We study the stability region for the columnar dimer state proposed as a candidate ground state for the square-lattice quantum antiferromagnet with first- and second-neighbor antiferromagnetic couplings ( ${\mathit{J}}_{1}$ - ${\mathit{J}}_{2}$ model). We use a boson representation of the spin operators suited to the perturbative expansion around a dimer ground state. At lowest order, the columnar dimer is found to be stable only at the classical critical value ${\mathit{J}}_{2}$ / ${\mathit{J}}_{2}$ =1/2. However, we show that the leading anharmonic corrections stabilize the dimerized phase in a region of a finite width around ${\mathit{J}}_{2}$ / ${\mathit{J}}_{1}$ =1/2. A comparison of the ground-state energies shows that among the possible dimerized states the columnar dimer is the most favorable candidate to separate the two ordered states in the S=1/2 antiferromagnetic with first- and second-neighbor exchange.We study the stability region for the columnar dimer state proposed as a candidate ground state for the square-lattice quantum antiferromagnet with first- and second-neighbor antiferromagnetic couplings (${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ model). We use a boson representation of the spin operators suited to the perturbative expansion around a dimer ground state. At lowest order, the columnar dimer is found to be stable only at the classical critical value ${\mathit{J}}_{2}$/${\mathit{J}}_{2}$=1/2. However, we show that the leading anharmonic corrections stabilize the dimerized phase in a region of a finite width around ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$=1/2. A comparison of the ground-state energies shows that among the possible dimerized states the columnar dimer is the most favorable candidate to separate the two ordered states in the S=1/2 antiferromagnetic with first- and second-neighbor exchange.

Physical review. B, Condensed matterDec 1, 199170 citations

Dimer Character of the Ground State of the One Dimensional t-J-J' Model

Kazuhiro Sano, Ken'ichi Takano

Journal of the Physical Society of JapanFeb 15, 19930 citations

Dimer Character of the Ground State of the One Dimensionalt-J-J′Model

Kazuhiro Sano, Ken'ichi Takano

Journal of the Physical Society of JapanDec 15, 19924 citations

Two-dimensional quantum antiferromagnet with a fourfold degenerate dimer ground state

Alain Gellé, Andreas Martin Läuchli, Brijesh Kumar +1 more

We study the competition between antiferromagnetic order and valence-bond-crystal formation in a two-dimensional frustrated spin- $1∕2$ model. The ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model on the square lattice is further frustrated by introducing products of three-spin projectors which stabilize four dimer-product states as degenerate ground state. These four states are reminiscent of the dimerized singlet ground state of the Shastry-Sutherland model. Using exact diagonalization, we study the evolution of the ground state by varying the ratio of interactions. For a large range of parameters $({J}_{2}\ensuremath{\gtrsim}0.25{J}_{1})$, our model shows a direct transition between the valence-bond-crystal phase and the collinear antiferromagnetic phase. For small values of ${J}_{2}$ , several intermediate phases appear which are also analyzed.We study the competition between antiferromagnetic order and valence-bond-crystal formation in a two-dimensional frustrated spin-$1∕2$ model. The ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model on the square lattice is further frustrated by introducing products of three-spin projectors which stabilize four dimer-product states as degenerate ground state. These four states are reminiscent of the dimerized singlet ground state of the Shastry-Sutherland model. Using exact diagonalization, we study the evolution of the ground state by varying the ratio of interactions. For a large range of parameters $({J}_{2}\ensuremath{\gtrsim}0.25{J}_{1})$, our model shows a direct transition between the valence-bond-crystal phase and the collinear antiferromagnetic phase. For small values of ${J}_{2}$, several intermediate phases appear which are also analyzed.

arXiv:0704.2352Physical Review BJan 15, 200814 citations

Double semion phase in an exactly solvable quantum dimer model on the kagome lattice

Oliver Buerschaper, Siddhardh C. Morampudi, Frank Pollmann

Quantum dimer models typically arise in various low energy theories like those of frustrated antiferromagnets. We introduce a quantum dimer model on the kagome lattice which stabilizes an alternative ${\mathbb{Z}}_{2}$ topological order, namely the so-called ``double semion'' order. For a particular set of parameters, the model is exactly solvable, allowing us to access the ground state as well as the excited states. We show that the double semion phase is stable over a wide range of parameters using numerical exact diagonalization. Furthermore, we propose a simple microscopic spin Hamiltonian for which the low-energy physics is described by the derived quantum dimer model.Quantum dimer models typically arise in various low energy theories like those of frustrated antiferromagnets. We introduce a quantum dimer model on the kagome lattice which stabilizes an alternative ${\mathbb{Z}}_{2}$ topological order, namely the so-called ``double semion'' order. For a particular set of parameters, the model is exactly solvable, allowing us to access the ground state as well as the excited states. We show that the double semion phase is stable over a wide range of parameters using numerical exact diagonalization. Furthermore, we propose a simple microscopic spin Hamiltonian for which the low-energy physics is described by the derived quantum dimer model.

arXiv:1407.8521Physical Review BNov 26, 201424 citations

Electronic states in the t-J model near magnetic phase transitions

Yu. A. Izyumov, B. M. Letfulov, E. V. Shipitsyn

Journal of Experimental and Theoretical PhysicsMay 1, 19940 citations

{\mathit{J}}_{1}

{\mathit{J}}_{2}

model). We use a boson representation of the spin operators suited to the perturbative expansion around a dimer ground state. At lowest order, the columnar dimer is found to be stable only at the classical critical value

{\mathit{J}}_{2}

{\mathit{J}}_{2}

=1/2. However, we show that the leading anharmonic corrections stabilize the dimerized phase in a region of a finite width around

{\mathit{J}}_{2}

{\mathit{J}}_{1}

=1/2. A comparison of the ground-state energies shows that among the possible dimerized states the columnar dimer is the most favorable candidate to separate the two ordered states in the S=1/2 antiferromagnetic with first- and second-neighbor exchange.

We study the competition between antiferromagnetic order and valence-bond-crystal formation in a two-dimensional frustrated spin-

1∕2

model. The ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model on the square lattice is further frustrated by introducing products of three-spin projectors which stabilize four dimer-product states as degenerate ground state. These four states are reminiscent of the dimerized singlet ground state of the Shastry-Sutherland model. Using exact diagonalization, we study the evolution of the ground state by varying the ratio of interactions. For a large range of parameters $({J}_{2}\ensuremath{\gtrsim}0.25{J}_{1})$, our model shows a direct transition between the valence-bond-crystal phase and the collinear antiferromagnetic phase. For small values of

{J}_{2}

, several intermediate phases appear which are also analyzed.

Quantum dimer models typically arise in various low energy theories like those of frustrated antiferromagnets. We introduce a quantum dimer model on the kagome lattice which stabilizes an alternative

{\mathbb{Z}}_{2}

topological order, namely the so-called ``double semion'' order. For a particular set of parameters, the model is exactly solvable, allowing us to access the ground state as well as the excited states. We show that the double semion phase is stable over a wide range of parameters using numerical exact diagonalization. Furthermore, we propose a simple microscopic spin Hamiltonian for which the low-energy physics is described by the derived quantum dimer model.