Ground-State Phase Diagram of the 1D t-J model

TL;DR

This paper maps the ground-state phase diagram of the 1D t-J model using DMRG, revealing various phases including Luttinger liquids, spin-gap, and phase separation, and clarifies discrepancies between different theoretical approaches.

Contribution

It provides a detailed phase diagram of the 1D t-J model, resolving conflicts between variational and RG results, and highlights the potential observability of preformed pairs at low fillings.

Findings

Identification of phase boundaries using correlation functions and energy gaps

Resolution of the discrepancy between variational and RG results on the spin-gap extent

Observation that the spin gap can be sizable (~0.1 t) at low fillings

Abstract

We examine the ground-state phase diagram of the t-J model in one dimension by means of the Density Matrix Renormalization Group. This model is characterized by a rich phase diagram as a function of the exchange interaction J and the density n, displaying Luttinger-liquid (LL) behavior both of repulsive and attractive (i.e. superconducting) nature, a spin-gap phase, and phase-separation. The phase boundaries separating the repulsive from the attractive LL phase as J is increased, and also the boundaries of the spin-gap region at low densities, and phase-separation at even larger J, are determined on the basis of correlation functions and energy-gaps. In particular, we shed light on a contradiction between variational and renormalization-group (RG) results about the extent of the spin-gap phase, that results larger than the variational but smaller than the RG one. Furthermore, we show that the spin gap can reach a sizable value (~ 0.1 t) at low enough filling, such that preformed pairs should be observable at temperatures below these energy scales. No evidence for a phase with clustering of more than two particles is found on approaching phase separation.