Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts

TL;DR

This study investigates how nonstoquastic interactions influence topological phase transitions in a frustrated quantum Ising ladder, finding that such catalysts do not eliminate topological obstacles in quantum annealing.

Contribution

It provides the first analysis of nonstoquastic effects on topological first-order phase transitions in a frustrated quantum Ising model.

Findings

First-order topological phase transition remains stable with nonstoquastic catalysts.

Symmetry-preserving RG and DMRG methods agree qualitatively.

Nonstoquastic catalysts are insufficient to remove topological barriers.

Abstract

The role of nonstoquasticity in the field of quantum annealing and adiabatic quantum computing is an actively debated topic. We study a strongly-frustrated quasi-one-dimensional quantum Ising model on a two-leg ladder to elucidate how a first-order phase transition with a topological origin is affected by interactions of the $\pm XX$-type. Such interactions are sometimes known as stoquastic (negative sign) and nonstoquastic (positive sign) "catalysts". Carrying out a symmetry-preserving real-space renormalization group analysis and extensive density-matrix renormalization group computations, we show that the phase diagrams obtained by these two methods are in qualitative agreement with each other and reveal that the first-order quantum phase transition of a topological nature remains stable against the introduction of both $XX$-type catalysts. This is the first study of the effects of nonstoquasticity on a first-order phase transition between topologically distinct phases. Our results indicate that nonstoquastic catalysts are generally insufficient for removing topological obstacles in quantum annealing and adiabatic quantum computing.