Abstract
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.
Highlights
Entanglement forces us to abandon the classical concept about locality [1] [2] [3]
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
We find that two kinds of spin correlation functions due to degenerate states are not zero when the lattice size is large but finite
Summary
Entanglement forces us to abandon the classical concept about locality [1] [2] [3]. there are many criticisms of abandoning the concept [4], experiments strongly support entanglement required by quantum mechanics [5]. In the previous paper [25], we have investigated the cluster property of spin 1/2 XXZ antiferromagnet on the square lattice For this antiferromagnet, the ground state realizes semi-classical Neel order [26], in other words, spontaneous symmetry breaking (SSB) [17] [27] of U(1) symmetry [28] [29] [30] [31] [32]. We will consider the Hamiltonian Heff ,V ≡ Heff +V1 +V2 and calculate the spin correlation functions due to the quasi-degenerate states We conclude that these functions violate the cluster property in Heisenberg antiferromagnet and their magnitudes are much larger than the largest magnitude in XXZ model.
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