arXiv:2407.05556 · Physical Review A

Ground-state phase diagram of the SU ( 4 ) Heisenberg model on a plaquette lattice

Ryui Kaneko, Shimpei Goto, Ippei Danshita

Published Aug 27, 2024• 1 citation

Abstract

We investigate the ground state of the $\mathrm{SU}(4)$ Heisenberg model on a square lattice with spatial anisotropy on each plaquette bond using the tensor-network method based on infinite projected entangled pair states. We find that the $\mathrm{SU}(4)$ singlet ground state appears in the strongly anisotropic limit, whereas N\'eel and valence-bond crystal orders coexist in the nearly isotropic limit. By examining the intermediate parameter region, we identify a phase transition between these phases. The nature of the phase transition is likely to be of first order, and the transition point is estimated to be around ${J}^{\ensuremath{'}}/J\ensuremath{\approx}0.85(5)$, where $J$ and ${J}^{\ensuremath{'}}$ are the interaction strengths of intra- and interplaquette bonds, respectively. We also calculate the anisotropy dependence of singlet correlations on a plaquette bond, which will be useful for future experiments of ultracold atoms in optical lattices.

DOI: 10.1103/physreva.110.023326

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arXiv:2407.05556 · Physical Review A

Ground-state phase diagram of the SU ( 4 ) Heisenberg model on a plaquette lattice

Ryui Kaneko, Shimpei Goto, Ippei Danshita

Published Aug 27, 2024• 1 citation

arXiv HTML PDF

Abstract

We investigate the ground state of the

\mathrm{SU}(4)

Heisenberg model on a square lattice with spatial anisotropy on each plaquette bond using the tensor-network method based on infinite projected entangled pair states. We find that the

\mathrm{SU}(4)

singlet ground state appears in the strongly anisotropic limit, whereas N'eel and valence-bond crystal orders coexist in the nearly isotropic limit. By examining the intermediate parameter region, we identify a phase transition between these phases. The nature of the phase transition is likely to be of first order, and the transition point is estimated to be around

{J}^{\ensuremath{'}}/J\ensuremath{\approx}0.85(5)

, where

J

and

{J}^{\ensuremath{'}}

are the interaction strengths of intra- and interplaquette bonds, respectively. We also calculate the anisotropy dependence of singlet correlations on a plaquette bond, which will be useful for future experiments of ultracold atoms in optical lattices.

DOI: 10.1103/physreva.110.023326

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Tensor network simulation of the phase diagram of the frustrated J1 - J2 Heisenberg model on a checkerboard lattice

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We use the recently developed tensor network algorithm based on infinite projected entangled pair states (iPEPS) to study the phase diagram of frustrated antiferromagnetic ${J}_{1}$ - ${J}_{2}$ Heisenberg model on a checkerboard lattice. The simulation indicates a N\'eel ordered phase when ${J}_{2}<0.88{J}_{1}$ , a plaquette valence bond solid state when $0.88<{J}_{2}/{J}_{1}<1.11$ , and a stripe phase when ${J}_{2}>1.11{J}_{1}$ , with two first-order transitions across the phase boundaries. The calculation shows that the cross dimer state proposed before is unlikely to be the ground state of the model, although such a state indeed arises as a metastable state in some parameter region.We use the recently developed tensor network algorithm based on infinite projected entangled pair states (iPEPS) to study the phase diagram of frustrated antiferromagnetic ${J}_{1}$-${J}_{2}$ Heisenberg model on a checkerboard lattice. The simulation indicates a N\'eel ordered phase when ${J}_{2}<0.88{J}_{1}$, a plaquette valence bond solid state when $0.88<{J}_{2}/{J}_{1}<1.11$, and a stripe phase when ${J}_{2}>1.11{J}_{1}$, with two first-order transitions across the phase boundaries. The calculation shows that the cross dimer state proposed before is unlikely to be the ground state of the model, although such a state indeed arises as a metastable state in some parameter region.

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Plaquette valence bond state in the spin- 12 J1−J2 XY model on the square lattice

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We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor ${J}_{1}$ and second-neighbor ${J}_{2}$ antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at ${J}_{2}/{J}_{1}<0.50$ and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor ${J}_{1}$ and second-neighbor ${J}_{2}$ antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at ${J}_{2}/{J}_{1}<0.50$ and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.

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The $U(1)$ -symmetric iPEPS study of the spin- $1/2$ square $J_{1}$ - $J_{2}$ Heisenberg modelThe $U(1)$-symmetric iPEPS study of the spin-$1/2$ square $J_{1}$-$J_{2}$ Heisenberg model

Reza Haghshenas, D. N. Sheng

We develop an improved variant of $U(1)$ -symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground state phase diagram of the spin- $1/2$ square $J_{1}$ - $J_{2}$ Heisenberg model. In order to improve the accuracy of the ansatz, we discuss a simple strategy to select automatically relevant symmetric sectors and also introduce an optimization method to treat second-neighbor interactions more efficiently. We show that variational ground-state energies of the model obtained by the $U(1)$ -symmetric iPEPS ansatz (for a fixed bond dimension $D$ ) set a better upper bound, improving previous tensor-network-based results. By studying N\'{e}el order parameter and correlation function in the large- $D$ limit, we find that a deconfined quantum-critical point occurs at $J^{c_1}_{2}=0.530(5)$ , where the correlation length of the system diverges as $\xi \sim D^{1.2}$ . The estimated critical anomalous exponents $\eta_{s}=0.65(5)$ and $\eta_{d}=1.9(1)$ for spin and dimer correlations respectively show strong deviation from those of the well-known $\mathcal{J}$ - $\mathcal{Q}$ model, suggesting possibly a different universality class. The pattern of local bond energy for the intermediate phase is compatible with the columnar valence bond solid (VBS) state, with a quite competitive variational ground-state energy in comparison with plaquette VBS one predicted by the density matrix renormalization group. We show that the associated VBS order parameter first monotonically increases with $J_2$ and finally a first-order quantum phase transition takes place at $J^{c_2}_{2}=0.610(3)$ to the conventional Stripe phase. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.We develop an improved variant of $U(1)$-symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground state phase diagram of the spin-$1/2$ square $J_{1}$-$J_{2}$ Heisenberg model. In order to improve the accuracy of the ansatz, we discuss a simple strategy to select automatically relevant symmetric sectors and also introduce an optimization method to treat second-neighbor interactions more efficiently. We show that variational ground-state energies of the model obtained by the $U(1)$-symmetric iPEPS ansatz (for a fixed bond dimension $D$) set a better upper bound, improving previous tensor-network-based results. By studying N\'{e}el order parameter and correlation function in the large-$D$ limit, we find that a deconfined quantum-critical point occurs at $J^{c_1}_{2}=0.530(5)$, where the correlation length of the system diverges as $\xi \sim D^{1.2}$. The estimated critical anomalous exponents $\eta_{s}=0.65(5)$ and $\eta_{d}=1.9(1)$ for spin and dimer correlations respectively show strong deviation from those of the well-known $\mathcal{J}$-$\mathcal{Q}$ model, suggesting possibly a different universality class. The pattern of local bond energy for the intermediate phase is compatible with the columnar valence bond solid (VBS) state, with a quite competitive variational ground-state energy in comparison with plaquette VBS one predicted by the density matrix renormalization group. We show that the associated VBS order parameter first monotonically increases with $J_2$ and finally a first-order quantum phase transition takes place at $J^{c_2}_{2}=0.610(3)$ to the conventional Stripe phase. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.

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Fatemeh Mirmojarabian, Saeed S. Jahromi, Jahanfar Abouie

We map out the ground state phase diagram of the spin- $\frac{1}{2}$ isotropic Kekul\'e-Kitaev model on the honeycomb lattice in the presence of the Heisenberg exchange couplings. Our study relies on large-scale tensor network simulations based on a graph-based projected entangled pair state approach and simple tensor update in the thermodynamic limit. We find that, on top of the quantum spin liquid and conventional magnetically ordered phases which are typical of the Kitaev-Heisenberg model, the Kekul\'e-Heisenberg phase diagram hosts two plaquette valence bond solid (VBS) phases with vanishing magnetic order. While the VBS phases preserve the symmetries of the original Hamiltonian, they differ markedly from the Kitaev spin liquid by having decorated plaquette ordering which is distinguished by a plaquette order parameter.We map out the ground state phase diagram of the spin-$\frac{1}{2}$ isotropic Kekul\'e-Kitaev model on the honeycomb lattice in the presence of the Heisenberg exchange couplings. Our study relies on large-scale tensor network simulations based on a graph-based projected entangled pair state approach and simple tensor update in the thermodynamic limit. We find that, on top of the quantum spin liquid and conventional magnetically ordered phases which are typical of the Kitaev-Heisenberg model, the Kekul\'e-Heisenberg phase diagram hosts two plaquette valence bond solid (VBS) phases with vanishing magnetic order. While the VBS phases preserve the symmetries of the original Hamiltonian, they differ markedly from the Kitaev spin liquid by having decorated plaquette ordering which is distinguished by a plaquette order parameter.

arXiv:2308.11010Physical review. B./Physical review. BNov 27, 20242 citations

We investigate the ground state of the

\mathrm{SU}(4)

Heisenberg model on a square lattice with spatial anisotropy on each plaquette bond using the tensor-network method based on infinite projected entangled pair states. We find that the

\mathrm{SU}(4)

{J}^{\ensuremath{'}}/J\ensuremath{\approx}0.85(5)

, where

J

and

{J}^{\ensuremath{'}}

We use the recently developed tensor network algorithm based on infinite projected entangled pair states (iPEPS) to study the phase diagram of frustrated antiferromagnetic

{J}_{1}

{J}_{2}

Heisenberg model on a checkerboard lattice. The simulation indicates a N\'eel ordered phase when

{J}_{2}<0.88{J}_{1}

, a plaquette valence bond solid state when

0.88<{J}_{2}/{J}_{1}<1.11

, and a stripe phase when

{J}_{2}>1.11{J}_{1}

, with two first-order transitions across the phase boundaries. The calculation shows that the cross dimer state proposed before is unlikely to be the ground state of the model, although such a state indeed arises as a metastable state in some parameter region.

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.

\mathrm{SU}(N)

symmetric fermions on a lattice, which can be realized in ultracold-atom-based quantum simulators, have very promising prospects for realizing exotic states of matter. Here we present the ground-state phase diagram of the repulsive SU(3) Hubbard model on a honeycomb lattice at 1/3 filling obtained from infinite projected entangled pair states tensor network calculations. In the strongly interacting limit the ground state has plaquette order. Upon decreasing the interaction strength

U/t

we find a first-order transition at

U/t=7.2(2)

into a dimerized, color-ordered state, which extends down to

U/t=4.5(5)

, at which the Mott transition occurs and the ground state becomes uniform. Our results may serve as a prediction and benchmark for future quantum simulators of SU(3) fermions.

We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor

{J}_{1}

and second-neighbor

{J}_{2}

antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at

{J}_{2}/{J}_{1}<0.50

and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.

The

U(1)

-symmetric iPEPS study of the spin-

1/2

square

J_{1}

J_{2}

Heisenberg model

We develop an improved variant of

U(1)

-symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground state phase diagram of the spin-

1/2

square

J_{1}

J_{2}

Heisenberg model. In order to improve the accuracy of the ansatz, we discuss a simple strategy to select automatically relevant symmetric sectors and also introduce an optimization method to treat second-neighbor interactions more efficiently. We show that variational ground-state energies of the model obtained by the

U(1)

-symmetric iPEPS ansatz (for a fixed bond dimension

D

) set a better upper bound, improving previous tensor-network-based results. By studying N\'{e}el order parameter and correlation function in the large-

D

limit, we find that a deconfined quantum-critical point occurs at

J^{c_1}_{2}=0.530(5)

, where the correlation length of the system diverges as

\xi \sim D^{1.2}

. The estimated critical anomalous exponents

\eta_{s}=0.65(5)

and

\eta_{d}=1.9(1)

for spin and dimer correlations respectively show strong deviation from those of the well-known

\mathcal{J}

\mathcal{Q}

model, suggesting possibly a different universality class. The pattern of local bond energy for the intermediate phase is compatible with the columnar valence bond solid (VBS) state, with a quite competitive variational ground-state energy in comparison with plaquette VBS one predicted by the density matrix renormalization group. We show that the associated VBS order parameter first monotonically increases with

J_2

and finally a first-order quantum phase transition takes place at

J^{c_2}_{2}=0.610(3)

to the conventional Stripe phase. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.

We map out the ground state phase diagram of the spin-

\frac{1}{2}

isotropic Kekul\'e-Kitaev model on the honeycomb lattice in the presence of the Heisenberg exchange couplings. Our study relies on large-scale tensor network simulations based on a graph-based projected entangled pair state approach and simple tensor update in the thermodynamic limit. We find that, on top of the quantum spin liquid and conventional magnetically ordered phases which are typical of the Kitaev-Heisenberg model, the Kekul\'e-Heisenberg phase diagram hosts two plaquette valence bond solid (VBS) phases with vanishing magnetic order. While the VBS phases preserve the symmetries of the original Hamiltonian, they differ markedly from the Kitaev spin liquid by having decorated plaquette ordering which is distinguished by a plaquette order parameter.