Bootstrapping Symmetries in Quantum Many-Body Systems from the Cross Spectral Form Factor

• URL: http://arxiv.org/abs/2604.01296v1
• Date: Wed, 01 Apr 2026 18:02:36 GMT
• Title: Bootstrapping Symmetries in Quantum Many-Body Systems from the Cross Spectral Form Factor
• Abstract summary: We introduce a bootstrap framework to reconstruct the representation theory of hidden finite group symmetries of quantum many-body lattice Hamiltonians.<n>Our framework applies equally well to chaotic and integrable many-body systems.
• Score: 6.8996092922585675
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Symmetries play a central role in quantum many-body physics, yet uncovering them systematically remains challenging. We introduce a bootstrap framework designed to reconstruct the representation theory of hidden finite group symmetries of quantum many-body lattice Hamiltonians, using only a known symmetry subgroup $N$ and spectral correlations between its symmetry sectors. We introduce a novel variant of the spectral form factor, the cross spectral form factor (xSFF), which we compute via exact diagonalization to seed the bootstrap algorithm. By applying the constraints derived from these data alongside the algebraic conditions of the fusion rules, our bootstrap procedure sharply restricts the set of candidate groups $G$. Remarkably, without any prior assumptions regarding the full symmetry group $G$, our method can systematically recover its representation-theoretic data, including the number and dimensions of the irreducible representations, their branching rules with respect to $N$, the fusion algebra, and the full character table. This framework applies equally well to chaotic and integrable many-body systems and accommodates both unitary and anti-unitary symmetries. Through various examples, we demonstrate that the underlying group $G$ can be uniquely identified. In particular, our bootstrap independently recovers the $\mathbb{Z}_4$ symmetry at the self-dual point of the three-state quantum torus chain, detects signatures of projective representations in the effective Hamiltonian of the driven Bose-Hubbard model, and rediscovers the $η$-pairing $\mathrm{SO}(4)$ symmetry of the one-dimensional Fermi-Hubbard model. Our framework thus establishes a practical route to identify symmetries directly from dynamical spectral observables.

Related papers

• A homotopy-type-theoretic generalization of neurosymbolic inference [46.36639624013224]
  neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $$-structures.<n>We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind reasoning shortcuts.
  arXiv  Detail & Related papers  (2026-06-16T12:22:12Z)
• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• $\mathcal{PT}$-like phase transitions from square roots of supersymmetric Hamiltonians [0.0]
  We introduce a general framework for realizing $mathcalPT$-like phase transitions in non-Hermitian systems.<n>This work uncovers new links between non-Hermitian physics and supersymmetry.
  arXiv  Detail & Related papers  (2025-11-16T23:38:51Z)
• Entanglement Sum Rule from Higher-Form Symmetries [0.0]
  We prove an entanglement sum rule for $(d-1)$-dimensional quantum lattice models with finite abelian higher-form symmetries.<n>The framework explains and generalizes known examples in fermion-$mathbbZ$ gauge theory.
  arXiv  Detail & Related papers  (2025-10-20T09:03:12Z)
• Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries [20.76275069383104]
  We show that simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras.<n>We show that our work provides a bridge between well-understood topological defect symmetries and those that arise in more realistic models.
  arXiv  Detail & Related papers  (2025-09-03T18:01:22Z)
• Axis-level Symmetry Detection with Group-Equivariant Representation [48.813587457507786]
  Recent heatmap-based approaches can localize potential regions of symmetry axes but often lack precision in identifying individual axes.<n>We propose a novel framework for axis-level detection of the two most common symmetry types-reflection and rotation.<n>Our method achieves state-of-the-art performance, outperforming existing approaches.
  arXiv  Detail & Related papers  (2025-08-14T15:26:53Z)
• Meson spectroscopy of exotic symmetries of Ising criticality in Rydberg atom arrays [39.58317527488534]
  Coupling two Ising chains in a ladder leads to an even richer $mathcalD(1)_8$ symmetries.<n>Here, we probe these emergent symmetries in a Rydberg atom processing unit, leveraging its geometry to realize both chain and ladder configurations.
  arXiv  Detail & Related papers  (2025-06-26T14:19:30Z)
• Symmetry, entanglement, and the $S$-matrix [0.0]
  We show that constraining the $S$-matrix to the span of minimally entangling operators is equivalent to realizing an emergent $SU(N)$ global symmetry.
  arXiv  Detail & Related papers  (2025-04-29T18:00:01Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Invariant Neural Network Ansatz for weakly symmetric Open Quantum Lattices [0.0]
  We show that, whenever the steady state is unique, one can introduce a neural network representation for the system density operator. We demonstrate the validity of our approach by determining the steady state structure of the one dimensional dissipative XYZ model in the presence of a uniform magnetic field.
  arXiv  Detail & Related papers  (2021-01-10T09:51:29Z)

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.