Coherent state path‐integral representation of supersymmetric lattice models

Abstract

A kind of high‐temperature superconductivity related lattice model is investigated within the framework of supergroup coherent state path‐integral representation. Symmetry properties are analyzed and the Hamiltonians are written in the symmetric form explicitly in terms of generators of the supergroup U(N/M). By a standard approach, general supergroup coherent states are constructed. Holstein–Primakoff realizations of the supergroup U(N/M) on the coset space U(N/M)/[U(1)⊗U(N−1/M)] are obtained. Vacuum persistence amplitudes are expressed in terms of parameters on the coset space U(2/M)/[U(1)⊗U(1/M)]. Symmetry‐breaking terms in the Hamiltonian are taken into account separately. The Lagrangians of these models are quadratic in Grassmann variables. Thus fermionic fields can be integrated out. The nonlinear σ model is arrived at as effective continuum field theory describing the low‐energy excitations of the supersymmetric lattice models.