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Physical review. B./Physical review. B

Ground state of SU(3) spin model on the checkerboard lattice

Junhao Zhang, Jie Hou, Jie Lou, Yan Chen

Published Aug 27, 2025• 0 citations
Publisher

Abstract

Geometric frustration in quantum spin systems can lead to exotic ground states. In this study, we investigate the $\mathrm{SU}(3)$ spin model on the checkerboard lattice to explore the effects of frustration arising from its point-connected $(N+1)$-site local structure. We employ the density matrix renormalization group (DMRG) and exact diagonalization (ED) techniques to determine the ground state properties. Our results reveal the absence of both three-sublattice antiferromagnetic order and valence cluster solid order. Instead, we identify ground states with bond stripe patterns sensitive to boundary conditions and system size, comprising staggered singlet arrays and uniform flat stripes. Notably, these stripes are relatively decoupled, and similar patterns can be reconstructed in quasi-one-dimensional ladders. These findings suggest that geometric frustration drives the system toward a mixed phase, combining characteristics of spin-liquid and valence cluster solid states, providing new insights into the behavior of frustrated quantum spin systems.

DOI
10.1103/g4ng-xr29

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Geometric frustration in quantum spin systems can lead to exotic ground states. In this study, we investigate the SU(3)\mathrm{SU}(3)SU(3) spin model on the checkerboard lattice to explore the effects of frustration arising from its point-connected (N+1)(N+1)(N+1)-site local structure. We employ the density matrix renormalization group (DMRG) and exact diagonalization (ED) techniques to determine the ground state properties. Our results reveal the absence of both three-sublattice antiferromagnetic order and valence cluster solid order. Instead, we identify ground states with bond stripe patterns sensitive to boundary conditions and system size, comprising staggered singlet arrays and uniform flat stripes. Notably, these stripes are relatively decoupled, and similar patterns can be reconstructed in quasi-one-dimensional ladders. These findings suggest that geometric frustration drives the system toward a mixed phase, combining characteristics of spin-liquid and valence cluster solid states, providing new insights into the behavior of frustrated quantum spin systems.
Ground State of SU(3)\mathrm{SU}\left(3\right)SU(3) spin model on the checkerboard lattice
Geometric frustration in quantum spin systems can lead to exotic ground states. In this study, we investigate the SU(3)\mathrm{SU}(3)SU(3) spin model on the checkerboard lattice to explore the effects of frustration arising from its point-connected (N+1)(N+1)(N+1)-site local structure. We employ density matrix renormalization group (DMRG) and exact diagonalization (ED) techniques to determine the ground state properties. Our results reveal the absence of both 3-sublattice antiferromagnetic order and valence cluster solid order. Instead, we identify ground states with bond stripe patterns sensitive to boundary conditions and system size, comprising staggered singlet arrays and uniform flat stripes. Notably, these stripes are relatively decoupled, and similar patterns can be reconstructed in quasi-one-dimensional ladders. These findings suggest that geometric frustration drives the system toward a mixed phase, combining characteristics of spin-liquid and valence cluster solid states, providing new insights into the behavior of frustrated quantum spin systems.
The intricate interplay between frustration and spin chirality has the potential to give rise to unprecedented phases in frustrated quantum magnets. We examine the ground state phase diagram of the spin-1/2 square lattice J1-J2-Jx model by employing critical level crossings and ground state fidelity susceptibility (FS) using exact diagonalization (ED) with full lattice symmetries. Our analysis reveals the evolution of highly symmetric energy levels as a function of J2 at fixed Jx. During a magnetic to non-magnetic phase transition, the precise identification of the phase boundary is achieved through critical level crossings between the gapless excitation of a magnetic phase and the quasi-degenerate ground state of a non-magnet phase. Conversely, a direct transition between two non-magnetic phases is characterized by a FS peak accompanied by an avoided ground state level crossing, serving as a distinctive signal. Within a substantial range of Jx, we identify an anticipated chiral spin liquid (CSL) state and an adjacent nematic spin liquid (NSL) phase with a degeneracy of two on a cylinder. These two phases are demarcated by a nearly vertical boundary line at J2 = 0.65. This critical line terminates at the lower boundary of a magnetic ordered chiral spin solid (CSS) phase. We validate the topological nature of the CSL using the modular S matrix of the minimum entangled states (MES) on a torus, along with the entanglement spectra (ES) of even and odd sectors on a cylinder, employing an SU(2)-symmetric density matrix renormalization group (DMRG) method. Furthermore, we delve into a comprehensive discussion on the nature of the NSL, exploring aspects such as ground state degeneracy, the local bond energy landscape, and the singlet and triplet gaps on various tori. These analysis provide substantial evidence supporting the nematic nature of the NSL.
We investigate the ground state of the d1{d}^{1}d1 spin-orbital model for triply degenerate t2g{t}_{2g}t2g​ orbitals on a triangular lattice that unifies intrinsic frustration of spin and orbital interactions with geometrical frustration. Using full or Lanczos exact diagonalization of finite clusters, we establish that the ground state of the spin-orbital model that interpolates between superexchange and direct exchange interactions on the bonds is characterized by valence-bond correlations. In the absence of Hund's exchange the model describes a competition between various possible valence-bond states. By considering the clusters with open boundary conditions we demonstrate that orbital interactions are always frustrated, but this frustration is removed by pronounced spin singlet correlations that coexist with dimer orbital correlations supporting them. Such local configurations contribute to the disordered ground states found for the clusters with periodic boundary conditions that interpolate between a highly resonating, dimer-based, entangled spin-orbital liquid phase and a valence-bond state with completely static spin-singlet states. We argue that these states are also realized for the infinite lattice and anticipate that pronounced transitions between different regimes found for particular geometries will turn out to smooth crossovers in the properties of the spin-orbital liquid in the thermodynamic limit. Finally, we provide evidence that the resonating spin-orbital liquid phase involves entangled states on the bonds. In such a phase classical considerations based on the mean-field theory cannot be used, spin exchange interactions do not determine spin bond correlations, and quantum fluctuations play a crucial role in the ground states and magnetic transitions.
The intricate interplay between frustration and spin chirality, induced by the Dzyaloshinskii-Moriya interaction, holds promise for unveiling novel phases in frustrated quantum magnets. This study investigates the ground state phase diagram of the spin-12\frac{1}{2}21​ square lattice ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model upon incorporation of the chiral interaction ${J}_{\ensuremath{\chi}}$. Employing exact diagonalization (ED) with full lattice symmetries, we analyze the phase evolution as a function of J2{J}_{2}J2​ at fixed ${J}_{\ensuremath{\chi}}$, utilizing highly symmetric energy levels. Critical level crossings and ground state fidelity susceptibility (FS) techniques aid in pinpointing phase boundaries: Magnetic to nonmagnetic phase transitions are identified through critical level crossings between gapless magnetic excitations and quasidegenerate ground states of nonmagnetic phases. Direct transitions between two nonmagnetic phases are characterized by FS peaks due to avoided ground state level crossing. Based on these observations, we identify an anticipated chiral spin liquid (CSL) state and an adjacent nematic spin liquid (NSL) phase within a significant range of ${J}_{\ensuremath{\chi}}$, demarcated by a nearly vertical boundary line at ${J}_{2}\ensuremath{\approx}0.65$. This critical line terminates at the lower boundary in ${J}_{\ensuremath{\chi}}$ of a magnetic ordered chiral spin solid phase, which gains prominence with increasing ${J}_{\ensuremath{\chi}}$ from both CSL and NSL phases. The topological nature of the CSL is confirmed using the modular S\mathcal{S}S matrix of minimally entangled states on a torus and the entanglement spectra of even and odd sectors on a cylinder, employing ED and SU(2)\mathrm{SU}(2)SU(2)-symmetric density matrix renormalization group method, respectively. Furthermore, a comprehensive discussion on the nature of the NSL is provided, exploring aspects such as ground state degeneracy, local bond energy landscape, and singlet and triplet gaps on various tori, offering substantial evidence supporting the nematic nature of the NSL.
We study a spin-half frustrated coupled ladder system, in which ladders with leg, rung, and diagonal interactions are linked via nearest-neighbor coupling. By introducing a leg-symmetric inter-ladder interaction that connects the left-to-left and right-to-right legs of adjacent ladders, the model is found to possess an exact dimer ground state, characterized by a product of two-spin singlets forming a columnar dimer phase. We analyze this model using bond-operator mean-field theory (BOMFT) and the density matrix renormalization group (DMRG) to probe the phase transitions that occur as one traverses the coupling space. The BOMFT reveals three distinct phases: a double-stripe ordered phase, a Néel ordered phase, and a quantum disordered dimerized phase. The critical points for the transitions are at $ J_1 = -0.81 $ (double-stripe to dimerized) and at $ J_1 = 2.81 $ (dimerized to Néel phase). Further, the DMRG results corroborate the exact ground state and refine the critical points to $ J_1 = -0.79 $ and $ J_1 = 2.29 $ for the respective transitions. Additionally, another transition is identified as the Néel order vanishes for $ J_1 \ge 4.5 $. The model can alternatively be represented as a network of orthogonal zigzag and fully frustrated spin ladders, offering a structural framework conducive to quantum materials engineering.
Large symmetry groups in quantum many-body systems could strongly enhance quantum fluctuations and thereby stabilize exotic quantum phases. Frustrated interactions were long known to have similar effects. Here we intertwine the large SU(N\mathrm{SU}(NSU(N) symmetry and the frustration in a ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{0.16em}{0ex}}\mathrm{SU}(N$) Heisenberg model on a honeycomb lattice, where J1{J}_{1}J1​ is the nearest-neighbor coupling and J2{J}_{2}J2​ is the next-nearest-neighbor coupling. With a large-NNN analysis, we obtain a rich phase diagram by varying both NNN and the ratio J2/J1{J}_{2}/{J}_{1}J2​/J1​. The ground states include Dirac spin liquid, chiral spin liquid, valence cluster solids, flux ordered state, and stripe states. The physical properties of each phase are discussed.