Yang-Lee の凝縮理論に対する注意

泰弘 阿久津

Xianzhi Wang

The Yang-Lee zeros of an antiferromagnetic Heisenberg ladder model are determined. It is found that if J4≤0 Yang-Lee zeros are located on the unit circle and on the negative real axis in the complex activity plane. In particular, if J4≤0 and 2J2≥J4, Yang-Lee zeros are located on the unit circle and the Yang-Lee circle theorem is valid. If J4>0, Yang-Lee zeros are located on some complicated curves.

Liang-Jun Zhai, Guang-Yao Huang, Huai‐Yu Wang

The quantum phase transition of a one-dimensional transverse field Ising model in an imaginary longitudinal field is studied. A new order parameter M is introduced to describe the critical behaviors in the Yang-Lee edge singularity (YLES). The M does not diverge at the YLES point, a behavior different from other usual parameters. We term this unusual critical behavior around YLES as the pseudo-YLES. To investigate the static and driven dynamics of M, the (1+1) dimensional ferromagnetic-paramagnetic phase transition ((1+1) D FPPT) critical region, (0+1) D YLES critical region and the (1+1) D YLES critical region of the model are selected. Our numerical study shows that the (1+1) D FPPT scaling theory, the (0+1) D YLES scaling theory and (1+1) D YLES scaling theory are applicable to describe the critical behaviors of M, demonstrating that M could be a good indicator to detect the phase transition around YLES. Since M has finite value around YLES, it is expected that M could be quantitatively measured in experiments.

三樹 和達, 清 十河, 守 打波 +1 more

Hong Ge Tao, Yuguo Su, Xingyu Zhang +2 more

The distribution of Lee-Yang zeros not only matters in thermodynamics and quantum mechanics, but also in mathematics. Hereby we propose a nonlinear quantum toy model and discuss the distribution of corresponding Lee-Yang zeros. Utilizing the coupling between a probe qubit and the nonlinear system, all Lee-Yang zeros can be detected in the dynamics of the probe qubit by tuning the coupling strength and linear coefficient of the nonlinear system. Moreover, the analytical expression of the quantum Fisher information matrix at the Lee-Yang zeros is provided and an interesting phenomenon is discovered. Both the coupling strength and temperature can simultaneously attain their precision limits at the Lee-Yang zeros. However, the probe qubit cannot work as a thermometer at a Lee-Yang zero if it sits on the unit circle.

Miki Wadati, Kiyoshi Sogo, M. Uchinami +1 more