Random matrix prediction of average entanglement entropy in non-Abelian symmetry sectors

• URL: http://arxiv.org/abs/2512.22942v1
• Date: Sun, 28 Dec 2025 14:10:16 GMT
• Title: Random matrix prediction of average entanglement entropy in non-Abelian symmetry sectors
• Authors: Anwesha Chakraborty, Lucas Hackl, Mario Kieburg,
• Abstract summary: We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global $mathrmSU(2)$ symmetry.<n>Our analysis uses features of random matrix ensembles and provides a fully analytical treatment for arbitrary spin densities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global $\mathrm{SU}(2)$ symmetry, constrained to fixed total spin $J$ and magnetization $J_z = 0$. Focusing on spin-$\tfrac12$ lattices and subsystem fractions $f < \frac{1}{2}$, we derive a asymptotic expression for the average entanglement entropy up to constant order in the system volume $V$. In addition to the expected leading volume law term, we prove the existence of a $\frac{1}{2}\log V$ finite-size correction resulting from the scaling of the Clebsch-Gordon coefficients and compute explicitly the $O(1)$ contribution reflecting angular-momentum coupling within magnetization blocks. Our analysis uses features of random matrix ensembles and provides a fully analytical treatment for arbitrary spin densities, thereby extending Page type results to non-Abelian sectors and clarifying how $\mathrm{SU}(2)$ symmetry shapes average entanglement.

Related papers

• Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition [46.176861415532095]
  We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions.<n>Our results exhibit a remarkable analogy to Anderson localization, with $G_AB$ corresponding to two-terminal conductance.<n>Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.
  arXiv  Detail & Related papers  (2025-07-15T13:44:14Z)
• Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond [40.79840141270367]
  Given an unnormalized probability density $piproptomathrme-V$, estimating its normalizing constant $Z=int_mathbbRdmathrme-V(x)mathrmdx$ or free energy $F=-log Z$ is a crucial problem in Bayesian statistics, statistical mechanics, and machine learning.<n>We propose a new algorithm based on reverse diffusion samplers, establish a framework for analyzing its complexity, and empirically demonstrate its efficiency in tackling multimodality.
  arXiv  Detail & Related papers  (2025-02-07T00:05:28Z)
• Entanglement asymmetry in the critical XXZ spin chain [0.0]
  We study the explicit breaking of a $SU(2)$ symmetry to a $U(1)$ subgroup employing the entanglement asymmetry. We consider as specific model the critical XXZ spin chain, which breaks the $SU(2)$ symmetry of spin rotations except at the isotropic point.
  arXiv  Detail & Related papers  (2024-07-08T22:16:22Z)
• Covariance-based method for eigenstate factorization and generalized singlets [0.0]
  We derive a general method for determining the necessary and sufficient conditions for exact factorization $|Psirangle=otimes_p |psi_prangle$ of an eigenstate of a many-body Hamiltonian $H$. The formalism is then used to derive exact dimerization and clusterization conditions in spin systems.
  arXiv  Detail & Related papers  (2023-11-08T01:43:33Z)
• Typical entanglement entropy in systems with particle-number conservation [3.692727995866036]
  We calculate the typical bipartite entanglement entropy $langle S_Arangle_N$ in systems containing indistinguishable particles of any kind.<n>We provide evidence that our results describe the entanglement entropy of highly excited eigenstates of quantum-chaotic spin and boson systems.
  arXiv  Detail & Related papers  (2023-10-30T18:00:00Z)
• Measurement-induced phase transition for free fermions above one dimension [46.176861415532095]
  Theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. Critical point separates a gapless phase with $elld-1 ln ell$ scaling of the second cumulant of the particle number and of the entanglement entropy.
  arXiv  Detail & Related papers  (2023-09-21T18:11:04Z)
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry [0.0]
  We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of local Hamiltonians and of random pure states. We provide numerical evidence that $s_A$ is smaller in highly excited eigenstates of integrable interacting Hamiltonians. In the context of Hamiltonian eigenstates we consider spins $mathfrakj=frac12$ and $1$, while for our calculations based on random pure states we focus on the spin $mathfrakj=frac12$ case
  arXiv  Detail & Related papers  (2023-05-18T18:00:00Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians [0.0]
  We show that the magnitude of the negative $O(1)$ correction is only slightly greater than the one predicted for random pure states. We derive a simple expression that describes the numerically observed $nu$ dependence of the $O(1)$ deviation from the prediction for random pure states.
  arXiv  Detail & Related papers  (2023-03-23T18:00:02Z)
• Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clustering [43.50783459690612]
  The method consists in randomly "puncturing" both the data matrix $XinmathbbCptimes n$ and its corresponding kernel (Gram) matrix $K$ through Bernoulli masks. We empirically confirm on GAN-generated image databases, that it is possible to drastically puncture the data, thereby providing possibly huge computational and storage gains.
  arXiv  Detail & Related papers  (2021-02-24T14:01:58Z)
• A Concentration of Measure and Random Matrix Approach to Large Dimensional Robust Statistics [45.24358490877106]
  This article studies the emphrobust covariance matrix estimation of a data collection $X = (x_1,ldots,x_n)$ with $x_i = sqrt tau_i z_i + m$. We exploit this semi-metric along with concentration of measure arguments to prove the existence and uniqueness of the robust estimator as well as evaluate its limiting spectral distribution.
  arXiv  Detail & Related papers  (2020-06-17T09:02:26Z)

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.