[논문 리뷰] Topological holography for fermions

Rui Wen, Weicheng Ye외 1명|arXiv (Cornell University)|2024. 04. 29.

Particle physics theoretical and experimental studies인용 수 5

한 줄 요약

대칭성 TFT 프레임워크를 페르미오닉 시스템으로 확장하여 페르미오닉 SymTFT를 도출하고, 1+1D 페르미오닉 SPTs, 에지 모드, 보손화를 분석하며 본질적으로 간격이 없는 페르미오닉 SPT를 제시한다.

ABSTRACT

Topological holography is a conjectured correspondence between the symmetry charges and defects of a $D$-dimensional system with the anyons in a $(D+1)$-dimensional topological order: the symmetry topological field theory (SymTFT). Topological holography is conjectured to capture the topological aspects of symmetry in gapped and gapless systems, with different phases corresponding to different gapped boundaries (anyon condensations) of the SymTFT. This correspondence was previously considered primarily for bosonic systems, excluding many phases of condensed matter systems involving fermionic electrons. In this work, we extend the SymTFT framework to establish a topological holography correspondence for fermionic systems. We demonstrate that this fermionic SymTFT framework captures the known properties of $1+1D$ fermion gapped phases and critical points, including the classification, edge-modes, and stacking rules of fermionic symmetry-protected topological phases (SPTs), and computation of partition functions of fermionic conformal field theories (CFTs). Beyond merely reproducing known properties, we show that the SymTFT approach can additionally serve as a practical tool for discovering new physics, and use this framework to construct a new example of a fermionic intrinsically gapless SPT phase characterized by an emergent fermionic anomaly.

연구 동기 및 목표

• 대칭으로 풍부해진 페르미오닉 시스템에 대해 SymTFT/토폴로지 홀로그래피 프로그램을 일반화한다.
• 페르미오닉 SymTFT가 알려진 1+1D 페르미오닉 SPT 특성(분류, 에지 모드, 스태킹)을 포착한다는 것을 보인다.
• 프레임워크의 실용적 활용으로 새로운 물리 현상을 발견한다, 포함하여 본질적으로 간격이 없는 페르미오닉 SPT를 포함한다.

제안 방법

• Z2^F를 포함하는 대칭 G^F를 가지는 1+1D 시스템에 대해 페르미오닉 SymTFT를 구성한다.
• 경질 소멸? 페르미온 anyon을 응축시켜 경계에 로컬 페르미온을 도입하여 페르미온 기준 경계를 구현한다.
• 페르미닉 기준 경계에서 스핀 구조 의존성이 나타남을 보이고 G^F-스핀 구조 데이터를 추출한다.
• 보손화가 SymTFT 내의 기준 경계의 변화로 나타난다.
• 프레임워크를 적용하여 Kitaev 체인, Majorana CFT 및 다양한 페르미오닉 SPT를 복원하고, 출현하는 페르미오닉 이상을 갖는 igSPT를 구성한다.

Figure 1: The SymTFT setup. (a). The SymTFT for a general symmetry category $\mathcal{A}$ is the Drinfeld center $\sf{Z}[\mathcal{A}]$ . The sandwich (left) reduces to the original system $\sf{T}$ (right) when viewed as an effective $1+1D$ system. (b). A non-trivial topological defect line near the

실험 결과

연구 질문

• RQ1 Can the fermionic SymTFT reproduce and classify 1+1D fermionic SPT phases and their stacking rules?
• RQ2 How does spin structure (G^F-spin structure) influence the fermionic SymTFT and edge physics?
• RQ3 What is the role of fermionic condensation on the reference boundary in encoding fermionic phases and anomalies?
• RQ4 How does bosonization manifest as a boundary change within the fermionic SymTFT?
• RQ5 Can one realize intrinsically fermionic and intrinsically gapless SPTs within this framework?

주요 결과

• The fermionic SymTFT framework yields the full classification of 1+1D fermionic SPTs and their stacking rules.
• Edge modes and spin-structure dependence of fermionic phases are naturally captured by the reference boundary construction.
• Bosonization/non-invertible dualities map to changes of the reference boundary within the SymTFT.
• The approach reproduces known phases such as the Kitaev chain and the Majorana CFT within a unifying topological framework.
• The framework enables construction of intrinsically-fermionic, intrinsically-gapless SPTs with emergent anomalous fermionic symmetry.
• It provides a practical field-theoretic route to bosonized descriptions of fermionic systems via SymTFT.

Figure 2: Local and non-local charges in SymTFT. (a). A gauge charge line in the SymTFT can be absorbed by the reference boundary. This corresponds to a local symmetry charge of $\sf{T}$ after dimensional reduction. The red dot represents an excitation created by the anyon line at $\sf{B_{phys}}$ .