Local broken symmetry and spin transport in frustrated Heisenberg model in low dimension*

The local spontaneous symmetry breaking is a general phenomena in condensed matter physics. It is characterized by the fact that the action has a local symmetry but the quantum theory, instead of having a unique vacuum state which respects this symmetry, has a family of degenerate vacua that transform into each other under the action of the symmetry group. A simple example is given by a ferromagnetic model in which the action governing its microscopic dynamics is invariant under spatial rotations. A kind of local gauge invariance or spontaneous breaking of U(1) gauge symmetry is realized in nature in the phenomenon of superconductivity.
We have proposed a Meissner mechanism for the spin transport in quantum spin systems. Besides, we study the behavior of the AC spin conductivity in the neighborhood of a quantum phase transition in a frustrated spin model such as the antiferromagnet in the compass lattice with single ion anisotropy at T = 0 .