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Physical Review C

Quantum phase transition in the U(4) vibron model and the E(3) symmetry

Yu Zhang, Zhanfeng Hou, Huan Chen, Haiqing Wei, Yu‐xin Liu

Published Aug 25, 2008• 26 citations
Publisher

Abstract

We study the details of the U(3)--O(4) quantum phase transition in the U(4) vibron model. Both asymptotic analysis in the classical limit and rigorous calculations for finite boson number systems indicate that a second-order phase transition is still there even for the systems with boson number $N$ ranging from tens to hundreds. Two kinds of effective order parameters, including $E1$ transition ratios $B(E1:{2}_{1}\ensuremath{\rightarrow}{1}_{1})/B(E1:{1}_{1}\ensuremath{\rightarrow}{0}_{1})$ and $B(E1:{0}_{2}\ensuremath{\rightarrow}{1}_{1})/B(E1:{1}_{1}\ensuremath{\rightarrow}{0}_{1})$, and the energy ratios ${E}_{{2}_{1}}/{E}_{{0}_{2}}$ and ${E}_{{3}_{1}}/{E}_{{0}_{2}}$ are proposed to identify the second-order phase transition in experiments. We also found that the critical point of phase transition can be approximately described by the E(3) symmetry, which persists even for moderate $N~10$ protected by the scaling behaviors of quantities at the critical point. In addition, a possible empirical example exhibiting roughly the E(3) symmetry is discussed.

DOI
10.1103/physrevc.78.024314

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