Dionys Baeriswyl, Département de physique, Université de Fribourg
Variational wave functions are very useful for describing the panoply of ground states found in interacting many-electron systems. Some particular trial states are "adiabatically'' linked to a reference state, from which they borrow the essential properties. A prominent example is the Gutzwiller ansatz consisting of an appropriate operator acting on the filled Fermi sea. A simple soluble example, the anisotropic XY chain, illustrates the adiabatic continuity of this class of wave functions [1]. While the exact solution exhibits a phase transition for infinitesimal anisotropy (with a diverging ground state fidelity susceptibility), a Gutzwiller-type ansatz does not lead to an instability of the symmetric phase (nor to a divergent fidelity susceptibility). To describe symmetry breaking, one has to modify the reference state accordingly, for instance by acting on a mean-field ground state of the BCS form [2]. Alternatively, a quantum phase transition can be described by a pair of variational wave functions, starting at weak and strong coupling, respectively.
[1] D. Baeriswyl, to appear in Ann. Phys. (Berlin) 19 (2011).
[2] A recent discussion of this approach for the two-dimensional Hubbard model can be found in D. Baeriswyl, D. Eichenberger and M. Menteshashvili, New J. Phys. 11, 075010 (2009).