Violation of Cluster Property in Quantum Antiferromagnet

2020

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There are some 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 the works recently published by the author, the extensive and quantitative examination has been made about the violation of cluster property in the correlation function of the spin operator for the quantum spin system. These works have shown that, when we include the symmetry breaking interaction, the effect by the violation is proportional to the inverse of the system size. Therefore this effect is tinny since the system size is quite large. In order to find the effect due to the violation even when the size is large, we propose a new system where additional spins couple with the spin system on the square lattice, where the coupling constant between these systems being assumed to be small. Applying the perturbation theory, we obtain the effective Hamiltonian for the additional system. This Hamiltonian includes Curie-Weiss model that is induced by the violation of the cluster property. Then we find that this effective Hamiltonian has the factor which is the inverse of the system size.Since Curie-Weiss model, which is known to be exactly soluble, has to contain this factor so that the thermodynamical properties are well-defined, the essential factor for the Hamiltonian is determined by the coupling and the strength of the symmetry breaking interaction. Our conclusion is, therefore, that it is possible to observe the effect by the violation of the cluster property at the inverse temperature whose order is given by these parameters. locality, which has been extensively studied by many researchers [1] [2] [3] [4][5]. One reason for this active study is the possibility of applying entanglement to quantum computer [6] [7] and quantum information [8] [9] [10].Entanglement found in many-body systems is reviewed in [11]. Its observation was discussed in [12]. Entanglement was discussed in terms of the spontaneous symmetry breaking [13] [14] [15] because the correlation must be found even at the long distance where the whole system changes entirely from the classically ordered state to the disordered one. The work [16] discussed quantum communication when the symmetry breaks spontaneously.plicitly. The newly added interaction, ˆe x V , consists of spin operators both on the additional system and on the square lattice. It contains a parameter u to represent the strength of the interaction.Applying the perturbation theory with small u, we obtain the effective Hamil- T. Munehisa, eff ex H for the spins in the additional system. We see that it includes Curie-Weiss model. In this model, it is known that the mean field approximation for the thermodynamic properties gives the exact results. We then find that this effective Hamiltonian , eff ex H h S J S S h J J = = =

Section: Spin System On the Square Latticementioning

confidence: 99%

Section: T Munehisamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum Curie-Weiss Magnet Induced by Violation of Cluster Property

2020

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Violation of Cluster Property in Heisenberg Antiferromagnet

2018

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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.

Degenerate States in Nonlinear Sigma Model with U(1) Symmetry <sub>—For Study on Violation of Cluster Property</sub>

2021

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Entanglement in quantum theory is a concept that has confused many scientists. This concept implies that the cluster property, which means no relations between sufficiently separated two events, is non-trivial. In the works for some quantum spin systems, which have been recently published by the author, extensive and quantitative examinations were made about the violation of cluster property in the correlation function of the spin operator. The previous study of these quantum antiferromagnets showed that this violation is induced by the degenerate states in the systems where the continuous symmetry spontaneously breaks. Since this breaking is found in many materials such as the high temperature superconductors and the superfluidity, it is an important question whether we can observe the violation of the cluster property in them. As a step to answer this question we study a quantum nonlinear sigma model with U(1) symmetry in this paper. It is well known that this model, which has been derived as an effective model of the quantum spin systems, can also be applied to investigations of many materials. Notifying that the existence of the degenerate states is essential for the violation, we made numerical calculations in addition to theoretical arguments to find these states in the nonlinear sigma model. Then, successfully finding the degenerate states in the model, we came to a conclusion that there is a chance to observe the violation of cluster property in many materials to which the nonlinear sigma model applies.