Study of the phase diagram of the Kitaev-Hubbard chain

TL;DR

This paper investigates the phase diagram of the Kitaev-Hubbard chain with interactions, revealing new phases such as the excited state charge density wave and analyzing the conditions for zero modes and topological phases.

Contribution

It provides a comprehensive analysis of the Kitaev-Hubbard chain with interactions, identifying new phases and clarifying the conditions for zero modes and topological order.

Findings

Identification of the excited state charge density wave phase.

Determination of the dynamical critical exponent z ≈ 1.8.

Exclusion of strong zero modes in large parts of the topological phase.

Abstract

We present a detailed study of the phase diagram of the Kitaev-Hubbard chain, that is the Kitaev chain in the presence of a nearest-neighbour density-density interaction, using both analytical techniques as well as DMRG. In the case of a moderate attractive interaction, the model has the same phases as the non-interacting chain, a trivial and a topological phase. For repulsive interactions, the phase diagram is more interesting. Apart from the previously observed topological, incommensurate and charge density wave phases, we identify the `excited state charge density wave' phase. In this phase, the ground state resembles an excited state of an ordinary charge density phase, but is lower in energy due to the frustrated nature of the model. We find that the dynamical critical exponent takes the value $z\simeq 1.8$. Interestingly, this phase only appears for even system sizes, and is sensitive to the chemical potential on the edges of the chain. For the topological phase, we present an argument that excludes the presence of a strong zero mode for a large part of the topological phase. For the remaining region, we study the time dependence of the edge magnetization (using the bosonic incarnation of the model). These results further expand the region where a strong zero mode does not occur.