RAPID COMMUNICATIONS PHYSICAL REVIEW A 78. 051801(R)(2008) Numerically exact solution to the finite- size dicke mod Qing-Hu Chen, Yu-Yu Zhang, Tao Liu, and Ke-Lin Wang 4 Center for Statistical and Theoretical Condensed Matter Physics, Zhejiang Normal University, Jinhua 321004, China Department of Physics, Zhejiang University, Hangzhou 310027, China Department of Physics, Southwest University of Science and Technology, Mianyang 621010, China Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China (Received 26 December 2007: published 3 November 2008) RAPID COMMUNICATIONS PHYSICAL REVIEW B 81. 121105(R)(2010) Quantum phase transition in the sub-Ohmic spin-boson model: An extended coherent-state approach Yu-Yu Zhang, Qing-Hu Chen, 2.1, and Ke-Lin Wang.4 Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China -Center for Statistical and Theoretical Condensed Matter Physics, Zhejiang Normal University, Jinhua 321004 People's Republic of china Department of Physics, Southwest University of Science and Technology, Mianyang 621010, People's Republic of China Department of Modern Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China (Received 27 January 2010; revised manuscript received 14 February 2010: published 26 March 2010