Previous investigations have suggested that the simplest spin-orbital model on the simplest frustrated lattice can host a nematic quantum spin-orbital liquid state. Namely, the orbital degeneracy of the SU(4) Kugel-Khomskii model tends to enhance quantum fluctuations and stabilize a quantum spin-orbital liquid exhibiting stripy features on the triangular lattice, as revealed by the state-of-the-art method of the density matrix renormalization group boosted by Gutzwiller projected wave functions. In this work, using the variational quantum Monte Carlo method, we study several spin-orbital liquid states, including a uniform $\ensuremath{\pi}$-flux state, three stripy states, and a plaquette state, on the $L\ifmmode\times\else\texttimes\fi{}L$ torus up to $L=24$ . It turns out that one of these stripy states, called the ``stripe-II'' state, is energetically favored. This ground state breaks the ${C}_{6}$ symmetry of the lattice, resulting in a reduced ${C}_{2}$ symmetry and doubled unit cells while preserving the SU(4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform $\ensuremath{\pi}$-flux state.Previous investigations have suggested that the simplest spin-orbital model on the simplest frustrated lattice can host a nematic quantum spin-orbital liquid state. Namely, the orbital degeneracy of the SU(4) Kugel-Khomskii model tends to enhance quantum fluctuations and stabilize a quantum spin-orbital liquid exhibiting stripy features on the triangular lattice, as revealed by the state-of-the-art method of the density matrix renormalization group boosted by Gutzwiller projected wave functions. In this work, using the variational quantum Monte Carlo method, we study several spin-orbital liquid states, including a uniform $\ensuremath{\pi}$-flux state, three stripy states, and a plaquette state, on the $L\ifmmode\times\else\texttimes\fi{}L$ torus up to $L=24$. It turns out that one of these stripy states, called the ``stripe-II'' state, is energetically favored. This ground state breaks the ${C}_{6}$ symmetry of the lattice, resulting in a reduced ${C}_{2}$ symmetry and doubled unit cells while preserving the SU(4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform $\ensuremath{\pi}$-flux state.

Physical review. B./Physical review. BMar 4, 20244 citations

Gap formation for the one-dimensional SU(4) spin–orbital model

Y Tsukamoto, N. Kawakami, Y Yamashita +1 more

Physica B Condensed MatterJun 1, 20004 citations

A variational Monte Carlo approach to the SU(4) spin-orbital model on the triangular lattice

Zhang, Chun, Hui-Ke Jin, Zhou, Yi

Previous investigations have suggested that the simplest spin-orbital model on the simplest frustrated lattice can host a nematic quantum spin-orbital liquid state. Namely, the orbital degeneracy of the SU(4) Kugel-Khomskii (KK) model tends to enhance quantum fluctuations and stabilize a quantum spin-orbital liquid exhibiting stripy features on the triangular lattice, as revealed by the state-of-the-art method of the density matrix renormalization group boosted by Gutzwiller projected wave functions. In this work, using the variational quantum Monte Carlo method, we have studied several spin-orbital liquid states, including a uniform $π$ flux state, three stripy states, and a plaquette state, on the $L\times{}L$ torus up to $L=24$ . It turns out that one of these stripy states, called the "stripe-II" state, is energetically favored. This ground state breaks the $C_6$ symmetry of the lattice, resulting in a reduced $C_2$ symmetry and doubled unit cells, while preserving the SU(4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform $π$ -flux state.Previous investigations have suggested that the simplest spin-orbital model on the simplest frustrated lattice can host a nematic quantum spin-orbital liquid state. Namely, the orbital degeneracy of the SU(4) Kugel-Khomskii (KK) model tends to enhance quantum fluctuations and stabilize a quantum spin-orbital liquid exhibiting stripy features on the triangular lattice, as revealed by the state-of-the-art method of the density matrix renormalization group boosted by Gutzwiller projected wave functions. In this work, using the variational quantum Monte Carlo method, we have studied several spin-orbital liquid states, including a uniform $π$ flux state, three stripy states, and a plaquette state, on the $L\times{}L$ torus up to $L=24$. It turns out that one of these stripy states, called the "stripe-II" state, is energetically favored. This ground state breaks the $C_6$ symmetry of the lattice, resulting in a reduced $C_2$ symmetry and doubled unit cells, while preserving the SU(4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform $π$-flux state.

arXiv:2311.02639Nov 5, 20230 citations

Plaquette ground state in the two-dimensional SU(4) spin-orbital model

Mathias van den Bossche, Fu‐Chun Zhang, Frédéric Mila

arXiv:cond-mat/0001051The European Physical Journal BOct 1, 200050 citations

Critical phenomena for a triangular spin lattice I

M. P. M. den Nijs, Adrianus M. M. Pruisken, J. M. J. van Leeuwen

Physica A Statistical Mechanics and its ApplicationsJan 1, 197614 citations

A unified theory for the SU(4) spin-orbital model on the triangular lattice

Hui-Ke Jin, Rong-Yang Sun, Hong-Hao Tu +1 more

By combining the density matrix renormalization group (DMRG) method with Gutzwiller projected wave functions, we provide clear evidence that the ground state of the SU(4) Kugel-Khomskii spin-orbital model on the triangular lattice can be well described by a ``single Gutzwiller projected wave function with an emergent parton Fermi surface, despite it exhibits strong finite size effect and even-odd discrepancy in quasi-one-dimensional cylinders. This ground state preserves SU(4) symmetry, but spontaneously breaks translational symmetry by doubling the unit cell along one of the lattice vector directions. The finite size effect and even-odd discrepancy can be resolved by the fact that the parton Fermi surface consists of open orbits in the reciprocal space. Thereby, a nematic spin-orbital liquid state is expected in the two-dimensional limit. Furthermore, our DMRG results indicate that the fluctuating stripes are critical and the central charge of each stripe is $c=3$ , in agreement with the SU(4) $_1$ Wess-Zumino-Witten conformal field theory. All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.By combining the density matrix renormalization group (DMRG) method with Gutzwiller projected wave functions, we provide clear evidence that the ground state of the SU(4) Kugel-Khomskii spin-orbital model on the triangular lattice can be well described by a ``single Gutzwiller projected wave function with an emergent parton Fermi surface, despite it exhibits strong finite size effect and even-odd discrepancy in quasi-one-dimensional cylinders. This ground state preserves SU(4) symmetry, but spontaneously breaks translational symmetry by doubling the unit cell along one of the lattice vector directions. The finite size effect and even-odd discrepancy can be resolved by the fact that the parton Fermi surface consists of open orbits in the reciprocal space. Thereby, a nematic spin-orbital liquid state is expected in the two-dimensional limit. Furthermore, our DMRG results indicate that the fluctuating stripes are critical and the central charge of each stripe is $c=3$, in agreement with the SU(4)$_1$ Wess-Zumino-Witten conformal field theory. All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.

Jun 17, 20210 citations

L=24

. It turns out that one of these stripy states, called the ``stripe-II'' state, is energetically favored. This ground state breaks the

{C}_{6}

symmetry of the lattice, resulting in a reduced

{C}_{2}

symmetry and doubled unit cells while preserving the SU(4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform $\ensuremath{\pi}$-flux state.

π

flux state, three stripy states, and a plaquette state, on the

L\times{}L

torus up to

L=24

. It turns out that one of these stripy states, called the "stripe-II" state, is energetically favored. This ground state breaks the

C_6

symmetry of the lattice, resulting in a reduced

C_2

symmetry and doubled unit cells, while preserving the SU(4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform

π

-flux state.

c=3

, in agreement with the SU(4)

_1

Wess-Zumino-Witten conformal field theory. All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.