Fugacity-Resolved Stabilizer Entropy in Critical Quantum Chains: Discrete Selberg Sums and Exactly Solvable Rényi Indices

• URL: http://arxiv.org/abs/2608.06995v1
• Date: Fri, 07 Aug 2026 09:12:41 GMT
• Title: Fugacity-Resolved Stabilizer Entropy in Critical Quantum Chains: Discrete Selberg Sums and Exactly Solvable Rényi Indices
• Abstract summary: We introduce a fugacity-resolved partition function for the critical transverse-field Ising chain.<n>We map the fugacity-resolved all-minors sum, for every positive Rényi index, to a checkerboard-weighted discrete Selberg ensemble.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stabilizer Rényi entropy quantifies the nonstabilizerness of a quantum state through Rényi moments of its Pauli expectation-value distribution. Its standard form sums over Pauli-string degrees and retains only the total Rényi weight. We introduce a fugacity-resolved partition function for the critical transverse-field Ising chain that resolves this degree in the balanced Majorana representation and generates its full counting statistics. This Ising problem extends beyond a single model: exact decimation identities and the correspondence with the half-filled \(XX\) chain establish it as a common finite-size building block for stabilizer and computational-basis Shannon--Rényi entropies. We map the fugacity-resolved all-minors sum, for every positive Rényi index, to a checkerboard-weighted discrete Selberg ensemble on a half-filled doubled root lattice. For positive integer indices, it reduces to a finite aliased Dyson constant term. At \(α=\tfrac12,1,2\), determinant and Pfaffian compressions yield product formulas. At \(α=4\), the generic-fugacity problem admits an exact inverse Jack--Kostka representation, while at unit fugacity a complementary middle-minor identity relates it to the square of the \(α=2\) result. These generating functions determine the balanced-degree statistics. Complement symmetry makes the distribution symmetric about \(k=L/2\), with an index-dependent width. It is exactly binomial at \(α=1\), has variance proportional to \(L\) at \(α=\tfrac12\), and develops an \(L\log L\) enhancement at \(α=2\). After variance rescaling, the centered distributions converge to Gaussian limits at all three indices. Beyond these solvable cases, finite-size numerics reveal an evolution from a central peak to a symmetric bimodal profile and eventually to endpoint dominance as the Rényi index increases.

Related papers

• Regularized barycentric Rényi divergences [6.599344783327054]
  Barycentric Rényi divergences were introduced in [Mosonyi, Bunth, Vrana, Linear Algebra and its Applications, 2024] as an alternative to standard Kubo-Ando constructions.<n>They are defined via a variational expression and depend on a finite collection of quantum relative entropies $Dq_x$.
  arXiv  Detail & Related papers  (2026-09-15T17:53:27Z)
• Finite-Time Node Separation in Recurrent Graph Neural Networks with Persistent Gaussian Perturbations [2.8427946758947304]
  We provide a complementary finite-time analysis of the same persistent-noise architecture.<n>We first prove an exact second-moment decomposition for the expected squared distance between any two node representations.
  arXiv  Detail & Related papers  (2026-09-12T13:06:41Z)
• Orientation-dependent Pauli noise in one-dimensional discrete-time quantum walks [41.99844472131922]
  We study the long-time dynamics of a one-dimensional discrete-time quantum walk under Pauli noise acting on the coin.<n>All channels induce a crossover from ballistic to diffusive spreading, with a second moment growing linearly at long times.<n>The quantum-to-classical transition is governed by the relative alignment of the noise, the coherent walk dynamics, and the initial state.
  arXiv  Detail & Related papers  (2026-09-11T18:02:03Z)
• A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition [39.146761527401424]
  This work introduces a proximal subgradient method for minimizing the sum of an expected cost.<n>We use the Kurdyka-Lojasiewicz (KL) property to guarantee convergence of the whole trajectory to a single stationary point.
  arXiv  Detail & Related papers  (2026-08-05T23:07:27Z)
• Universal Crossovers of Stabilizer Entropy Beyond Criticality [0.0]
  We show that stabilizer entropy contains universal critical data and boundary-sensitive terms.<n>We derive exact finite-size formulas for both full periodic chains and finite intervals of the infinite chain.<n>Our results provide an exact lattice benchmark for the emerging QFT description of stabilizer entropy beyond isolated conformal points.
  arXiv  Detail & Related papers  (2026-06-11T18:27:11Z)
• A Note on Stability for Orthogonalized Matrix Momentum with Client Sampling [7.035974899001363]
  We derive a finite-round upper-tail guarantee from a coupled-neighbor recursion stability and a weighted concentration step.<n>A one-dimensional counterexample shows why a gap, smoothing, or regularity condition is necessary.
  arXiv  Detail & Related papers  (2026-06-01T05:36:26Z)
• 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)
• Stabilizing Fixed-Point Iteration for Markov Chain Poisson Equations [49.702772230127465]
  We study finite-state Markov chains with $n$ states and transition matrix $P$.<n>We show that all non-decaying modes are captured by a real peripheral invariant subspace $mathcalK(P)$, and that the induced operator on the quotient space $mathbbRn/mathcalK(P) is strictly contractive, yielding a unique quotient solution.
  arXiv  Detail & Related papers  (2026-01-31T02:57:01Z)
• Stabilizer-Shannon Renyi Equivalence: Exact Results for Quantum Critical Chains [0.0]
  Shannon-Renyi and stabilizer entropies are key diagnostics of structure, non-stabilizerness, phase transitions, and in quantum many-body states.<n>Specializing to the transverse-field Ising (TFI) chain, the TFI ground state stabilizer entropies maps to the Shannon-Renyi entropies of the XX-chain ground state of length $2L$.<n>Building on this correspondence, together with other exact identities we prove, closed expressions for the stabilizer entropy at indices $alpha=frac12,2,4$ for a broad class of critical
  arXiv  Detail & Related papers  (2025-09-12T21:32:10Z)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• On noise in swap ASAP repeater chains: exact analytics, distributions and tight approximations [9.32782060570252]
  Losses are one of the main bottlenecks for the distribution of entanglement in quantum networks.<n>We analytically investigate the case of equally-spaced repeaters.<n>We find exact analytic formulae for all moments of the fidelity up to 25 segments.
  arXiv  Detail & Related papers  (2024-04-10T16:24:51Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Toward Better Generalization Bounds with Locally Elastic Stability [41.7030651617752]
  We argue that locally elastic stability implies tighter generalization bounds than those derived based on uniform stability. We revisit the examples of bounded support vector machines, regularized least square regressions, and gradient descent.
  arXiv  Detail & Related papers  (2020-10-27T02:04:53Z)
• On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration [115.1954841020189]
  We study the inequality and non-asymptotic properties of approximation procedures with Polyak-Ruppert averaging. We prove a central limit theorem (CLT) for the averaged iterates with fixed step size and number of iterations going to infinity.
  arXiv  Detail & Related papers  (2020-04-09T17:54:18Z)

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.