# Pairing versus phase coherence of doped holes in distinct quantum spin backgrounds

## TL;DR

This study investigates how different quantum spin backgrounds affect hole pairing and phase coherence, revealing a non-BCS pairing mechanism influenced by spin states, with implications for understanding pseudogap phenomena.

## Contribution

It demonstrates the impact of spin background on pairing phase coherence and introduces a non-BCS pairing mechanism controlled by intrinsic spin-related phase fluctuations.

## Key findings

- Strong hole binding in both phases
- Phase fluctuations significantly affect pairing coherence
- Symmetry-protected topological phase weakens Cooper pairing

## Abstract

We examine the pairing structure of holes injected into two \emph{distinct} spin backgrounds: a short-range antiferromagnetic phase versus a symmetry protected topological phase. Based on density matrix renormalization group (DMRG) simulation, we find that although there is a strong binding between two holes in both phases, \emph{phase fluctuations} can significantly influence the pair-pair correlation depending on the spin-spin correlation in the background. Here the phase fluctuation is identified as an intrinsic string operator nonlocally controlled by the spins. We show that while the pairing amplitude is generally large, the coherent Cooper pairing can be substantially weakened by the phase fluctuation in the symmetry-protected topological phase, in contrast to the short-range antiferromagnetic phase. It provides an example of a non-BCS mechanism for pairing, in which the paring phase coherence is determined by the underlying spin state self-consistently, bearing an interesting resemblance to the pseudogap physics in the cuprate.