Tunneling density of states in a Y junction of Tomonaga-Luttinger liquid wires: A density matrix renormalization group study

TL;DR

This study uses DMRG to investigate the tunneling density of states in a symmetric Y junction of Tomonaga-Luttinger liquid wires, revealing anomalous enhancements near the junction for certain interaction strengths and identifying distinct fixed points.

Contribution

It provides the first DMRG analysis of TDOS in a Y junction of TLL wires, uncovering anomalous enhancements and fixed point behaviors for different interaction parameters.

Findings

TDOS is anomalously enhanced near the junction for g>1

Suppression of TDOS occurs for g<1 in both bosonic and fermionic cases

Enhancement follows different power laws for bosons and fermions, indicating distinct fixed points

Abstract

It is well known that the pristine bulk of an interacting one-dimensional system in Tomonaga-Luttinger liquid (TLL) phase shows power law suppression of quasi-particle tunneling amplitude for all values of TLL parameter $g$, in the zero energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting bosons case and (b) interacting fermions case, when $g>1$. We also observe suppression of TDOS for $g<1$ for both bosonic and fermionic cases. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points, owing to statistical correlations which play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fixed point for $1<g<3$ resembles the mysterious $M$ fixed point of Y junction predicted by Oshikawa, Chamon, and Affleck [J. Stat. Mech. P02008 (2006)]. We also show that the TDOS enhancement spans over a length scale of $\propto \omega^{-1}$ from the junction, for $1<g<3$.