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Scientific Reports

Quantum phase transition in the Casten pyramid using entanglement entropy in the semi-classical approximation of IBM-2

Maryam Ghapanvari, M Sayedi, M. A. Jafarizadeh, Narjes Amiri

Published Jul 1, 2025• 1 citation
Publisher

Abstract

In this research, the quantum phase transition (QPT) in the Casten pyramid has been investigated using entanglement entropy. Energy surfaces and the entanglement entropy have been obtained within the framework of semi-classical approximation interacting boson model-2 (IBM-2) using Schmidt decomposition and coherent states formalism. The results showed that the entanglement entropy is a suitable and efficient tool for investigating QPT and determining critical points in the connected pathes to the $${U_{\pi \nu }}\left( 5\right)$$ limit, and pathes of $$S{U_{\pi \nu }}\left( 3 \right) \leftrightarrow {O_{\pi \nu }}\left( 6 \right) \leftrightarrow \overline{S{U_{\pi \nu }}\left( 3 \right) }$$ and $$SU_{\pi \nu }^*\left( 3 \right) \leftrightarrow {O_{\pi \nu }}\left( 6 \right) \leftrightarrow \overline{SU_{\pi \nu }^*\left( 3 \right) }$$ . The description of QPT using numerical analysis of energy surfaces confirms the results of entanglement entropy.

DOI
10.1038/s41598-025-06585-7

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Abstract In this work, the von Neumann entropy has been calculated and employed as a probe to analyse quantum phase transitions (QPTs) within the -Interacting Boson Model ( -IBM). The von Neumann entropy between the -boson and -boson sectors is used as an indicator of QPTs and as a robust observable for the theoretical analysis of the isotopes. The von Neumann entropy correctly characterises the QPT in the transition region. The numerical results show that the and isotopes are located in the and limits, respectively.
Analysis of the U(5)↔SU(3)U(5)\leftrightarrow SU(3)U(5)↔SU(3) transitional region from an entanglement-based perspective
The degree of entanglement between components of a bipartite system can serve as a useful criterion for studying Quantum Phase Transitions (QPT). The von Neumann entropy and generalized concurrence serve as measures, while Schmidt number and Schmidt gap are quantifiers; together, they are key tools for identifying QPT. Using these tools, we have examined the QPT in the [Formula: see text] region within the first version of the semiclassical approximation of the Interacting Boson Model (IBM-1). Additionally, the Kullback-Leibler divergence (KLD) was employed as a criterion to compare two probability distribution functions in order to identify the transition region and the critical point. The theoretical results indicated that the Schmidt number and Schmidt gap, the von Neumann entropy, generalized concurrence, and the KLD can characterize the transition behavior and critical point (X(5)) in this region. To verify these results in real nuclei, the Dysprosium isotopic chain was selected. Using the suggested entanglement measures, the symmetry limits and the critical point were identified. The results obtained are fully consistent with experimental evidence.
The entanglement exhibits extremal or singular behavior near quantum critical points (QCPs) in many condensed matter models. These intriguing phenomena, however, still call for a widely accepted understanding. In this paper we study this issue in holographic framework. We investigate the connection between the holographic entanglement entropy (HEE) and the quantum phase transition (QPT) in a lattice-deformed Einstein-Maxwell-Dilaton theory. Novel backgrounds exhibiting metal-insulator transitions (MIT) have been constructed in which both metallic phase and insulating phase have vanishing entropy density in zero temperature limit. We find that the first order derivative of HEE with respect to lattice parameters exhibits extremal behavior near QCPs. We propose that it would be a universal feature that HEE or its derivatives with respect to system parameters can characterize QPT in a generic holographic system. Our work opens a window for understanding the relation between entanglement and the QPT from a holographic perspective.
Abstract Based on the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), we study the quantum phase transition (QPT) of a spin-1/2 frustrated Heisenberg chain and show that QMA entropy can be a useful tool to detect QPT. For the six-site case, we choose the reduced two-site as the detecting system and obtain the analytical result of QMA entropy and its bound. We find that the QMA entropy of the ground state is discontinuous at the first-order QPT point. Meanwhile for the excited state, the catastrophe point of QMA entropy approaches the infinite-order QPT point, which is confirmed by the numerical results in the 8-, 10- and 12-site cases. Moreover, we study the behavior of QMA entropy undergoing the dephasing process. Interestingly, two-site QMA entropy can still indicate the QPT point when the state degenerates into a mixed state. In this sense, QMA entropy is more effective than quantum correlation in reflecting the quantum criticality.