Class of variational Ansätze for the spinincoherent ground state of a Luttinger liquid coupled to a spin bath
Abstract
Interacting onedimensional electron systems are generally referred to as “Luttinger liquids,” after the effective lowenergy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The “spinincoherent Luttinger liquid” describes a finitetemperature regime that is realized when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. Similar physics can take place in the ground state, when a Luttinger liquid is coupled to a spin bath, which effectively introduces a “spin temperature” through its entanglement with the spin degree of freedom. We show that the spinincoherent state can be written as a factorized wave function, with a spin wave function that can be described within a valence bond formalism. This enables us to calculate exact expressions for the momentum distribution function and the entanglement entropy. This picture holds not only for two antiferromagnetically coupled tJ chains, but also for the tJKondo chain with strongly interacting conduction electrons. We argue that this theory is quite universal and may describe a family of problems that could be dubbed “spin incoherent.”
 Publication:

Physical Review B
 Pub Date:
 November 2012
 DOI:
 10.1103/PhysRevB.86.205120
 arXiv:
 arXiv:1211.0982
 Bibcode:
 2012PhRvB..86t5120S
 Keywords:

 71.10.Pm;
 71.10.Fd;
 71.15.Qe;
 Fermions in reduced dimensions;
 Lattice fermion models;
 Excited states: methodology;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 Accepted for publication in PRB