Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2509.17473 · Physical review. B./Physical review. B

Entanglement manifestation of link topology in a non-Hermitian lattice

Guoying Zhang, Li Wang, Shu Chen

Published Feb 9, 2026• 1 citation
arXivHTMLPDF

Abstract

Although the homotopy-knot theory has been utilized to implement effective topological classification for non-Hermitian systems, the physical implications underlying distinct knot topologies remain ambiguous and are rarely addressed. In this work, we propose a one-dimensional non-Hermitian four-band lattice model and map out its phase diagram according to the distinct knot structures residing in the moment space. The topological phase diagram is ascertained through a spectral winding number. Furthermore, we derive the exact analytic formula for the phase boundaries that delineate different knot topologies. To explore the concrete physical implications of distinct knot topologies, we investigate the many-body ground state entanglement entropy for free fermions loaded on such non-Hermitian lattice in real space. It turns out that different knot topologies imply different magnitudes of entanglement. Moreover, we show that the central charge c extracted from systematic finite-size scaling of entanglement entropy provides effective description of the phase diagram of the knot topology. Finally, we further confirm the phase boundaries for the topological phase transitions alternatively by numerical calculations of the many-body ground state fidelity susceptibility. Our results showcase the connection between knot topology and entanglement of non-Hermitian systems and may facilitate further exploration of the profound and practical physical implications of knot topology.

DOI
10.1103/qcdc-1bdv

Related papers

Entanglement signatures of quantum criticality in Floquet non-Hermitian topological systems

Siyuan Cheng, Rui Xie, Xiaosen Yang +2 more

The entanglement entropy can be an effective diagnostic tool for probing topological phase transitions. In one-dimensional single particle systems, the periodic driving generates a variety of topological phases and edge modes. In this work, we investigate the topological phase transition of the one-dimensional Floquet Su-Schrieffer-Heeger model using entanglement entropy, and construct the phase diagram based on entanglement entropy. The entanglement entropy exhibits pronounced peaks and follows the logarithmic scaling law at the phase transition points, from which we extract the central charge $c=1$. We further investigate the entanglement spectrum to accurately distinguish the different topological phases. In addition, the coupling between zero and $π$ modes leads to characteristic splittings in the entanglement spectrum, signaling their hybridization under periodic driving. These results remain robust in non-Hermitian regimes and in the presence of next-nearest-neighbor hopping, demonstrating the reliability and universality of entanglement entropy as a diagnostic for topological phase transitions.

quant-pharXiv:2601.03002•Jan 7, 2026•0 citations

Knot Topology in Quantum Spin System

X. M. Yang, L. Jin, Z. Song

Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of the phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.

arXiv:1906.09016•Jun 21, 2019•0 citations

Characterizing bulk-boundary correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy

Weitao Chen, Liangtao Peng, Hantao Lu +1 more

Dramatically different from the Hermitian systems, the conventional bulk-boundary correspondence (BBC) is broken in the non-Hermitian systems. In this paper, we use edge entanglement entropy to characterize the topological properties of non-Hermitian Su-Schrieffer-Heeger Hubbard model. For free fermions, we study the scaling behavior of entanglement entropy and demonstrate that the edge entanglement entropy is a good indicator to delimit different phases of non-Hermitian systems. We further generalize the edge entanglement entropy to the non-Hermitian interacting Hubbard chain and obtain the topological phase diagram in the plane of interaction and non-Hermitian hopping amplitudes. It is found that the Hubbard interaction diminishes and weakens the breakdown of the bulk-boundary correspondence, which eventually disappears at some critical value of interaction.

arXiv:2108.00607•Physical review. B./Physical review. B•Feb 14, 2022•16 citations

Entangled multi-knot lattice model of anyon current

Tieyan Si

We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyon. This knot lattice model bears abelian and non-abelian anyons as well as integral and fractional filling states that is similar to quantum Hall system. The fusion rules of anyon are explicitly demonstrated by braiding on crossing states of the multi-knot lattice. The statistical character of anyon is quantified by topological linking number of multi-knot link. Long-range coupling interaction is a fundamental character of this knot lattice model. The short range coupling models, such as Ising model, fermion paring model, Kitaev honeycomb lattice model and so on, appears as the short range coupling case of the knot lattice model. We introduced link lattice pattern as geometric representation of the eigenstate of quantum many body model to explore the topological nature of quantum eigen-states. For example, a convection flow loop is introduced into the well-know BCS fermions pairing model to show the Pseudo-gap state in unconventional super-conducting state. The integral and fractional filling numbers in quantum Hall system is directly quantized by topological linking number. The quantum phase transition between different quantum states in quantum spin model is also directly quantified by the change of topological linking number, which revealed topological character of phase transition. This multi-knot lattice has a promising physical implementation by circularized photons in optical firbre network. It may also provide another different path to topological quantum computation.

arXiv:1810.03094•Chinese Physics B•Apr 1, 2019•4 citations

Topological Knots in Quantum Spin Systems

X. M. Yang, L. Jin, Z. Song

Knot theory provides a powerful tool for understanding topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in a quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other, forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.

Chinese Physics Letters•Jun 1, 2021•2 citations

Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension

Wen-Hao Zhong, Haiqing Lin, Xue-Jia Yu

Quantum entanglement can be an effective diagnostic tool for probing topological phases protected by global symmetries. Recently, the notion of nontrivial topology in critical systems has been proposed and is attracting growing attention. In this work, as a concrete example, we explore the quantum entanglement properties of fermionic symmetry-enriched quantum critical points by constructing exactly solvable models based on stacked multiple Kitaev chains. We first analytically establish the global phase diagram using entanglement entropy and reveal three topologically distinct gapped phases with different winding numbers, along with three topologically distinct transition lines separating them. Importantly, we unambiguously demonstrate that two transition lines exhibit fundamentally different topological properties despite sharing the same central charge. Specifically, they display nontrivial topological degeneracy in the entanglement spectrum under periodic boundary conditions, thereby generalizing the Li-Haldane bulk-boundary correspondence to a broader class of fermionic symmetry-enriched criticality. Additionally, we identify a novel Lifshitz multicritical point at the intersection of the three transition lines, which also exhibits nontrivial topological degeneracy. This work provides a valuable reference for investigating gapless topological phases of matter from the perspective of quantum entanglement.

arXiv:2502.18178•Physical review. B./Physical review. B•Aug 1, 2025•12 citations
Although the homotopy-knot theory has been utilized to implement effective topological classification for non-Hermitian systems, the physical implications underlying distinct knot topologies remain ambiguous and are rarely addressed. In this work, we propose a one-dimensional non-Hermitian four-band lattice model and map out its phase diagram according to the distinct knot structures residing in the moment space. The topological phase diagram is ascertained through a spectral winding number. Furthermore, we derive the exact analytic formula for the phase boundaries that delineate different knot topologies. To explore the concrete physical implications of distinct knot topologies, we investigate the many-body ground state entanglement entropy for free fermions loaded on such non-Hermitian lattice in real space. It turns out that different knot topologies imply different magnitudes of entanglement. Moreover, we show that the central charge c extracted from systematic finite-size scaling of entanglement entropy provides effective description of the phase diagram of the knot topology. Finally, we further confirm the phase boundaries for the topological phase transitions alternatively by numerical calculations of the many-body ground state fidelity susceptibility. Our results showcase the connection between knot topology and entanglement of non-Hermitian systems and may facilitate further exploration of the profound and practical physical implications of knot topology.
The entanglement entropy can be an effective diagnostic tool for probing topological phase transitions. In one-dimensional single particle systems, the periodic driving generates a variety of topological phases and edge modes. In this work, we investigate the topological phase transition of the one-dimensional Floquet Su-Schrieffer-Heeger model using entanglement entropy, and construct the phase diagram based on entanglement entropy. The entanglement entropy exhibits pronounced peaks and follows the logarithmic scaling law at the phase transition points, from which we extract the central charge c=1c=1c=1. We further investigate the entanglement spectrum to accurately distinguish the different topological phases. In addition, the coupling between zero and πππ modes leads to characteristic splittings in the entanglement spectrum, signaling their hybridization under periodic driving. These results remain robust in non-Hermitian regimes and in the presence of next-nearest-neighbor hopping, demonstrating the reliability and universality of entanglement entropy as a diagnostic for topological phase transitions.
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of the phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.
Dramatically different from the Hermitian systems, the conventional bulk-boundary correspondence (BBC) is broken in the non-Hermitian systems. In this paper, we use edge entanglement entropy to characterize the topological properties of non-Hermitian Su-Schrieffer-Heeger Hubbard model. For free fermions, we study the scaling behavior of entanglement entropy and demonstrate that the edge entanglement entropy is a good indicator to delimit different phases of non-Hermitian systems. We further generalize the edge entanglement entropy to the non-Hermitian interacting Hubbard chain and obtain the topological phase diagram in the plane of interaction and non-Hermitian hopping amplitudes. It is found that the Hubbard interaction diminishes and weakens the breakdown of the bulk-boundary correspondence, which eventually disappears at some critical value of interaction.
We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyon. This knot lattice model bears abelian and non-abelian anyons as well as integral and fractional filling states that is similar to quantum Hall system. The fusion rules of anyon are explicitly demonstrated by braiding on crossing states of the multi-knot lattice. The statistical character of anyon is quantified by topological linking number of multi-knot link. Long-range coupling interaction is a fundamental character of this knot lattice model. The short range coupling models, such as Ising model, fermion paring model, Kitaev honeycomb lattice model and so on, appears as the short range coupling case of the knot lattice model. We introduced link lattice pattern as geometric representation of the eigenstate of quantum many body model to explore the topological nature of quantum eigen-states. For example, a convection flow loop is introduced into the well-know BCS fermions pairing model to show the Pseudo-gap state in unconventional super-conducting state. The integral and fractional filling numbers in quantum Hall system is directly quantized by topological linking number. The quantum phase transition between different quantum states in quantum spin model is also directly quantified by the change of topological linking number, which revealed topological character of phase transition. This multi-knot lattice has a promising physical implementation by circularized photons in optical firbre network. It may also provide another different path to topological quantum computation.
Knot theory provides a powerful tool for understanding topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in a quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other, forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.
Quantum entanglement can be an effective diagnostic tool for probing topological phases protected by global symmetries. Recently, the notion of nontrivial topology in critical systems has been proposed and is attracting growing attention. In this work, as a concrete example, we explore the quantum entanglement properties of fermionic symmetry-enriched quantum critical points by constructing exactly solvable models based on stacked multiple Kitaev chains. We first analytically establish the global phase diagram using entanglement entropy and reveal three topologically distinct gapped phases with different winding numbers, along with three topologically distinct transition lines separating them. Importantly, we unambiguously demonstrate that two transition lines exhibit fundamentally different topological properties despite sharing the same central charge. Specifically, they display nontrivial topological degeneracy in the entanglement spectrum under periodic boundary conditions, thereby generalizing the Li-Haldane bulk-boundary correspondence to a broader class of fermionic symmetry-enriched criticality. Additionally, we identify a novel Lifshitz multicritical point at the intersection of the three transition lines, which also exhibits nontrivial topological degeneracy. This work provides a valuable reference for investigating gapless topological phases of matter from the perspective of quantum entanglement.