Emergent Pair Density Wave Order Across a Lifshitz Transition

TL;DR

This work investigates PDW order in the one-dimensional Kondo-Heisenberg chain using DMRG and time-dependent methods to analyze momentum- and energy-resolved spectra. It identifies a Lifshitz-like transition from a two-momentum to a four-momentum Fermi-surface topology, driven by an emergent next-nearest-neighbor hopping $t_2$ that relieves magnetic frustration, and shows that PDW features manifest as in-gap bound states and a $K_{PDW}= ext{π}$ modulation. The low-energy physics in the PDW regime mirrors a generalized $t_1-t_2-J$ model in the hole language, with spectra resembling those of the $t_1-t_2-J$ system and a clear transition to uniform superconductivity at larger $J_K$. The results provide a concrete microscopic pathway to realize and detect PDW in KH-like systems and offer guidance for exploring related models and experimental platforms.

Abstract

We numerically investigate the telltale signs of pair-density-wave order (PDW) in the Kondo-Heisenberg chain by focusing on the momentum resolved spectrum in different parameter regimes. Density matrix renormalization group calculations reveal that this phase is characterized by a dispersion with two minima and four Fermi points, indicating the emergence of an effective next-nearest-neighbor hopping that arises as a second-order effect to avoid magnetic frustration. The pairs appear in the spectrum as in-gap bound states with weight concentrated in the hole pockets. The low-energy physics can be understood by means of a generalized t-J model with next-nearest-neighbor hopping. Our results offer a guide for searching for experimental signatures, and for other models that can realize PDW physics.

Figures (10)

• Figure 1: (a) Pairing correlations for $L=64$, $N=56$; (b) momentum distribution function for $L=32$, $N=28$ (c) Pairing correlations for $L=64$, $N=48$, (d) momentum distribution function for $L=32$, $N=24$.
• Figure 2: Photoemission and inverse-photoemission spectra for $J_H=1$, $J_K=2$ to 5 for the Kondo-Heisenberg model. The single-particle removal spectra and single-particle addition spectra are separated by the solid magenta lines noting the Fermi levels with $1/8$ hole doping. The solid white lines mark the spin (and charge) gaps; the solid orange lines represent the energy of $3 J_K/4$ above Fermi level; and the solid blue lines are at $J_K$ above Fermi level. The vertical lines demark $k_F$ ($k_{F1}$)
• Figure 3: Left: Single-particle removal spectrum for the Kondo-Heisenberg model; Right: Same for the $t_1-t_2-J$ model in the hole language (see text). The spectral weight is in log-scale. Same color scale is applied to both panels.
• Figure 4: Spin gaps as a function of $J_K$ for $J_H=1$. Inset: spin gaps extrapolated to the thermodynamic limit for various values of $J_K$; the length of the chain ranges from $L=32$ to $L=80$.
• Figure 5: $ln(\Delta / t)$ vs. $t/J_K$ for $J_K=0.1$, 1, 2, and 3.