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

TL;DR

This paper introduces a class of variational wave-functions to describe the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath, providing exact results for key physical quantities and suggesting a universal framework.

Contribution

The authors develop a variational ansatz for the spin-incoherent ground state of coupled Luttinger liquids, enabling exact calculations and broadening understanding of spin-incoherent regimes.

Findings

Factorized wave-function for spin-incoherent state

Exact expressions for momentum distribution and entanglement entropy

Applicable to multiple models including t-J and Kondo chains

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 t-J chains, but also for the t-J-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".