Quantum phase transitions

We applied the Liouville-von Neumann (LvN) method, a canonical method, to nonequilibrium quantum phase transitions. The essential idea of the LvN method is first to solve the LvN equation and then to find exact wave functionals of time-dependent quantum systems. The LvN method has several advantages that it can easily incorporate thermal theory in terms of density operators and that it can also be extended to thermofield dynamics (TFD) by using the time-dependent creation and annihilation operators, invariant operators. Combined with the oscillator representation, the LvN method provides the Fock space of a Hartree-Fock type quadratic part of the Hamiltonian, and further allows to improve wave functionals systematically either by the Green function or perturbation technique. In this sense the LvN method goes beyond the Hartree-Fock approximation. 

For 7=1 the Hamiltonian reduces to the Ising model and for y = 0 to the XY model. For the pure homogeneous case, /,, +i = / and = B, the system exhibits a quantum phase transition at a dimensionless coupling constant... 

Dimensional scaling theory [109] provides a natural means to examine electron-electron correlation, quantum phase transitions [110], and entanglement. The primary effect of electron correlation in the D 00 limit is to open up the dihedral angles from their Hartree-Fock values [109] of exactly 90°. Angles in the correlated solution are determined by the balance between centrifugal effects, which always favor 90°, and interelectron repulsions, which always favor 180°. Since the electrons are localized at the D 00 limit, one might need to add the first harmonic correction in the 1/D expansion to obtain... 

S. Sachdev, Quantum Phase Transitions, Cambridge University lYess, Cambridge, 1999. 

V. QUANTUM PHASE TRANSITIONS AND STABILITY OF ATOMIC AND MOLECULAR SYSTEMS... 

The stability of three-body Coulomb systems is an old problem which has been treated in many particular cases [143-145] and several authors reviewed this problem [146,147]. For example, the He atom (ae e ) and H2 (ppa ) are stable systems, H (pe e ) has only one bound state [108], and the positronium negative ion Ps (e+e e ) has a bound state [148], while the positron-hydrogen system (e pe+) is unbound and the proton-electron-negative-muon pe i ) is an unstable system [149]. In this section, we show that all three-body ABA Coulomb systems undergo a first-order quantum phase transition from the stable phase of ABA to the unstable breakup phase of AB + A as their masses and charges varies. Using the FSS method, we calculate the transition line that... 

Let us consider the stability and quantum phase transitions of the three-body ABA Hamiltonian given by Eq. (36). The Hamiltonian, Eq. (36), formally separated the motion of the center of mass and depends linearly on the parameters X and k. 

The field of quantum critical phenomena in atomic and molecular physics is still in its infancy and there are many open questions about the interpretations of the results, including whether or not these quantum phase transitions really do exist. The possibility of exploring these phenomena experimentally in the... 

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