Identifying chiral topological order in microscopic spin models by modular commutator

• URL: http://arxiv.org/abs/2510.06086v1
• Date: Tue, 07 Oct 2025 16:12:33 GMT
• Title: Identifying chiral topological order in microscopic spin models by modular commutator
• Authors: Avijit Maity, Aman Kumar, Vikram Tripathi,
• Abstract summary: We numerically obtain $c_-$ directly from single ground-state wave functions of two-dimensional interacting spin models with chiral topological order.<n>We find that the modular commutator yields results consistent with the expected topological quantum field theories.
• Score: 2.084969478024457
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The chiral central charge $c_-$ is a key topological invariant of the edge characterizing the bulk two-dimensional chiral topological order, but its direct evaluation in microscopic spin models has long been a challenge, especially for non-abelian topological order. Building on the recently developed modular commutator formalism, we numerically obtain $c_-$ directly from single ground-state wave functions of two-dimensional interacting spin models that have chiral topological order. This provides a geometry-independent and bulk diagnostic of chirality. We study two nonintegrable systems -- the Zeeman-Kitaev honeycomb model and the kagome antiferromagnet -- both subjected to scalar spin chirality perturbations. We find that the modular commutator yields results consistent with the expected topological quantum field theories. We also compute the topological entanglement entropy which provides an independent diagnostic of the topological orders. Our work establishes modular commutators as a powerful numerical probe of chiral topological order in strongly correlated quantum magnets.

Related papers

• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors [40.72140849821964]
  We consider the massive Thirring and Gross-Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$.<n>We prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$.<n>Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models.
  arXiv  Detail & Related papers  (2026-02-25T19:00:01Z)
• Probing disorder-driven topological phase transitions via topological edge modes with ultracold atoms in Floquet-engineered honeycomb lattices [37.09823149373976]
  We study disorder-driven phase transitions between two distinct Floquet topological phases using the characteristic properties of topological edge modes with ultracold atoms.<n>Our measurements confirm that disorder indeed favors the anomalous Floquet topological regime over conventional Hall systems.
  arXiv  Detail & Related papers  (2025-08-27T17:54:40Z)
• From Chern to Winding: Topological Invariant Correspondence in the Reduced Haldane Model [0.4249842620609682]
  We present an exact analytical investigation of the topological properties and edge states of the Haldane model defined on a honeycomb lattice with zigzag edges.<n>We show that the $nu$ exactly reproduces the Chern number of the parent model in the topologically nontrivial phase.<n>Our analysis further reveals the critical momentum $ k_c $ where edge states traverse the bulk energy gap.
  arXiv  Detail & Related papers  (2025-05-26T19:11:43Z)
• Amorphous quantum magnets in a two-dimensional Rydberg atom array [44.99833362998488]
  We propose to explore amorphous quantum magnets with an analog quantum simulator. We first present an algorithm to generate amorphous quantum magnets, suitable for Rydberg simulators of the Ising model. We then use semiclassical approaches to get a preliminary insight of the physics of the model.
  arXiv  Detail & Related papers  (2024-02-05T10:07:10Z)
• Emergent Topology in Many-Body Dissipative Quantum Matter [0.0]
  We study the dissipative dynamics of pseudo-Hermitian many-body quantum systems.<n>We find the same topological features for a wide range of parameters suggesting that they are universal.<n>In the limit of weak coupling to the bath, topological modes govern the approach to equilibrium.
  arXiv  Detail & Related papers  (2023-11-24T18:15:22Z)
• Low-dimensional polaritonics: Emergent non-trivial topology on exciton-polariton simulators [0.0]
  Polaritonic lattice configurations in dimensions $D=2$ are used as simulators of topological phases, based on symmetry class A Hamiltonians. We provide a comprehensive mathematical framework, which fully addresses the source and structure of topological phases in coupled polaritonic array systems.
  arXiv  Detail & Related papers  (2023-10-31T04:22:58Z)
• Higher-order topological Peierls insulator in a two-dimensional atom-cavity system [58.720142291102135]
  We show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The pattern opens a non-trivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states. Our work shows how atomic quantum simulators can be harnessed to investigate novel strongly-correlated topological phenomena.
  arXiv  Detail & Related papers  (2023-05-05T10:25:14Z)
• Chiral spin liquid in a $\mathbb{Z}_3$ Kitaev model [5.744548689698076]
  We study a $mathbbZ_3$ Kitaev model on the honeycomb lattice with nearest neighbor interactions. We find evidence that, with ferromagnetic isotropic couplings, the model realizes a chiral spin liquid.
  arXiv  Detail & Related papers  (2023-02-10T05:34:04Z)
• $U(1)$ symmetry-enriched toric code [0.0]
  We study a generalization of Kitaev's $mathbb Z$ toric code on a square lattice with an additional global $U(1)$ symmetry. We find strong evidence for a topologically ordered ground state manifold with indications of UV/IR mixing. We propose a candidate experimental realization of the model in an array of superconducting quantum wires.
  arXiv  Detail & Related papers  (2023-02-07T19:00:23Z)
• Intrinsically Interacting Higher-Order Topological Superconductors [19.52773844535185]
  We propose a minimal interacting lattice model for two-dimensional class-$D$ higher-order topological superconductors. A Lieb-Schultz-Mattis-type constraint is proposed and applied to guide our lattice model construction.
  arXiv  Detail & Related papers  (2022-12-26T04:48:28Z)
• Measuring quantum geometric tensor of non-Abelian system in superconducting circuits [21.82634956452952]
  We use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. We reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.
  arXiv  Detail & Related papers  (2022-09-26T01:08:39Z)
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice [0.0]
  We consider a non-Hermitian Hamiltonian with pseudo-Hermiticity for a system of bosons in a honeycomb lattice. Such a system is capable of acting as a topological amplifier, under time-reversal symmetry. We construct a convenient analytical description for the edge modes of the Haldane model in semi-infinite planes.
  arXiv  Detail & Related papers  (2021-10-07T02:00:12Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.