There are concepts that are accepted in our daily life, but are not trivial in physics.One of them is the cluster property that means there exist no relations between two events which are sufficiently separated.In a paper recently published by the author, it has been pointed out that this cluster property violates in the correlation function of the spin operator for the spin 1/2 XXZ antiferromagnet on the square lattice.In this paper, we investigate the spin 1/2 Heisenberg antiferromagnet on the square lattice, which has SU(2) symmetry.In order to study the cluster property, we need to calculate the ground state accurately.For this purpose, we employ the effective model based on the magnetization of the sub-lattices.Then we can define the quasi-degenerate states to calculate the ground state.Including two kinds of interactions which break SU(2) symmetry into the Hamiltonian, we obtain the ground state quantitatively.We find that two kinds of spin correlation functions due to degenerate states are not zero when the lattice size is large but finite.The magnitude of one of them is the same as the one previously found in the XXZ antiferromagnet, while another one is much larger when the additional interaction is strong.We then conclude that in Heisenberg antiferromagnet correlation functions violate the cluster property and the magnitude of the violation qualitatively differs from the one in the XXZ antiferromagnet.There are concepts that are accepted in our daily life, but are not trivial in physics.One of them is the cluster property that means there exist no relations between two events which are sufficiently separated.In a paper recently published by the author, it has been pointed out that this cluster property violates in the correlation function of the spin operator for the spin 1/2 XXZ antiferromagnet on the square lattice.In this paper, we investigate the spin 1/2 Heisenberg antiferromagnet on the square lattice, which has SU(2) symmetry.In order to study the cluster property, we need to calculate the ground state accurately.For this purpose, we employ the effective model based on the magnetization of the sub-lattices.Then we can define the quasi-degenerate states to calculate the ground state.Including two kinds of interactions which break SU(2) symmetry into the Hamiltonian, we obtain the ground state quantitatively.We find that two kinds of spin correlation functions due to degenerate states are not zero when the lattice size is large but finite.The magnitude of one of them is the same as the one previously found in the XXZ antiferromagnet, while another one is much larger when the additional interaction is strong.We then conclude that in Heisenberg antiferromagnet correlation functions violate the cluster property and the magnitude of the violation qualitatively differs from the one in the XXZ antiferromagnet.

World Journal of Condensed Matter PhysicsJan 1, 20183 citations

Vacancy-induced spin texture in a one-dimensional S=12 Heisenberg antiferromagnet

Sambuddha Sanyal, Argha Banerjee, Kedar Damle

We study the effect of a missing spin in a one-dimensional $S=1/2$ antiferromagnet with nearest-neighbor Heisenberg exchange $J$ and six-spin coupling $Q=4qJ$ using quantum Monte-Carlo (QMC) and bosonization techniques. For $q<{q}_{c}\ensuremath{\approx}0.04$, the system is in a quasilong range ordered power-law antiferromagnetic phase, which gives way to a valence-bond solid state that spontaneously breaks lattice translation symmetry for $q>{q}_{c}$ . We study the ground-state spin texture $\ensuremath{\Phi}(r)=\ensuremath{\langle}{G}_{\ensuremath{\uparrow}}|{S}^{z}(r)|{G}_{\ensuremath{\uparrow}}\ensuremath{\rangle}$ in the the ${S}_{\text{tot}}^{z}=1/2$ ground state $|{G}_{\ensuremath{\uparrow}}\ensuremath{\rangle}$ of the system with a missing spin, focusing on the alternating part ${N}_{z}(r)$ . We find that our QMC results for ${N}_{z}$ at $q={q}_{c}$ take on the scaling form expected from bosonization considerations, but violate scaling for $q<{q}_{c}$ . Within the bosonization approach, such violations of scaling arise from the presence of a marginally irrelevant sine-Gordon interaction, whose effects we calculate using renormalization group (RG) improved perturbation theory. Our field-theoretical predictions are found to agree well with the QMC data for $q<{q}_{c}$ .We study the effect of a missing spin in a one-dimensional $S=1/2$ antiferromagnet with nearest-neighbor Heisenberg exchange $J$ and six-spin coupling $Q=4qJ$ using quantum Monte-Carlo (QMC) and bosonization techniques. For $q<{q}_{c}\ensuremath{\approx}0.04$, the system is in a quasilong range ordered power-law antiferromagnetic phase, which gives way to a valence-bond solid state that spontaneously breaks lattice translation symmetry for $q>{q}_{c}$. We study the ground-state spin texture $\ensuremath{\Phi}(r)=\ensuremath{\langle}{G}_{\ensuremath{\uparrow}}|{S}^{z}(r)|{G}_{\ensuremath{\uparrow}}\ensuremath{\rangle}$ in the the ${S}_{\text{tot}}^{z}=1/2$ ground state $|{G}_{\ensuremath{\uparrow}}\ensuremath{\rangle}$ of the system with a missing spin, focusing on the alternating part ${N}_{z}(r)$. We find that our QMC results for ${N}_{z}$ at $q={q}_{c}$ take on the scaling form expected from bosonization considerations, but violate scaling for $q<{q}_{c}$. Within the bosonization approach, such violations of scaling arise from the presence of a marginally irrelevant sine-Gordon interaction, whose effects we calculate using renormalization group (RG) improved perturbation theory. Our field-theoretical predictions are found to agree well with the QMC data for $q<{q}_{c}$.

arXiv:1107.1493Physical Review BDec 21, 201123 citations

Scaling in the disordered quantum antiferromagnetic chain

J. Chalupa

Solid State CommunicationsMay 1, 19811 citation

Excitations in the antiferromagnetic Heisenberg chain

András Sütö, P. Fazekas

Springer eBooksOct 29, 20052 citations

Scaling theory of antiferromagnetic Heisenberg ladder models

Naomichi Hatano, Y Nishiyama

The S=1/2 antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as Delta E approximately J perpendicular to , where J perpendicular to is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge c=1 extends over the whole region of J perpendicular to >0.The S=1/2 antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as Delta E approximately J perpendicular to , where J perpendicular to is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge c=1 extends over the whole region of J perpendicular to >0.

arXiv:cond-mat/9506052Journal of Physics A Mathematical and GeneralJul 21, 199521 citations

We study the effect of a missing spin in a one-dimensional

S=1/2

antiferromagnet with nearest-neighbor Heisenberg exchange

J

and six-spin coupling

Q=4qJ

using quantum Monte-Carlo (QMC) and bosonization techniques. For $q<{q}_{c}\ensuremath{\approx}0.04$, the system is in a quasilong range ordered power-law antiferromagnetic phase, which gives way to a valence-bond solid state that spontaneously breaks lattice translation symmetry for

q>{q}_{c}

. We study the ground-state spin texture $\ensuremath{\Phi}(r)=\ensuremath{\langle}{G}_{\ensuremath{\uparrow}}|{S}^{z}(r)|{G}_{\ensuremath{\uparrow}}\ensuremath{\rangle}$ in the the

{S}_{\text{tot}}^{z}=1/2

ground state $|{G}_{\ensuremath{\uparrow}}\ensuremath{\rangle}$ of the system with a missing spin, focusing on the alternating part

{N}_{z}(r)

. We find that our QMC results for

{N}_{z}

q={q}_{c}

take on the scaling form expected from bosonization considerations, but violate scaling for

q<{q}_{c}

. Within the bosonization approach, such violations of scaling arise from the presence of a marginally irrelevant sine-Gordon interaction, whose effects we calculate using renormalization group (RG) improved perturbation theory. Our field-theoretical predictions are found to agree well with the QMC data for

q<{q}_{c}