Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far...Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.展开更多
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...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.展开更多
文摘Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.
文摘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.
