Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0006485 · Physical Review Letters

Spontaneous Plaquette Formation in the SU(4) Spin-Orbital Ladder

Mathias van den Bossche, P. Azaria, P. Lecheminant, Frédéric Mila

Published Apr 30, 2001• 53 citations
arXivHTMLPDF

Abstract

The low-energy properties of the SU(4) spin-orbital model on a two-leg ladder are studied by a variety of analytical and numerical techniques. As in the case of SU(2) models, there is a singlet-multiplet gap in the spectrum, but the ground state is twofold degenerate. An interpretation in terms of SU(4)-singlet plaquettes is proposed. The implications for general two-dimensional lattices are outlined.

DOI
10.1103/physrevlett.86.4124

Related papers

SU(4) spin-orbital two-leg ladder, square, and triangle lattices

Shun-Qing Shen

Based on the generalized valence bond picture, a Schwinger boson mean-field theory is applied to the symmetric SU(4) spin-orbital systems. For a two-leg SU(4) ladder, the ground state is a spin-orbital liquid with a finite energy gap, in good agreement with recent numerical calculations. In two-dimensional square and triangle lattices, the SU(4) Schwinger bosons condense at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ and $(\ensuremath{\pi}/3,\ensuremath{\pi}/3),$ respectively. Spin, orbital, and coupled spin-orbital static susceptibilities become singular at the wave vectors; the Bose condensation arises at twice this value. It is also demonstrated that there are spin, orbital, and coupled spin-orbital long-range orderings in the ground state.

arXiv:cond-mat/0211074•Physical review. B, Condensed matter•Dec 19, 2002•6 citations

Tetramerization in a SU(4) Heisenberg model on the honeycomb lattice

Miklós Lajkó, Karlo Penc

The SU(4) Heisenberg model can serve as a low-energy model of the Mott insulating state in materials where the spins and orbitals are highly symmetric or in systems of alkaline-earth atoms on an optical lattice. Recently, it has been argued that on the honeycomb lattice, the model exhibits a unique spin-orbital liquid phase with an algebraic decay of correlations [P. Corboz et al., Phys. Rev. X 2, 041013 (2012)]. Here we study the instability of the algebraic spin-orbital liquid toward the spontaneous formation of SU(4) singlet plaquettes (tetramerization). Using a variational Monte Carlo approach to evaluate the projected wave function of fermions with $\ensuremath{\pi}$-flux state, we find that the algebraic liquid is robust and that a small finite value of the next-nearest exchange is needed to induce tetramerization. We also studied the phase diagram of a model which interpolates between the nearest-neighbor Heisenberg model and a Hamiltonian for which the singlet-plaquette-product state is an exact ground state.

arXiv:1303.6297•Physical Review B•Jun 27, 2013•21 citations

Phases of the generalized two-leg spin ladder: A view from the SU(4) symmetry

P. Lecheminant, Kiyohito Totsuka

The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point that unifies different competing dimerized orders and a scalar chirality phase that breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is dominated by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of a $\mathrm{U}(1)$ self-duality symmetry.

arXiv:cond-mat/0405275•Physical Review B•Jan 27, 2005•23 citations

Formation of clusters in the ground state of the t–J model on a two-leg ladder

Andreas Fledderjohann, A. Langari, K.-H. Mütter

We investigate the ground state properties of the $t-J$ model on a two leg ladder with anisotropic couplings ($t,α=J/t$) along rungs and ($t',α'=J'/t'$) along legs. We have implemented a cluster approach based on 4-site plaqettes. In the strong asymmetric cases $α/α'\ll 1$ and $α'/α\ll 1$ the ground state energy is well described by plaquette clusters with charges $Q=2,4$. The interaction between the clusters favours the condensation of plaquettes with maximal charge -- a signal for phase separation. The dominance of Q=2 plaquettes explains the emergence of tightly bound hole pairs. We have presented the numerical results of exact diagonalization to support our cluster approach.

arXiv:cond-mat/0410709•Journal of Physics Condensed Matter•Nov 13, 2004•2 citations

Exact spontaneous plaquette ground states for high-spin ladder models

Shu Chen, Congjun Wu, Shoucheng Zhang +1 more

We study the exchange physics in high-spin Mott insulating systems with $S=3∕2$ which is realizable in ultracold atomic systems. The high symmetry of $\mathit{SO}(5)$ or $\mathit{SU}(4)$ therein renders stronger quantum fluctuations than the usual spin-$1∕2$ systems. A spontaneous plaquette ground state without any site and bond spin orders is rigorously proved in a ladder spin-$3∕2$ model, whose topological excitations exhibit fractionalization behavior. The generalization to the $\mathit{SU}(N)$ plaquette state is also investigated.

arXiv:cond-mat/0507234•Physical Review B•Dec 15, 2005•55 citations

Two-leg SU(2n) spin ladder: A low-energy effective field theory approach

P. Lecheminant, Alexei M. Tsvelik

We present a field-theory analysis of a model of two $\mathrm{SU}(2n)$-invariant magnetic chains coupled by a generic interaction preserving time-reversal and inversion symmetry. Contrary to the SU(2)-invariant case the zero-temperature phase diagram of such two-leg spin ladder does not contain topological phases. Only generalized valence bond solid phases are stabilized when $n>1$ with different wave vectors and ground-state degeneracies. In particular, we find a phase which is made of a cluster of $2n$ spins put in an $\mathrm{SU}(2n)$ singlet state. For $n=3$, this cluster phase is relevant to $^{173}\mathrm{Yb}$ ultracold atoms, with an emergent SU(6) symmetry, loaded in a double-well optical lattice.

arXiv:1502.04515•Physical Review B•May 7, 2015•13 citations
The low-energy properties of the SU(4) spin-orbital model on a two-leg ladder are studied by a variety of analytical and numerical techniques. As in the case of SU(2) models, there is a singlet-multiplet gap in the spectrum, but the ground state is twofold degenerate. An interpretation in terms of SU(4)-singlet plaquettes is proposed. The implications for general two-dimensional lattices are outlined.
Based on the generalized valence bond picture, a Schwinger boson mean-field theory is applied to the symmetric SU(4) spin-orbital systems. For a two-leg SU(4) ladder, the ground state is a spin-orbital liquid with a finite energy gap, in good agreement with recent numerical calculations. In two-dimensional square and triangle lattices, the SU(4) Schwinger bosons condense at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ and $(\ensuremath{\pi}/3,\ensuremath{\pi}/3),$ respectively. Spin, orbital, and coupled spin-orbital static susceptibilities become singular at the wave vectors; the Bose condensation arises at twice this value. It is also demonstrated that there are spin, orbital, and coupled spin-orbital long-range orderings in the ground state.
The SU(4) Heisenberg model can serve as a low-energy model of the Mott insulating state in materials where the spins and orbitals are highly symmetric or in systems of alkaline-earth atoms on an optical lattice. Recently, it has been argued that on the honeycomb lattice, the model exhibits a unique spin-orbital liquid phase with an algebraic decay of correlations [P. Corboz et al., Phys. Rev. X 2, 041013 (2012)]. Here we study the instability of the algebraic spin-orbital liquid toward the spontaneous formation of SU(4) singlet plaquettes (tetramerization). Using a variational Monte Carlo approach to evaluate the projected wave function of fermions with $\ensuremath{\pi}$-flux state, we find that the algebraic liquid is robust and that a small finite value of the next-nearest exchange is needed to induce tetramerization. We also studied the phase diagram of a model which interpolates between the nearest-neighbor Heisenberg model and a Hamiltonian for which the singlet-plaquette-product state is an exact ground state.
The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point that unifies different competing dimerized orders and a scalar chirality phase that breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is dominated by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of a U(1)\mathrm{U}(1)U(1) self-duality symmetry.
We investigate the ground state properties of the t−Jt-Jt−J model on a two leg ladder with anisotropic couplings (t,α=J/tt,α=J/tt,α=J/t) along rungs and (t′,α′=J′/t′t',α'=J'/t't′,α′=J′/t′) along legs. We have implemented a cluster approach based on 4-site plaqettes. In the strong asymmetric cases α/α′≪1α/α'\ll 1α/α′≪1 and α′/α≪1α'/α\ll 1α′/α≪1 the ground state energy is well described by plaquette clusters with charges Q=2,4Q=2,4Q=2,4. The interaction between the clusters favours the condensation of plaquettes with maximal charge -- a signal for phase separation. The dominance of Q=2 plaquettes explains the emergence of tightly bound hole pairs. We have presented the numerical results of exact diagonalization to support our cluster approach.
We study the exchange physics in high-spin Mott insulating systems with S=3∕2S=3∕2S=3∕2 which is realizable in ultracold atomic systems. The high symmetry of SO(5)\mathit{SO}(5)SO(5) or SU(4)\mathit{SU}(4)SU(4) therein renders stronger quantum fluctuations than the usual spin-1∕21∕21∕2 systems. A spontaneous plaquette ground state without any site and bond spin orders is rigorously proved in a ladder spin-3∕23∕23∕2 model, whose topological excitations exhibit fractionalization behavior. The generalization to the SU(N)\mathit{SU}(N)SU(N) plaquette state is also investigated.
We present a field-theory analysis of a model of two SU(2n)\mathrm{SU}(2n)SU(2n)-invariant magnetic chains coupled by a generic interaction preserving time-reversal and inversion symmetry. Contrary to the SU(2)-invariant case the zero-temperature phase diagram of such two-leg spin ladder does not contain topological phases. Only generalized valence bond solid phases are stabilized when n>1n>1n>1 with different wave vectors and ground-state degeneracies. In particular, we find a phase which is made of a cluster of 2n2n2n spins put in an SU(2n)\mathrm{SU}(2n)SU(2n) singlet state. For n=3n=3n=3, this cluster phase is relevant to 173Yb^{173}\mathrm{Yb}173Yb ultracold atoms, with an emergent SU(6) symmetry, loaded in a double-well optical lattice.