Hidden Order and Dynamics in Supersymmetric Valence Bond Solid States -- Super-Matrix Product State Formalism

TL;DR

This paper introduces a supersymmetric matrix product state framework to analyze doped valence bond solid models, revealing hidden order and detailed physical properties, including excitation spectra and superconducting correlations.

Contribution

It develops a supersymmetric matrix product formalism for VBS models with doping, enabling exact evaluation of physical properties and revealing hidden order in these systems.

Findings

Exact hole-doping behavior of physical quantities

Identification of generalized hidden order

Analysis of entanglement spectrum and string order

Abstract

Supersymmetric valence bond solid models are extensions of the VBS model, a paradigmatic model of `solvable' gapped quantum antiferromagnets, to the case with doped fermionic holes. In this paper, we present a detailed analysis of physical properties of the models. For systematic studies, a supersymmetric version of the matrix product formalism is developed. On 1D chains, we exactly evaluate the hole-doping behavior of various physical quantities, such as the spin/charge excitation spectrum, superconducting order parameter. A generalized hidden order is proposed, and the corresponding string non-local order parameter is also calculated. The behavior of the string order parameter is discussed in the light of the entanglement spectrum.