Article
Mathematics, Applied
Chris Bourne, Yoshiko Ogata
Summary: This paper introduces an index for symmetry-protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group G, and shows that this index is an invariant of the classification of SPT phases. It also derives a fermionic matrix product representative with on-site symmetry for ground states that are translation invariant and have density matrices with uniformly bounded rank on finite intervals.
FORUM OF MATHEMATICS SIGMA
(2021)
Article
Materials Science, Multidisciplinary
Shang-Qiang Ning, Chenjie Wang, Qing-Rui Wang, Zheng-Cheng Gu
Summary: In this study, the Abelian Chern-Simons theory was used to analyze fermionic SPT phases protected by arbitrary Abelian total symmetry G(f). Compared to bosonic SPT phases, these fermionic phases exhibit new features such as support for gapless Majorana fermion edge modes and the effect of nontrivial symmetry extensions on bosonic SPT phases. This research also sheds light on the realization of intrinsic fSPT phases in interacting fermionic systems.
Article
Physics, Multidisciplinary
Tian-Shu Deng, Lei Pan, Yu Chen, Hui Zhai
Summary: This study investigates the stability of Kramers degeneracy and nontrivial topological states under time-reversal symmetry against coupling to the environment. The results show that dissipation can lead to splitting of spectral functions for degenerate states and induce backscattering between counterpropagating edge states, causing the absence of accurate quantization of conductance in the case of the quantum spin Hall effect. The findings have implications for interacting topological phases protected by time-reversal symmetry.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Kai Li, Jiong-Hao Wang, Yan-Bin Yang, Yong Xu
Summary: Recent theoretical studies suggest that structural disorder can induce a topological insulator from a crystalline material, but experimental observation is challenging. With the experimentally realized randomly positioned Rydberg atoms, studying structural disorder induced topological phase transitions becomes feasible. The research reveals symmetry-protected topological amorphous insulators and structural disorder induced topological phase transition at a single-particle level in an experimentally accessible system.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Alex Turzillo, Minyoung You
Summary: This study investigates the boundary supersymmetry of one-dimensional fermionic phases beyond SPT phases, calculating the number of protected boundary supercharges based on bulk phase invariants. Using the connection between Majorana edge modes and real supercharges, the researchers were able to derive this information.
PHYSICAL REVIEW LETTERS
(2021)
Article
Materials Science, Multidisciplinary
Rui Aquino, Nei Lopes, Daniel G. Barci
Summary: In this study, we investigate non-Hermitian topological phase transitions using real-space edge states as a tool. We focus on the simplest non-Hermitian variant of the Su-Schrieffer-Heeger model and analyze the behavior of the zero-energy edge states in nontrivial topological phases. Depending on the parameters, these edge states may penetrate into the bulk, similar to Hermitian topological phase transitions. We also use the topological characterization of exceptional points to describe the intricate chiral behavior of the edge states across the entire phase diagram, and determine the criticality of the model through numerical calculations.
Article
Physics, Multidisciplinary
Abhishodh Prakash, Juven Wang
Summary: It has been proven that the boundaries of all nontrivial (1 + 1)-dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or antiunitary), are supersymmetric quantum mechanical systems. This supersymmetry arises as a consequence of the boundary 't Hooft anomaly that classifies the phase, and is distinct from other well-known degeneracies such as Kramers doublets.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Kyle Monkman, Jesko Sirker
Summary: We discuss the general properties of symmetry-resolved entanglement entropy in systems with particle number conservation and describe how to obtain bounds on entanglement components from correlation functions in Gaussian systems. We introduce majorization as an important tool for deriving entanglement bounds and derive lower bounds for the number and configurational entropy of chiral and Cn-symmetric topological phases. In some cases, our considerations also improve the previously known lower bounds for entanglement entropy in such systems.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Materials Science, Multidisciplinary
Robert A. Jones, Max A. Metlitski
Summary: This paper investigates the boundary problem of root SPT phase with symmetry group G = Z(2) x Z(2)(f) in (2+1)D fermion SPTs. By processing the bulk model, it derives a one-dimensional lattice model for the boundary and finds that it realizes an Ising conformal field theory with a stable gapless boundary state.
Article
Physics, Multidisciplinary
Austin K. Daniel, Akimasa Miyake
Summary: This study demonstrates advantageous strategies for nonlocal games on one-dimensional symmetry-protected topological orders, when the twist phase of SPTOs is nontrivial and -1. It shows that sufficiently large string order parameters of such SPTOs indicate globally constrained correlations that are useful for unconditional computational separation.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Mathematical
Yoshiko Ogata
Summary: The study focuses on SPT phases with on-site finite group G symmetry in two-dimensional Fermion systems, and derives an invariant for classification.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Helene Spring, Anton Akhmerov, Daniel Varjas
Summary: In amorphous topological materials, protection of topological surface states is improved due to continuous rotation symmetry, resulting in critical scaling of transport and protection of edge from localization in the topological phase.
Article
Materials Science, Multidisciplinary
Chao-Ming Jian, Xiao-Chuan Wu, Yichen Xu, Cenke Xu
Summary: This study explores the physical constructions and boundary properties of various symmetry-protected topological phases involving 1-form symmetries, from one spatial dimension to four spatial dimensions. It also examines anomalies of 3d states of matter and discusses the connection between SPT states with 1-form symmetries and condensed-matter systems in lower dimensions. Additionally, the potential trivial gapped phases of quantum dimer models are explored based on the nature of their corresponding bulk states in higher dimensions.
Article
Physics, Multidisciplinary
Ruochen Ma, Chong Wang
Summary: In this study, we demonstrate that symmetry-protected topological (SPT) phases can also be applied to average symmetries, where local quenched disorders break the symmetries but restore them upon disorder averaging. We classify and characterize a large class of average SPT phases using a decorated domain wall approach, and show that the boundary states of such phases will almost certainly be long-range entangled. We also develop a theory for generalized average SPT phases based on density matrices and quantum channels, indicating that topological quantum phenomena associated with average symmetries can be as rich as those with exact symmetries.
Article
Physics, Multidisciplinary
Jing Zhang, Cheng-Pu Lv, Yan-Chao Li
Summary: Researchers based on the SSH and Kitaev models, studied the Berry phase to detect different types of topological phases, and found that low energy spectra play a significant role in determining the Berry phase value. Through analysis of the Berry phase, entanglement entropy, and electron occupation, a new quantum phase is discovered, revealing the influence of interactions on different types of topological phases.