Gapless Topological Behaviors in a Long-Range Quantum Spin Chain

Sheng Yang, Hai-Qing Lin and Xue-Jia Yu

Yang, Sheng, Hai‐Qing Lin, Yu, Xue-Jia

Topology in condensed matter physics is typically associated with a bulk energy gap. However, recent research has shifted focus to topological phases without a bulk energy gap, exhibiting nontrivial gapless topological behaviors. In this letter, we explore a cluster Ising chain with long-range antiferromagnetic interactions that decay as a power law with the distance. Using complementary numerical and analytical techniques, we demonstrate that long-range interactions can unambiguously induce an algebraic topological phase and a topological Gaussian universality, both of which exhibit nontrivial gapless topological behaviors. Our study not only provides a platform to investigate the fundamental physics of quantum many-body systems but also offers a novel route toward searching for gapless topological phases in realistic quantum simulators.

Abhinav Saket

Sheng Yang, Hai‐Qing Lin, Xue-Jia Yu

Topology is a fascinating phenomena in condensed-matter physics typically associated with a bulk gap. However, recent research shifts focus to quantum critical points or phases that exhibit nontrivial topological properties. Here we explore a cluster-Ising chain with long-range antiferromagnetic interactions that decay as a power law with distance. Using large-scale density matrix renormalization group simulations, we demonstrate that the nontrivial topology at the critical point remains stable against long-range interactions, resulting in a topologically nontrivial critical line. Moreover, even within the gapped region, the interplay between topology and long-range interaction can give rise to a topological phase featuring algebraically decaying correlations and edge modes, similar to gapless topological phases. We refer to this phase as the algebraic topological phase, which exhibits nontrivial gapless topological behaviors and arises solely from long-range interactions without short-range counterparts. The findings pave the way for more studies on topological states in long-range systems. Long-range interactions play a crucial role in condensed-matter systems and can lead to range of emerging and exotic physical phenomenon. Here using simulations, the authors investigate the non-trivial topological properties that can arise in a cluster Ising chain with long-range antiferromagnetic interactions, finding evidence for what they classify as an algebraic symmetry-protected topological phase.

Hong‐Chen Jiang, Jiadong Zang, Zheng-Yu Weng +1 more

Wen-Hao Zhong, Wei-Lin Li, Y L Chen +1 more

Long-range interactions can fundamentally alter properties in gapped topological phases such as emergent massive edge modes. However, recent research has shifted attention to topological nontrivial critical points or phases, and it is natural to explore how long-range interactions influence them. In this work, we investigate the topological behavior at the quantum critical point of extended Kitaev chains with long-range interactions, which can be derived from the critical Ising model via the Jordan-Wigner transformation in the short-range limit. Specifically, we analytically find that the critical edge modes at the critical point remain stable against long-range interactions. More importantly, we observe that these critical edge modes remain massless even when long- range interactions become very strong. As a by-product, we numerically find that the critical behavior of the long-range model belongs to the free-Majorana-fermion universality class, which is entirely different from the long-range universality class in the usual long-range spin models. Our work could shed new light on the interplay between long-range interactions (frustrated) and the gapless topological phases of matter.