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

• URL: http://arxiv.org/abs/2012.07144v2
• Date: Mon, 11 Oct 2021 15:46:47 GMT
• Title: Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts
• Authors: Kabuki Takada, Shigetoshi Sota, Seiji Yunoki, Bibek Pokharel, Hidetoshi Nishimori, Daniel A. Lidar
• Abstract summary: We study how a first-order phase transition with a topological origin is affected by interactions of the $pm XX$-type. This is the first study of the effects of nonstoquasticity on a first-order phase transition between topologically distinct phases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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