A useful way to obtain the central charge of entanglement Hamiltonian -- Nested entanglement entropy

In this paper, we review how to obtain the central charge of a critical entanglement Hamiltonian through the nested entanglement entropy which was first introduced in [J. Lou et al. PRB 84, 245128 (2011)]. The critical phenomena of the entanglement Hamiltonian can be identified by the central charge obtained by the nested entanglement entropy. We review our previous studies[J. Lou et al. PRB 84, 245128 (2011), S. Tanaka et al. PRA 87, 214401 (2013)] in which we investigated certain entanglement nature of two-dimensional valence-bond-solid (VBS) state and quantum hard-square models on square and triangle ladders using the nested entanglement entropy.Comment: 5 pages, 3 figures, to appear in Interdisciplinary Information Science

Dynamical properties of temperature chaos and memory effect

In the frustrated interaction systems, the nature of ordered configuration can be intrinsically temperature dependent. There, the idea of effective coupling of decorated and frustrated bond plays an important role. The idea of effective coupling is verified in the study of equilibrium properties. We will study how the effective coupling is realized in the dynamical processes, e.g. the relaxation time after a change of temperature. We also study the memory phenomena which have been found in the spin glass.Comment: 4pages, 3figures, Proceedings of SPDSA200

A Method to Change Phase Transition Nature -- Toward Annealing Method --

In this paper, we review a way to change nature of phase transition with annealing methods in mind. Annealing methods are regarded as a general technique to solve optimization problems efficiently. In annealing methods, we introduce a controllable parameter which represents a kind of fluctuation and decrease the parameter gradually. Annealing methods face with a difficulty when a phase transition point exists during the protocol. Then, it is important to develop a method to avoid the phase transition by introducing a new type of fluctuation. By taking the Potts model for instance, we review a way to change the phase transition nature. Although the method described in this paper does not succeed to avoid the phase transition, we believe that the concept of the method will be useful for optimization problems.Comment: 27 pages, 3 figures, revised version will appear in proceedings of Kinki University Quantum Computing Series Vo.

Quantum Annealing Effect on Entropic Slowing Down in Frustrated Decorated Bond System

We propose that the importance of the quantum annealing procedure to find the ground state of frustrated decorated bond systems where 'entropic slowing down' happens due to peculiar density of states. Here, we use the time dependent Schr\"odinger equation to analyze the real time dynamics of the process. It is found that the quantum annealing is very efficient comparing to the thermal annealing for searching the ground state of the systems. We analyze the mechanism of quantum annealing from a view point of adiabatic process.Comment: 2 pages, 4 figures, proceedings of ICM200