Signatures of quantum phase transitions and excited state quantum phase transitions in the vibrational bending dynamics of triatomic molecules

Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

“…Finally, the vibron model was also proposed by Iachello to describe the rovibrational structure of molecules [52] and the 2DVM was introduced [53] to model molecular bending dynamics (e.g., see Ref. [54] and references therein). The 2DVM is the simplest two-level model which still retains a nontrivial angular momentum quantum number and it has been used as a playground to illustrate ground state and excited state QPTs features in bosonic models [55,56].…”

A study of the bending motion in tetratomic molecules by the algebraic operator expansion method

“…36 A computer code has been written to diagonalizeĤ and used to study a variety of single benders. 21,22,47 To the HamiltonianĤ of Eq. (1) there corresponds a potential function which can be obtained by the method of coherent 38,[41][42][43][44][45][46] states.…”

“…15,16 Extensive work on the dynamics of tetratomic molecules related to both spectra and potential surfaces has been done, 15,16 especially from the point of view of "bifurcations" of normal modes. [17][18][19] This work is particularly important and relevant to the study of quantum phase transitions in tetratomic molecules, [20][21][22] which may provide a guide of how the method presented here could be extended. Also, van Vleck perturbation theory has been used in the study of the mid-size molecules 23, 24 CHF 3 and HFCO by a combination of perturbative and variational methods within the framework of the "polyad" method of Kellman et al 25,26 The algebraic expansion operator method can be viewed as a generalization of the van Vleck approach to anharmonic potentials.…”

“…For single-benders it has been used to study non-rigid molecules 28,29 and quantum phase transitions. [20][21][22] For coupled benders after the original treatment of linear molecules, 27 it was used to treat nonplanar molecules (H 2 O 2 ) by Oss and co-workers. 30,31 In recent years it has been used to provide a systematic approach 32,33 to all configurations of Fig.…”

Excited-state quantum phase transitions studied from a non-Hermitian perspective

“…This divergence in the density states at the lowest energy moves to higher energies as the control parameter increases above the QPT critical point. The energy value where the density of states peaks marks the point of the ESQPT.ESQPTs have been analyzed in various theoretical models [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and have also been observed experimentally [22][23][24][25][26][27]. They have been linked with the bifurcation phenomenon [20] and with the exceedingly slow evolution of initial states with energy close to the ESQPT critical point [18][19][20].…”