Title

"Singular value decomposition picture of double Hilbert space on thermo field dynamics"

Speaker

Yoichiro Hashizume (Tokyo University of Science), Masuo Suzuki (Riken)

Abstract

We investigate the tilde space on thermo field dynamics from the view point of a singular value decomposition. As is well known, the singular value decomposition is applied to density matrix renormalization group (DMRG) methods including MERA networks. Furthermore, recently we have also clarified how to perform the singular value decomposition using such quantum information method as the quantum annealing. On the other hand, the thermo field dynamics (TFD) was introduced by Fano, Prigogine, Takahashi, and Umezawa mainly in order to connect the formulations of quantum physics and statistical physics. To achieve the aim, it was required to extend the Hilbert space, namely double-Hilbert space, which includes original and tilde spaces. This tilde space is introduced from the mathematical aspects and its physical meanings are still not clear. In the present study, we discuss the physical meanings of the tilde space by means of the singular value decompositions.

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