Abstract
Spontaneous break down of translational invariance along the Matsubara time axis in a fermionic system is predicted and investigated using an exactly solvable model in analytical form. The broken symmetry state possesses discrete translational invariance along the Matsubara time axis and is characterized by the quantum order parameter (QOP) formed by condensed collective bosonic degrees of freedom of interacting fermions. The QOP’s Green’s function is finite and periodic along the Matsubara axis, but Wick-rotated to the axis of real frequencies it reveals a periodic “chain” of second order poles. Hence, QOP is not dissipative and, therefore, is “invisible” having a zero scattering cross section. Despite this, QOP changes measurable fermionic properties: instead of Landau quasi-particles with Fermi-velocity, there appear light-mass coherent fermionic states in the narrow vicinity of the Fermi-level, surrounded with overdamped states region (“pseudo-gap”) of a width proportional to QOP amplitude. Relevance of the picture to high-T c “hidden order” and pseudo-gap state is discussed.
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