Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath

Mohammad Soltanieh-ha and Adrian E. Feiguin
Phys. Rev. B 86, 205120 – Published 19 November 2012

Abstract

Interacting one-dimensional electron systems are generally referred to as “Luttinger liquids,” after the effective low-energy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The “spin-incoherent Luttinger liquid” describes a finite-temperature 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 spin-incoherent 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 tJ-Kondo 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.”

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  • Received 18 July 2012

DOI:https://doi.org/10.1103/PhysRevB.86.205120

©2012 American Physical Society

Authors & Affiliations

Mohammad Soltanieh-ha and Adrian E. Feiguin

  • Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

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Issue

Vol. 86, Iss. 20 — 15 November 2012

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