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

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 exactly 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”.Accepted manuscrip

Spectral function of the U→∞U \rightarrow \infty one dimensional Hubbard model at finite temperature and the crossover to the spin incoherent regime

The physics of the strongly interacting Hubbard chain (with $t/U \ll 1$) at finite temperatures undergoes a crossover to a spin incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective "spin temperature". We use the time-dependent density matrix renormalization group method (tDMRG) to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by $k_F$ of the minimum of the dispersion.Comment: 4+pages, 3 fig