By using exact diagonalization method and density matrix renormalization group method,the author studies the ground states of the two-leg spin-1/2 mixed comb model,of which the nearest-neighbor interaction is ferromagnetic(FM) and the diagonal next-nearest-neighbor interaction is antiferromagnetic(AF).The ground state energy and the total spin are analyzed.When α≤0.25,the ground states are simply FM.With the diagonal AF frustration increasing,the ground state transforms from FM state to a canted state region,and then to the S=0 AF state.Differently in the mixed ladder model,the ground state directly transforms from FM state to AF state.By using exact diagonalization method and density matrix renormalization group method,the author studies the ground states of the two-leg spin-1/2 mixed comb model,of which the nearest-neighbor interaction is ferromagnetic(FM) and the diagonal next-nearest-neighbor interaction is antiferromagnetic(AF).The ground state energy and the total spin are analyzed.When α≤0.25,the ground states are simply FM.With the diagonal AF frustration increasing,the ground state transforms from FM state to a canted state region,and then to the S=0 AF state.Differently in the mixed ladder model,the ground state directly transforms from FM state to AF state.

Journal of Yangzhou UniversityJan 1, 20120 citations

A model for an antiferromagnet

A.S. De Vries, Ger Vertogen, Jan Kraak

PhysicaFeb 1, 19738 citations

Antiferromagnetic chain

Harold Falk, Th.W. Ruijgrok

PhysicaJul 1, 19613 citations

Ground State Phase Transition in S=1 Distorted Kagomé Heisenberg Antiferromagnets

Kazuo Hida

The ground state phase transition in the distorted S=1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of the perturbational calculation and numerical exact diagonalization method. For strong $\sqrt{3} \times \sqrt{3}$ lattice distortion, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and new singlet state, large HSS (LHSS) state, which is globally different from the HSS state is realized. The quantum phase transition between these two singlet states is analogous to the Haldane-dimer transition in the S=1 antiferromagnetic Heisenberg chain. The presence of this transition supports the validity of the HSS picture of the ground state of the uniform S=1 KHAF.The ground state phase transition in the distorted S=1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of the perturbational calculation and numerical exact diagonalization method. For strong $\sqrt{3} \times \sqrt{3}$ lattice distortion, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and new singlet state, large HSS (LHSS) state, which is globally different from the HSS state is realized. The quantum phase transition between these two singlet states is analogous to the Haldane-dimer transition in the S=1 antiferromagnetic Heisenberg chain. The presence of this transition supports the validity of the HSS picture of the ground state of the uniform S=1 KHAF.

arXiv:cond-mat/0106293Journal of the Physical Society of JapanApr 1, 20023 citations

Ground States of the Antiferromagnetic Heisenberg Chains

Hal Tasaki

Graduate texts in physicsJan 1, 20200 citations

Existence of Long-Range Magnetic Order in the Ground State of Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets

Martin Indergand, Manfred Sigrist

We give a rigorous proof of the existence of long-range antiferromagnetic order in the ground state of several two-dimensional spin-1/2 Heisenberg systems.Three types of systems are considered.The first type consists of an even number, N , of coupled square lattices with antiferromagnetic nearest-neighbor Heisenberg interactions.In this case, we prove the existence of long-range order (LRO) in the ground state for an interplane to inplane coupling ratio r in the range 0.16 ≤ r ≤ 2.1 for N ≥ 4. Further, we prove that the antiferromagnetic bilayer with ferromagnetic next-nearest-neighbor (nnn) interplane couplings possesses LRO in the ground state for 0.21 ≤ r < 1/4, where r is the absolute value of the ratio of the ferromagnetic and antiferromagnetic couplings.The final example consists of two antiferromagnetic spin-1/2 square lattices that are coupled via an antiferromagnetic nnn interplane coupling r.For r = 1, this system is effectively a spin-1 square lattice and has an ordered ground state.We show that LRO exists in the region 0.85 ≤ r ≤ 1. * ) Note that E r q in the notation of KLS corresponds to 2 + r -E q in our notation.We give a rigorous proof of the existence of long-range antiferromagnetic order in the ground state of several two-dimensional spin-1/2 Heisenberg systems.Three types of systems are considered.The first type consists of an even number, N , of coupled square lattices with antiferromagnetic nearest-neighbor Heisenberg interactions.In this case, we prove the existence of long-range order (LRO) in the ground state for an interplane to inplane coupling ratio r in the range 0.16 ≤ r ≤ 2.1 for N ≥ 4. Further, we prove that the antiferromagnetic bilayer with ferromagnetic next-nearest-neighbor (nnn) interplane couplings possesses LRO in the ground state for 0.21 ≤ r < 1/4, where r is the absolute value of the ratio of the ferromagnetic and antiferromagnetic couplings.The final example consists of two antiferromagnetic spin-1/2 square lattices that are coupled via an antiferromagnetic nnn interplane coupling r.For r = 1, this system is effectively a spin-1 square lattice and has an ordered ground state.We show that LRO exists in the region 0.85 ≤ r ≤ 1. * ) Note that E r q in the notation of KLS corresponds to 2 + r -E q in our notation.

Progress of Theoretical PhysicsJan 1, 20072 citations

\sqrt{3} \times \sqrt{3}

lattice distortion, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and new singlet state, large HSS (LHSS) state, which is globally different from the HSS state is realized. The quantum phase transition between these two singlet states is analogous to the Haldane-dimer transition in the S=1 antiferromagnetic Heisenberg chain. The presence of this transition supports the validity of the HSS picture of the ground state of the uniform S=1 KHAF.