Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the sqrt[3]×sqrt[3] state (i.e., the state with 120^{∘} spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m/m_{s}=1/3,23/27, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a T^{2} behavior, and the susceptibility approaches a finite constant as T→0. Our TN results of thermodynamic properties are compared with those from high-temperature series expansion. In addition, we disclose a quantum phase transition between q=0 state (i.e., the state with 120^{∘} spin configuration within a unit cell containing three sites) and sqrt[3]×sqrt[3] state in a spin-3/2 kagome XXZ model at the critical point Δ_{c}=0.54. This study provides reliable and useful information for further explorations on high-spin kagome physics.
By utilizing tensor-network-based methods, we investigate the zero- and finite-temperature properties of the spin-1/2 Heisenberg antiferromagnetic (HAF) model on an infinite Husimi lattice that contains 3/2 sites per triangle. The ground state of this model is found to possess vanishing local magnetization and is featureless; the spin-spin and dimer-dimer correlation functions are verified to decay exponentially, and its ground-state energy per site is determined to be ${e}_{0}=\ensuremath{-}0.4343(1)$, which is very close to that [${e}_{0}=\ensuremath{-}0.4386(5)$] of the intriguing kagome HAF model. The magnetization curve shows the absence of a zero-magnetization plateau, implying a gapless excitation. A
1/3-magnetization plateau with spin-up-up-down state is observed, which is selected and stabilized by quantum fluctuations. A ground-state phase diagram under magnetic fields is presented. Moreover, both magnetic susceptibility and the specific heat are studied, whose low-temperature behaviors reinforce the conclusion that the HAF model on the infinite Husimi lattice owns a gapless and featureless spin-liquid ground state.
We investigate the spin-1 kagome-lattice Heisenberg antiferromagnet using large-scale Lanczos diagonalization and the finite-temperature Lanczos method. The zero-temperature magnetization process exhibits plateaus at m = 0 , 1 / 3 , 7 / 9 , and 8 / 9 , where m is the normalized magnetization. The m = 0 plateau is identified as a trimer valence-bond-crystal state, while the high-field plateaus at m = 7 / 9 and 8 / 9 are identified as magnon crystals. In particular, the m = 8 / 9 plateau corresponds to the exact localized-magnon crystal state. A smoothed zero-temperature magnetization curve constructed using the Gaussian-kernel smoothing method indicates magnetization jumps at the lower-field edge of the m = 1 / 3 plateau and at the upper-field edges of the m = 7 / 9 and 8 / 9 plateaus. At finite temperatures, the specific heat exhibits a double-peak structure with peaks around T / J ≃ 0.1 and T / J ≃ 1.1 , and the low-temperature peak may be related to trimer valence-bond-crystal ordering. The finite-temperature magnetization curves show that the m = 1 / 3 plateau remains visible at low temperatures, whereas the high-field plateaus are rapidly smeared out by thermal effects. These results provide benchmark data for thermodynamic and high-field magnetization measurements in candidate spin-1 kagome-lattice materials.
We investigate the ground-state and finite-temperature properties of the kagome antiferromagnetic Heisenberg model with three inequivalent couplings, dubbed the
3J model, which is designed for the candidate Dirac quantum spin liquid (QSL) material YCu
3(OH)
6Br
2[Br
1−x(OH)
x] (see, e.g., Zeng et al., 2024). Employing large-scale density-matrix renormalization group (DMRG) supplemented by neural quantum states (NQS) simulations, we identify an intermediate QSL phase between two magnetically ordered phases. We also find that this QSL is separated from the kagome spin liquid ground state at the isotropic limit. To establish a direct comparison with experiments, we compute the specific heat of the model by means of advanced exponential (XTRG) and tangent-space (tanTRG) thermal tensor-network methods. In the magnetically ordered phase, the specific heat over temperature exhibits a shoulder at a temperature that is a fraction of the coupling strength
Jh, which disappears in the QSL phase. These universal behaviors are consistent with the experimentally observed specific heat in
3J materials for both ordered and QSL candidate samples. Our work thus connects microscopic models with experimentally measurable signatures, exemplifying an integrated approach to understanding QSL phenomena in frustrated quantum magnets~ (see Meng et al., 2026), with
3J materials serving as a representative case and providing a foundation for future studies.
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.
Over the last decade, the interest in the spin-
1/2 Heisenberg antiferromagnet (HAF) on the square kagome (also called shuriken) lattice has been growing as a model system of quantum magnetism with a quantum paramagnetic ground state, flat-band physics near the saturation field, and quantum scars. A further motivation to study this model comes from the recent discovery of a gapless spin liquid in the square kagome magnet
KCu6AlBiO4(SO4)5Cl [M. Fujihala et al., Nat. Commun. 11, 3429 (2020)]. Here, we present large-scale numerical investigations of the specific heat
C(T), the entropy
S(T), as well as the susceptibility $\ensuremath{\chi}(T)$ by means of the finite-temperature Lanczos method for system sizes of
N=18,24,30,36,42,48, and
N=54. We find that the specific heat exhibits a low-temperature shoulder below the major maximum which can be attributed to low-lying singlet excitations filling the singlet-triplet gap, which is significantly larger than the singlet-singlet gap. This observation is further supported by the behavior of the entropy
S(T), where a change in curvature is present just at about
T/J=0.2, the same temperature where the shoulder in
C sets in. For the susceptibility the low-lying singlet excitations are irrelevant, and the singlet-triplet gap leads to an exponentially activated low-temperature behavior. The maximum in $\ensuremath{\chi}(T)$ is found at a pretty low temperature
Tmax/J=0.146 (for
N=42) compared to
Tmax/J=0.935 for the unfrustrated square-lattice HAF signaling the crucial role of frustration also for the susceptibility. We find a striking similarity of our square kagome data with the corresponding ones for the kagome HAF down to very low
T. The magnetization process featuring plateaus and jumps and the field dependence of the specific heat that exhibits characteristic peculiarities attributed to the existence of a flat one-magnon band are discussed as well.
We investigate the ground-state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site ${e}_{0}=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}90(2)$, with
D∗=8 multiplets retained (i.e., a bond dimension of
D=24), and ${e}_{0}=\ensuremath{-}1.4116(4)$ from large-
D extrapolation, by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $\ensuremath{\delta}\ensuremath{\approx}19%$, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state to be a simplex valence-bond crystal. We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground-state phase diagram. Moreover, we implement non-Abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.