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Scaling of entanglement entropy and correlations in the variable-range extended Ising model

Harikrishnan K J1, Debasis Sadhukhan2,3, and Amit Kumar Pal1

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Phys. Rev. A 113, 052444 – Published 20 May, 2026

DOI: https://doi.org/10.1103/vgrd-dg8j

Abstract

We study the two-point correlation functions and the bipartite entanglement in the ground state of the exactly solvable variable-range extended Ising model of qubits in the presence of a transverse field on a one-dimensional lattice. We introduce the variation in the range of interaction by varying the coordination number Z of each qubit, where the interaction strength between a pair of qubits at a distance r varies as approximately r−α. We show that the algebraic nature of the correlation functions is present only up to r=Z, above which it exhibits short-range exponential scaling. We also show that at the critical point, the bipartite entanglement exhibits a power-law decrease (approximately Z−γ) with increasing coordination number irrespective of the partition size and the value of α for α>1. We further consider a sudden quench of the system starting from the ground state of the infinite-field limit of the system Hamiltonian via turning on the critical Hamiltonian and demonstrate that the long-time-averaged bipartite entanglement exhibits a qualitatively similar variation (approximately Z−γ) with Z.

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Phys. Rev. A 113, 052444– Published 20 May, 2026
  • Received 13 August 2025
  • Revised 22 February 2026
  • Accepted 22 April 2026
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