Adiabatic continuity and broken symmetry in many-electron systems: a variational perspective

TL;DR

This paper discusses how variational wave functions, such as the Gutzwiller ansatz, can describe ground states in many-electron systems, highlighting adiabatic continuity and symmetry breaking through a variational perspective.

Contribution

It introduces a variational framework for understanding adiabatic continuity and symmetry breaking in many-electron systems, with illustrative examples like the XY chain.

Findings

Adiabatic continuity links trial states to reference states.

Symmetry breaking requires modifying the reference state.

Quantum phase transitions can be modeled by pairs of variational wave functions.

Abstract

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, where one starts with the filled Fermi sea. A simple soluble example, the anisotropic XY chain, illustrates the adiabatic continuity of this class of wave functions. To describe symmetry breaking, one has to modify the reference state accordingly. Alternatively, a quantum phase transition can be described by a pair of variational wave functions, starting at weak and strong coupling, respectively.