Duality and domain wall dynamics in a twisted Kitaev chain

TL;DR

This paper introduces the twisted Kitaev chain model to describe the domain wall dynamics in CoNb₂O₆, revealing a universal duality-related ratio and novel quantum behaviors near criticality.

Contribution

It proposes the twisted Kitaev chain as a new model for CoNb₂O₆, demonstrating duality, topological effects, and universal critical behavior in a real material.

Findings

Domain wall excitations follow the Su-Schrieffer-Heeger model.

The excitation gap closes at twice the rate in the ferromagnetic regime.

First direct measurement of the universal ratio 2 related to Kramers-Wannier duality.

Abstract

The Ising chain in transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, topological defects, quantum criticality, and duality. Although the quasi-1D ferromagnet CoNb$_2$O$_6$ has been put forward as the best material example of the transverse field Ising model, it exhibits significant deviations from ideality. Through a combination of THz spectroscopy and theory, we show that CoNb$_2$O$_6$ in fact is well described by a different model with strong bond dependent interactions, which we dub the {\it twisted Kitaev chain}, as these interactions share a close resemblance to a one-dimensional version of the intensely studied honeycomb Kitaev model. In this model the ferromagnetic ground state of CoNb$_2$O$_6$ arises from the compromise between two distinct alternating axes rather than a single easy axis. Due to this frustration, even at zero applied field domain-wall excitations have quantum motion that is described by the celebrated Su-Schriefer-Heeger model of polyacetylene. This leads to rich behavior as a function of field. Despite the anomalous domain wall dynamics, close to a critical transverse field the twisted Kitaev chain enters a universal regime in the Ising universality class. This is reflected by the observation that the excitation gap in CoNb$_2$O$_6$ in the ferromagnetic regime closes at a rate precisely twice that of the paramagnet. This originates in the duality between domain walls and spin-flips and the topological conservation of domain wall parity. We measure this universal ratio `2' to high accuracy -- the first direct evidence for the Kramers-Wannier duality in nature.