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arXiv:cond-mat/0209493

Geometry and topological order in the non-relativistic Luttinger liquid

H. V. Kruis, Ian P. McCulloch, Zohar Nussinov, Jan Zaanen

Published Sep 20, 2002• 0 citations
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Abstract

We demonstrate that the notion of spin-charge separation as follows from the Tomonaga-Luttinger theory of relativistic fermions does not suffice to completely specify the Luttinger liquid state associated with the fermions of condensed matter physics. The latter carries in addition a form of topological order which can be made visible using non-local correlation functions familiar from lattice gauge theory.

DOI
10.48550/arxiv.cond-mat/0209493

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We demonstrate that the notion of spin-charge separation as follows from the Tomonaga-Luttinger theory of relativistic fermions does not suffice to completely specify the Luttinger liquid state associated with the fermions of condensed matter physics. The latter carries in addition a form of topological order which can be made visible using non-local correlation functions familiar from lattice gauge theory.
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We demonstrate that in the scaling limit the phenomenon of spin-charge separation as encountered in Luttinger liquids defined on the lattice can be associated with the emergence of local Ising symmetry. This Z_2 gauge field is of geometrical nature (sublattice parity) and the Luttinger liquid corresponds with the critical point where the symmetry is on the verge of becoming local. We argue that in a true one dimensional superconductor the local symmetry will be fully realized as long as the geometrical structure associated with spin-charge separation is maintained.
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We discuss certain physical contents of the two-dimensional Luttinger liquid state using the spin and charge current backflow in strongly correlated electron systems. Also we attempt a description of the Luttinger liquid state in the slave boson formalism. Conventional slave boson mean field theory does not possess an important property expected of a Luttinger liquid, namely a pseudo fermi surface for holons. This arises from the bose condensation of holes. We attempt to rectify this by discussing the physics of the fermionic backflow associated with the hole motion. We argue that the fermionic backflow suppresses the Bose condensation. To understand this we introduce the notion of ‘Statistics Transfer’-the medium transfer certain statistics to the slave particle (e's). A variational wave function in which boson condensation is manifestly absent is introduced. The form of the wave function is justified by the concept of statistics transfer. The spinon and holon excitations both exhibiting pseudo fermi surfaces are constructed.