研究発表

対称性が課されたもとで現れる多彩なトポロジカル相に注目が集まっている。対称性のもとで初めてトポロジカルな性質を獲得する相を「対称性で保護されたトポロジカル相」、もともと持っていたトポロジカルな性質が多様化されて現れる相を「対称性で多様化（富化）されたトポロジカル相」と呼ぶ。冷却原子系の持つ高い操作性を利用して、これらの相を実現できるかどうかは興味深い。冷却原子系においては、構成原子の多様さに加え、近年、磁場やスピン・軌道結合と同等の効果を光学的に誘起する人工ゲージ場の技術も発展している。ここでは、人工磁場中のn成分ボース気体の示す量子ホール状態についての我々の最近の研究を紹介し、対称性による保護と富化について議論する。

Recently, Smith et al. investigated a topological phase transition in a spin chain by measuring string order parameters on the IBM quantum computers [Phys. Rev. Research 4, L022020 (2022)]. The measured quantities showed appreciable reduction from theoretical values, owing to inherent noise in the devices. In this work, we reproduce their results in the noisy quantum circuit simulator (Qiskit Aer), and improve the accuracy of the measurements by exploiting the error mitigation technique called the virtual distillation. This technique enables an exponential error suppression given the preparation of n copies of the original circuits and some additional gates.

We study the ground-state phase diagram of a spin-1/2 XXZ model with a chirality-chirality interaction (CCI) on a two-leg ladder. This model offers a minimal setup to study an interplay between spin and chirality degrees of freedom. The spin-chirality duality transformation allows us to relate the regimes of weak and strong CCIs. We perform numerical simulations to confirm the predicted phase structure and critical properties. We mainly used the iDMRG algorithm to determine the phase boundary, determine the nature of the transition, calculate the order parameter, and calculate topological indices associated with each topologically non-trivial phase.

We study the ground-state phase diagram of a spin-1/2 XXZ model with four-spin ring exchange on a two-leg ladder. The spin-chirality duality transformation allows us to relate the regimes of weak and strong four-spin interactions. By applying the Abelian bosonization and the duality, we analyze a simplified model in which part of the four-spin interactions is removed, and predict a phase diagram that contains distinct gapped featureless and ordered phases. In particular, we predict Neel and vector chiral orders in the presence of easy-axis anisotropy, and two distinct symmetry protected topological phases in the presence of easy-plane anisotropy. We performed numerical simulations for both the simplified and full models to confirm the predicted phase structure. We demonstrated that the two SPT phases and a trivial phase are distinguished by topological indices in the presence of certain symmetries.

We study the ground-state phase diagram of a spin-1/2 XXZ model with a four-spin ring exchange on a two-leg ladder. The spin-chirality duality transformation allows us to relate the regimes of weak and strong four-spin interactions. By applying the Abelian bosonization and the duality, we analyze a simplified model in which part of the four-spin interactions is removed, and predict a phase diagram that contains eight distinct gapped phases. In particular, a vector chiral ordered phase and a twisted Haldane phase appear between the scalar chiral ordered phase and the dominant vector chirality phase in the regime of strong four-spin interactions. We perform numerical simulations for both the simplified and full models to confirm the predicted phase structure.