Brute-force positivization of $J_1-J_2$ model ground states

TL;DR

This paper investigates a brute-force method to transform the ground states of the one-dimensional $J_1 - J_2$ model into positive wave functions, analyzing boundary conditions and chain parity effects.

Contribution

It introduces a brute-force protocol using single-qubit transformations to positivize quantum ground states of the $J_1 - J_2$ model under various boundary conditions.

Findings

Positivization protocols differ between periodic and open boundary conditions.

Sign structure depends on the parity of the spin chain.

The method reveals how frustration affects wave function sign structures.

Abstract

Exploring sign structures of quantum wave functions attracts considerable attention due to the potential for advances in modeling complex phases of matter. This stimulates developing different optimization procedures for imitating and manipulating sign structures of quantum states. In this work, utilizing a brute force approach based on a set of single-qubit transformations we evaluate protocols enabling positivization of the one-dimensional $J_1 -J_2$ model ground states in the regime of strong frustration. Based on the obtained positivization results, we show the difference between the cases of periodic and open boundary conditions, and also establish the dependence of the sign structure on parity of the simulated spin chains.