Superconductivity in the doped $t$-$J$ model: results for four-leg cylinders

TL;DR

This study uses density-matrix renormalization group methods to analyze the lightly doped $t$-$J$ model on a four-leg cylinder, revealing coexistence of superconductivity and density-wave orders consistent with a Luther-Emery liquid.

Contribution

First detailed DMRG analysis of the doped $t$-$J$ model on a 4-leg cylinder showing power-law superconducting correlations in a nearly 2D system.

Findings

Power-law superconducting correlations observed.

Charge-density-wave correlations with wavelength inversely proportional to doping.

System exhibits characteristics of a Luther-Emery liquid.

Abstract

We report a density-matrix renormalization group study of the lightly doped $t$-$J$ model on a 4-leg cylinder with doped hole concentrations per site $\delta=5\%\sim 12.5\%$. By keeping an unusually large number of states and long system sizes, we are able to accurately document the interplay between d-wave superconductivity (SC) and spin and charge-density-wave (CDW) orders. The long-distance behavior is consistent with that of a Luther-Emery liquid with a spin-gap, power-law CDW correlations with wave-length $\lambda =1/2\delta$, and power-law SC correlations. This is the widest (most nearly 2D) such system for which power law SC correlations have been established.