Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts
Kabuki Takada, Shigetoshi Sota, Seiji Yunoki, Bibek Pokharel, Hidetoshi Nishimori, Daniel A. Lidar · Physical Review Research · 2021
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 $\ifmmode\pm\else\textpm\fi{}XX$-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.