Berry phase and entanglement in the icosahedralH⊗(g⊕2h)Jahn-Teller system with trigonal minima

Abstract

The H ͑g 2h͒ Jahn-Teller problem in the trigonal regime offers an example of a dynamic ground-state crossover from a degenerate to a singlet state. This crossover is connected to a change in tunneling paths which results in a loss of Berry phase. Previous studies tried to explain the entanglement which lies at the basis of this phenomenon using two-dimensional ͑2D͒ cuts through coordinate space but have reached opposite interpretations. In this paper we introduce a method which scans the topology of the full coordinate space using a net of triangular cross sections between the ten D 3d minima. It is shown that the Berry phase of every loop on the potential energy hypersurface can be expressed in terms of these 2D triangular cross sections. Using this method we show that the absence of Berry phase for the cycles containing five trigonal wells originates from two seams of conical intersections going through these cycles. The connection between this analysis and previous treatments is established and the apparent dilemma of interpretation is resolved.

Adiabatic approximation and related issues including topological implications

“…In this case too, only two adiabaticsheets of the fivefold manifold are predicted to manifest GP: case(2,3). Such a result seem at first to contradict existing evidence on the nature of the dynamic ground state adiabatic PES, which has been examined in detail[47,139,140].In fact, the JT effect of the icosahedral quintuplet term in the trigonal regime shows an intriguing crossover of dynamic states from a degenerate to a singlet state, with coupling strength showing an apparent correlation with the phase of the tunneling paths through such minima. At stronger coupling the dominant tunneling process is believed to consist of closed loops spanning cycles of five wells, with a vanishing GP associated with these loops.…”

“…Belonging to the symmetry group [11] SO (5) In line with the other JT problems, use will then be made of the rotation matrix [47], who have scanned the topology of the full coordinate space using a net of triangular cross sections between the ten D 3d minima. By expressing the GP of every loop on the PES in terms of such 2D triangular cross sections, they have found [47] that the absence of GP for the cycles containing five trigonal wells originates from two seams of conical intersections going through these cycles. Suffice it to note that the absence of GP effect on the adiabatic ground state PES does not invalidate our prediction that only two sheets of the fivefold electronic manifold manifest GP.…”

“…Indeed, it is a task that we did not even complete in the 4D and 5D phase spaces of the subsystems G ⊗ g and G ⊗ h." In 1998, Manini and De los Rios [28] and, more recently, Lijnen and Ceulemans [47] investigated the GP effect on the manifold of JT potential minima ( JTM) of such species. Other developments are due to Manolopoulos and Child [43] who have utilized a model Hamiltonian to investigate the possible sign changes that can occur when N real quantum states are transported adiabatically around a N -fold electronic degeneracy.…”

Vibronic coupling in the icosahedralC602+Jahn-Teller cation: Repercussions of the nonsimple reducibility of theH⊗HHands1, Dunn2, Diery3 et al. 2006Phys. Rev. B11070View full textAdd to dashboardCite

“…The JT effects in these systems are interesting because the icosahedral symmetry results in high electronic and vibrational degeneracies, 4 with additional complications arising due to the nonsimple reducibility of the H representation. 5,6 In this paper, we will concentrate on JT effects in the C 60 2+ cation, in which coupling between the two holes of H u symmetry to eight vibrational modes of h g symmetry is taken into account. The holes also couple to two a g modes and six g g modes, but it has been shown that these modes do not result in any significant distortions 7 so they will not be considered here.…”

Vibronic Ground-State Degeneracies and the Berry Phase: A Continuous Symmetry Perspective

“…Vibronic ground-state degeneracy (VGSD) in JT models appears frequently when linear vibronic couplings dominate [10,11] (for a recent proposal of direct noninterferometric experimental verification of VGSD, see e.g., [15,16]), although there are exceptions [17][18][19][20]. More specifically, there exists a particular class of JT models for which VGSD is guaranteed to exist whenever the adiabatic approximation (Born-Oppenheimer [21] with inclusion of Berry phase effects [22,23]) is valid [10,11,24].…”