method. Based on the analysis of close Padé approximants, we find ground-state energy e 0 = − 0.53064 ... − 0.53023 in good agreement with numerical results. The specific heat c ( T ) has a typical maximum at rather low temperatures T ≈ 0.379 and the uniform susceptibility χ ( T ) at T ≈ 0.49 . We also estimate the value of χ ( T ) at zero temperature χ 0 ≈ 0.05 ... 0.06 . The ground-state order manifests itself in the divergence of the so-called generalized Wilson ratio.
Abstract We study the Heisenberg antiferromagnet on the maple-leaf lattice using several numerical approaches, focusing on the numerical linked-cluster expansion (NLCE), which exhibits an unconventional convergence extending to low and even zero temperatures. We evaluate thermodynamic properties as well as spin–spin correlations through the equal-time structure factor. Within NLCE, the specific heat capacity reveals a two-peak structure at T 1 ≈ 0.479 J and T 2 ≈ 0.131 J, reminiscent of the corresponding result for the triangular lattice. At intermediate temperatures, the spin–spin structure factor develops features that reflect the absence of reflection symmetry in the lattice. The zero-temperature convergence of NLCE enables reliable estimates of the ground-state energy and points to a short-range correlated paramagnetic ground state composed of resonating hexagonal motifs. The NLCE results are benchmarked against pseudo-Majorana functional renormalization group, finite-temperature Lanczos, and classical Monte Carlo simulations.
We establish a remarkably rich ground state phase diagram in the maple-leaf lattice spin-1/2 Heisenberg antiferromagnet as a function of the three symmetry-inequivalent nearest-neighbor bonds using exact diagonalization and tower-of-states analysis on clusters up to N=36 sites. Besides a hexagonal plaquette state, a star-shaped valence bond solid state is discovered in close vicinity to the (canted) 120∘ magnetic phase, strongly reminiscent of a de-confined critical point or Dirac spin liquid scenario on the triangular lattice antiferromagnets. Moreover, an exact dimer product-state is observed next to a collinear Néel-state, similar to the Shastry-Sutherland model. All identified phases compete in a parameter regime close to the isotropic point, providing a promising region for spin liquids to emerge. By analyzing Gutzwiller-projected wave-functions we identify a sliver of parameter regime where a gapped Z2 spin liquid Ansatz is in astonishing agreement with the exact N=36 ground state. This rich competition of paramagnetic phases demonstrates that the maple-leaf antiferromagnet is a promising platform for exotic states of matter and quantum critical phenomena.
Abstract We study the quantum phase diagram of the spin-1/2 nearest-neighbor Heisenberg model on the maple-leaf lattice using infinite projected entangled pair states (iPEPS) combined with a corner transfer matrix renormalization group scheme adapted to C 3 -symmetric lattices. Focusing on the fully antiferromagnetic J – J d model with J h = J t ≔ J , we map out the ground-state phase diagram as a function of the dimer coupling J d . Our results show that the system hosts only two phases: a magnetically ordered canted-120° phase and an exact dimer singlet product phase. We identify a first-order transition between these two phases at J d / J ≈ 1.45. Within the magnetically ordered phase, we observe small but finite magnetic moments. We also resolve the quantum renormalization of the canting angle, which deviates from the classical prediction over almost the entire magnetically ordered phase.
Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin-1/2 Heisenberg model on the maple-leaf lattice with three symmetry-inequivalent nearest-neighbor interactions. It has been argued that the parameter regime with antiferromagnetic couplings on hexagons Jh and ferromagnetic couplings on triangles Jt and dimer Jd bonds, is potentially host to a cornucopia of emergent phases with unconventional orders. Our analysis indeed identifies an extended region where any conventional dipolar magnetic order is absent. A hexagonal singlet state is found in the region around Jd=Jt=0, while a dimerized hexagonal singlet order of a lattice nematic character appears proximate to the phase boundary with the c120∘ antiferromagnetic order. Interestingly, upon traversing the bulk of the paramagnetic (PM) region, we find a variety of distinct correlation profiles, which are qualitatively different from those of the hexagonal singlet and dimerized hexagonal singlet orders but feature no appreciable spin-nematic response, while the boundary with the ferromagnetic phase shows evidence of spin-nematic order. This PM region is thus likely host to an ensemble of nonmagnetic phases which could putatively include quantum spin liquids. Our phase diagram is built from a complementary application of state-of-the-art implementations of the cluster mean-field and pseudo-fermion functional renormalization group approaches, together with an unconstrained Luttinger-Tisza treatment of the model providing insights from the semi-classical limit.
We study the quantum phase diagram of the spin-1/2 nearest-neighbor Heisenberg model on the maple-leaf lattice using infinite projected entangled pair states (iPEPS) combined with a corner transfer matrix renormalization group scheme adapted to C3-symmetric lattices. Focusing on the fully antiferromagnetic J-Jd model with Jh=Jt:=J, we map out the ground-state phase diagram as a function of the dimer coupling Jd. Our results show that the system hosts only two phases: a magnetically ordered canted-120∘ phase and an exact dimer singlet product phase. We identify a first-order transition between these two phases at Jd/J≈1.45. Within the magnetically ordered phase, we observe small but finite magnetic moments. We also resolve the quantum renormalization of the canting angle, which deviates from the classical prediction over almost the entire magnetically ordered phase.
We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling J1>0 and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.