Presentations -

Symmetry-protected topological phases and entanglement swapping in spin-1/2 ladder systems

Shunsuke Furukawa

[Domestic presentation]  高次にもつれた量子相探索の展開 (基礎物理学研究所、京都大学、京都) , 

2025.09

, 

Oral presentation (general)

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The concept of symmetry-protected topological (SPT) phases has been proposed and extensively developed over the past 15 years. While bosonic SPT phases in one spatial dimension is fully classified by projective representations of the symmetry group, it is interesting to examine when nontrivial SPT phases emerge and how they compete with conventional ordered phases in concrete physical systems. Here we explore this issue in spin-1/2 XXZ ladders with four-spin interactions. We find that weak XXZ anisotropy crucially affects the phase structure, inducing SPT phases in the easy-plane regime and magnetic and chiral ordered phases in the easy-axis regime. The SPT phases identified here can be regarded as twisted variants of the well-known Haldane phase, and are distinguished by topological indices linked to the system's symmetries. Motivated by the deepening interplay between quantum magnetism and quantum information, we further explore a many-body extension of the entanglement swapping protocol, in which entangled spin pairs are replaced by quantum phases of spin-1/2 ladders. We show that Bell measurements performed between legs of topological and trivial ladder states, followed by postselection of uniform outcomes, lead to the generation of a topological state on the unmeasured legs.

Topological entanglement swapping in spin-ladder systems

Mizuki Hamada, Shunsuke Furukawa

[International presentation]  SQAI-NCTS Workshop on Quantum Technologies and Machine Learning (National Taiwan University, Taipei) , 

2025.08

, 

Poster presentation

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We study how quantum measurements can transform quantum phases in spin ladder systems through an entanglement swapping protocol. Consecutive Bell measurements are performed between the legs of two independent ladders, followed by uniform post-selection of the measurement outcomes. We analyze the resulting phase realized in the unmeasured outer legs.
Our analysis is based on topological indices protected by the D_2=Z_2×Z_2 spin rotational symmetry as well as the lattice translation symmetry. We find that these indices remain unchanged through the measurement process, leading to a nontrivial inheritance rule. Namely, the output state is topological if only one of the ladders is initially topological, while it becomes trivial if both are.
To illustrate this, we explicitly construct post-measurement states using matrix product states (MPS), in which the rung singlet (trivial) and Haldane (SPT) phases are represented by a product of singlets and a valence bond solid state, respectively. The MPS results are consistent with the index characterization and further reveal that the correlation length increases after measurement, indicating enhanced fluctuations.
Finally, we perform a field-theoretical analysis using bosonization. By identifying the locking positions of bosonic fields associated with string order parameters, we determine the resulting phase and confirm consistency with both the index argument and MPS analysis., Interestingly, the post-measurement correlation length is approximately equal to the sum of those before measurement.

スピン梯子系におけるトポロジカルエンタングルメントスワッピング

濱田瑞貴, 古川俊輔

[Domestic presentation]  第70回物性若手夏の学校 (白浜荘、滋賀) , 

2025.07

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2025.08

, 

Poster presentation

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近年、量子測定が量子多体系に与える影響に広く関心が集まっている。本研究ではその一例として、二つのスピン梯子系に対してエンタングルメントスワッピングを施し、測定後に実現される量子相の特定を試みる。具体的には、独立な二つのスピン梯子系の各脚にベル測定を行い、測定結果が一様となるよう事後選択を行った上で、直接測定を施していない梯子の脚に現れる状態が属する相を解析する。スピン梯子系は、トポロジカル相（Haldane 相）や自明相（rung singlet 相; RS 相）を実現するだけでなく、異方性や多体相互作用の導入によって多彩な相構造を示す。これらの相は局所的な秩序変数では検出できないが、特定の対称性を課している限り、トポロジカル指数を用いて区別することが可能である。本研究では、離散的なスピン回転対称性D2=Z2 X Z2 と並進対称性に保護された三つのトポロジカル指数に注目し、二系の合成系における指数が測定前後で不変であるという事実を基に、測定後の相の同定を行った。この議論は一般的であるが、測定後の状態の詳細が不明であるため、行列積状態（matrix product state; MPS）およびボソン化による具体的な解析も実施した。MPS を用いた解析では、Haldane 相の代表例であるvalence bond solid 状態がMPS で表現できることを利用し、測定後の状態を明示的に構成してトポロジカル指数を評価した。その結果は、トポロジカル指数のみに基づく一般的議論と整合的であり、さらに転送行列の解析を通じて、測定後の状態では相関長が増加する傾向も確認された。一方、ボソン化の枠組みでは、RS 相やHaldane 相などのギャップのある状態は、有効ハミルトニアン中のcos 項によってボソン場がロックされることに対応し、ロックされる場の種類や位置がストリング秩序変数と密接に関係することを用いた。ボソン化した有効ハミルトニアンの基底状態を求め、測定後の状態を計算し、ボソン場がロックされる位置を解析することで測定後に実現される相を特定した。ボソン化による結果も、トポロジカル指数やMPS を用いた解析と整合する。更に、測定後の状態の相関長が、測定前の各梯子の相関長の和で与えられることを解析的に導出し、MPS により観測された相関長の増加を説明した。

Topological entanglement swapping in spin-ladder systems

Mizuki Hamada, Shunsuke Furukawa

[International presentation]  The 4th Young Researchers' Workshop of the Extreme Universe Collaboration (Kyukamura Irago, Aichi) , 

2025.06

-

2025.07

, 

Oral presentation (general)

　View Summary

We study how quantum measurements can transform quantum phases in spin ladder systems through an entanglement swapping protocol. Consecutive Bell measurements are performed between the legs of two independent ladders, followed by uniform post-selection of the measurement outcomes. We analyze the resulting phase realized in the unmeasured outer legs.
Our analysis is based on topological indices protected by the D_2=Z_2×Z_2 spin rotational symmetry as well as the lattice translation symmetry. We find that these indices remain unchanged through the measurement process, leading to a nontrivial inheritance rule. Namely, the output state is topological if only one of the ladders is initially topological, while it becomes trivial if both are.
To illustrate this, we explicitly construct post-measurement states using matrix product states (MPS), in which the rung singlet (trivial) and Haldane (SPT) phases are represented by a product of singlets and a valence bond solid state, respectively. The MPS results are consistent with the index characterization and further reveal that the correlation length increases after measurement, indicating enhanced fluctuations.
Finally, we perform a field-theoretical analysis using bosonization. By identifying the locking positions of bosonic fields associated with string order parameters, we determine the resulting phase and confirm consistency with both the index argument and MPS analysis., Interestingly, the post-measurement correlation length is approximately equal to the sum of those before measurement.

System-environment entanglement phase transitions for open boundary conditions

Yuheng Sui, Shunsuke Furukawa

[International presentation]  The 4th Young Researchers' Workshop of the Extreme Universe Collaboration (Kyukamura Irago, Aichi) , 

2025.06

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2025.07

, 

Oral presentation (general)

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A quantum channel described by a CPTP map generally turns a pure quantum state into a mixed state, which can be viewed as development of system-environment entanglement. We study a phase transition in the system-environment Renyi entanglement entropy (EE) when the XXZ chain with open boundary conditions is subject to continuous density measurements. We show that the EE exhibits a volume law followed by a subleading logarithmic term; the coefficient of the latter changes from 0 to 1/4 as a function of the measurement strength. We also study the expectation value of a certain twist operator in the doubled Hilbert space formalism, that is expected to detect the phase transition. We compare our results with previous results for the periodic boundary condition as well as the boundary renormalization group analysis.

スピン梯子系におけるトポロジカルエンタングルメントスワッピング

濱田瑞貴, 古川俊輔

[Domestic presentation]  日本物理学会2025年春季大会 (オンライン) , 

2025.03

, 

Oral presentation (general)

スピン梯子系におけるトポロジカルエンタングルメントスワッピング

濱田瑞貴, 古川俊輔

[Domestic presentation]  サスティナブル量子AI研究拠点第5回全体会議 (慶應義塾大学日吉キャンパス ) , 

2025.02

, 

Poster presentation

量子多体系における測定と場の理論

古川俊輔

[Domestic presentation]  場の理論の新しい計算方法2024 (東京大学駒場Ⅱキャンパス) , 

2024.12

, 

Public lecture, seminar, tutorial, course, or other speech

Investigation of topological phases and transitions via quantum control, quantum entanglement, and duality

Shunsuke Furukawa

[Domestic presentation]  The 4th ExU Annual Meeting of the Extreme Universe Collaboration (Nambu Yoichiro Hall, Osaka University) , 

2024.09

, 

Oral presentation (general)

Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction

M. Fontaine, K. Sugimoto, S. Furukawa

[International presentation]  SUN2024 : SU(N) physics in quantum many-body systems: theory, experiment, and numerics (Sendai) , 

2024.07

, 

Poster presentation

Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction

M. Fontaine, K. Sugimoto, and S. Furukawa

[International presentation]  SQAI-NCTS Workshop on Tensor Network and Quantum Embedding (Hongo Campus, University of Tokyo) , 

2024.03

, 

Poster presentation

Error-mitigated quantum computation of string order parameters across a topological phase transition

R. Kawase and S. Furukawa

[International presentation]  SQAI-NCTS Workshop on Tensor Network and Quantum Embedding (Hongo Campus, University of Tokyo) , 

2024.03

, 

Poster presentation

Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction

M. Fontaine, K. Sugimoto, and S. Furukawa

[Domestic presentation]  サスティナブル量子AI研究拠点第3回全体会議 (東京大学本郷キャンパス山上会館) , 

2024.02

, 

Poster presentation

Error-mitigated quantum computation of string order parameters across a topological phase transition

R. Kawase and S. Furukawa

[International presentation]  The 2nd young researchers' workshop of the Extreme Universe Collaboration (Shirahamaso, Shiga) , 

2024.02

, 

Oral presentation (general)

Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction

M. Fontaine, K. Sugimoto, and S. Furukawa

[International presentation]  The 2nd young researchers' workshop of the Extreme Universe Collaboration (Shirahamaso, Shiga) , 

2024.02

, 

Oral presentation (general)

Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction

M. Fontaine, K. Sugimoto, and S. Furukawa

[International presentation]  The 6th R-CCS International Symposium (Kobe International Conference Center) , 

2024.01

, 

Poster presentation

Error-mitigated quantum computation of string order parameters across a topological phase transition

R. Kawase and S. Furukawa

[International presentation]  Computational Approaches to Quantum Many-Body Systems (SONIC CITY, Saitama) , 

2023.10

, 

Poster presentation

　View Summary

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.

Vector chiral order and symmetry-protected topological phases in a spin-1/2 XXZ ladder with a four-spin interaction

M. Fontaine, K. Sugimoto, and S. Furukawa

[International presentation]  Computational Approaches to Quantum Many-Body Systems (SONIC CITY, Saitama) , 

2023.10

, 

Poster presentation

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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.

Phase diagram of a spin-1/2 XXZ ladder with four-spin ring exchange

M. Fontaine, K. Sugimoto, and S. Furukawa

[International presentation]  YIPQS Long-Term Workshop: Quantum Information, Quantum Matter, and Quantum Gravity (Kyoto University) , 

2023.09

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2023.10

, 

Poster presentation

　View Summary

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.

多成分ボース気体の量子ホール物理：対称性による保護と富化

古川俊輔

量子物理学・ナノサイエンス第367回セミナー, 

2023.07

, 

Public lecture, seminar, tutorial, course, or other speech

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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。