Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Analysis of the $$U(5)\leftrightarrow SU(3)$$ transitional region from an entanglement-based perspective

Maryam Ghapanvari, M Sayedi, N. Amiri, Jafarizadeh

Published Jun 24, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-026-43378-y

Related papers

Probing quantum phase transitions in the sdg -Interacting Boson Model using von neumann entropy

Maryam Ghapanvari, M Sayedi, Narjes Amiri +1 more

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.

Chinese Physics C•Jun 2, 2026•0 citations

Ground-state entanglement and preserved dynamical symmetry in the interacting boson model

Feng Pan, Yingxin Wu, L. R. Dai +1 more

We introduce an exact bipartite entanglement entropy between the s - and d -boson degrees of freedom in the interacting boson model (IBM), evaluated from finite- N eigenstates with good angular momentum. Unlike coherent-state approaches, the present formulation avoids mixing different angular-momentum sectors. The entanglement entropy reproduces the expected signatures of the U(5)–SU(3) [ S U ‾ (3)] and U(5)–O(6) shape transitions, while revealing a pronounced minimum at the O(6) point along the SU(3)–O(6)– S U ‾ (3) path, in sharp contrast to previous coherent-state results. We show that critical quantum fluctuations govern the local enhancement of entanglement near transition regions, whereas the entanglement hierarchy at the dynamical-symmetry limits is governed by the preserved local dynamical symmetry of the Schmidt-partitioned s - d space. The entanglement is weakest at the U(5) limit, intermediate at the O(6) limit, and strongest at the SU(3) [ S U ‾ (3)] limits, revealing an inverse correlation between preserved local dynamical symmetry and quantum entanglement in the finite- N IBM.

Physics Letters B•Oct 12, 2026•0 citations

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 +1 more

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.

Scientific Reports•Jul 1, 2025•1 citation

Entanglement entropy as a signature of a quantum phase transition in nuclei in the framework of the interacting boson model and interacting boson-fermion model

M. A. Jafarizadeh, Maryam Ghapanvari, Narjes Amiri

Background: One of the fundamental problems of quantum information science is quantum entanglement. Recently, quantum phase transition in nuclear systems is studied in connection with quantum entanglement.Purpose: In this paper, the use of entanglement entropy as a suitable signal for the study of quantum phase transition in the even-even and odd-$A$ nuclei is investigated. The effect of the coupling of a single fermion to a boson core on entanglement entropy is studied.Method: By use of the affine $SU(1,1)$ Lie algebra and through the Schmidt decomposition in the framework of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), entanglement entropy in the even-even and odd-$A$ are obtained. The entanglement entropy is used for tracking and studying the shape phase transition in these nuclei.Results: The entanglement entropy in the IBM and the IBFM is calculated. The entanglement entropy values of the low-lying states of $^{122--134}\mathrm{Xe}, ^{102--110}\mathrm{Pd}$, and $^{123--133}\mathrm{Xe}$ were calculated and analyzed. It is found that entanglement entropy is a suitable order parameter to detect shape phase transition in nuclear systems.Conclusions: The obtained results indicate that the entropy of entanglement is sensitive to the shape-phase transition between spherical and $\ensuremath{\gamma}$-unstable regions in nuclei. The results show that entanglement entropy is a powerful tool for identifying shape phase transitions in nuclei. It is found that the coupling of the single fermion with angular momentum $j$ to the even-even system does not change the geometry imposed by the boson core performing the transition and only the entanglement entropy values have been shifted by the addition of the odd particle with respect to the even case.

Physical Review C•Jan 6, 2022•14 citations

Quantum Phase Transitions, Entanglement Spectrum, and Schmidt Gap in Bond-AlternativeS= 1 Antiferromagnetic Chain

Guanghua Liu, Yu Zhang, Guang-Shan Tian

Bipartite entanglement, entanglement spectrum, and Schmidt gap in S=1 bond-alternative antiferromagnetic Heisenberg chain are investigated by the infinite time-evolving block decimation (iTEBD) method. The quantum phase transition (QPT) from the singlet-dimer phase to the Haldane phase can be detected by the singular behavior of bipartite entanglement, the sudden change of the entanglement spectrum, and the completely vanishing of the Schmidt gap. The critical point is determined to be around r c ≃ 0.587, and the second-order character of the QPT is verified. Doubly degenerate entanglement spectra of both even and odd bonds are observed in the Haldane phase, by which one can distinguish the Haldane phase from the singlet-dimer phase easily. Nearest-neighbor antiferromagnetic correlations and next-nearest-neighbor ferromagnetic correlations are found in the whole parameter region. At the critical massless point, although exponentially decaying antiferromagnetic correlation is observed, it approaches to a constant value finally. Therefore, long-range correlations exist and the correlation length becomes divergent at the critical point.

Communications in Theoretical Physics•Jun 1, 2014•7 citations

Emergent spectral degeneracies in the quantum phase transitions in the interacting boson model

Yu Zhang, Qiu‐Yue Li, Xiao-Xia Wang

The spectral degeneracies emerging in the critical region of the interacting boson model are systematically investigated. The results indicate that the level crossings in the transitions from the U(5) to the SU(3) quasidynamical symmetry can induce the approximate spectral degeneracies along the first-order transitional line for large boson number $N$. The remnants of these types of degeneracies in finite-$N$ systems have been preliminarily identified from the low-lying spectra of $^{150}\mathrm{Nd}$. In addition, the similar approximate degeneracies emerging in the phase transition between the U(5) and SO(6) quasidynamical symmetries are parallel emphasized and those in other critical models are also mentioned.

Physical Review C•May 31, 2016•1 citation
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.
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.
We introduce an exact bipartite entanglement entropy between the s - and d -boson degrees of freedom in the interacting boson model (IBM), evaluated from finite- N eigenstates with good angular momentum. Unlike coherent-state approaches, the present formulation avoids mixing different angular-momentum sectors. The entanglement entropy reproduces the expected signatures of the U(5)–SU(3) [ S U ‾ (3)] and U(5)–O(6) shape transitions, while revealing a pronounced minimum at the O(6) point along the SU(3)–O(6)– S U ‾ (3) path, in sharp contrast to previous coherent-state results. We show that critical quantum fluctuations govern the local enhancement of entanglement near transition regions, whereas the entanglement hierarchy at the dynamical-symmetry limits is governed by the preserved local dynamical symmetry of the Schmidt-partitioned s - d space. The entanglement is weakest at the U(5) limit, intermediate at the O(6) limit, and strongest at the SU(3) [ S U ‾ (3)] limits, revealing an inverse correlation between preserved local dynamical symmetry and quantum entanglement in the finite- N IBM.
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 Uπν(5){U_{\pi \nu }}\left( 5\right)Uπν​(5) limit, and pathes of SUπν(3)↔Oπν(6)↔SUπν(3)‾S{U_{\pi \nu }}\left( 3 \right) \leftrightarrow {O_{\pi \nu }}\left( 6 \right) \leftrightarrow \overline{S{U_{\pi \nu }}\left( 3 \right) }SUπν​(3)↔Oπν​(6)↔SUπν​(3)​ and SUπν∗(3)↔Oπν(6)↔SUπν∗(3)‾SU_{\pi \nu }^*\left( 3 \right) \leftrightarrow {O_{\pi \nu }}\left( 6 \right) \leftrightarrow \overline{SU_{\pi \nu }^*\left( 3 \right) }SUπν∗​(3)↔Oπν​(6)↔SUπν∗​(3)​ . The description of QPT using numerical analysis of energy surfaces confirms the results of entanglement entropy.
Background: One of the fundamental problems of quantum information science is quantum entanglement. Recently, quantum phase transition in nuclear systems is studied in connection with quantum entanglement.Purpose: In this paper, the use of entanglement entropy as a suitable signal for the study of quantum phase transition in the even-even and odd-AAA nuclei is investigated. The effect of the coupling of a single fermion to a boson core on entanglement entropy is studied.Method: By use of the affine SU(1,1)SU(1,1)SU(1,1) Lie algebra and through the Schmidt decomposition in the framework of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), entanglement entropy in the even-even and odd-AAA are obtained. The entanglement entropy is used for tracking and studying the shape phase transition in these nuclei.Results: The entanglement entropy in the IBM and the IBFM is calculated. The entanglement entropy values of the low-lying states of 122−−134Xe,102−−110Pd^{122--134}\mathrm{Xe}, ^{102--110}\mathrm{Pd}122−−134Xe,102−−110Pd, and 123−−133Xe^{123--133}\mathrm{Xe}123−−133Xe were calculated and analyzed. It is found that entanglement entropy is a suitable order parameter to detect shape phase transition in nuclear systems.Conclusions: The obtained results indicate that the entropy of entanglement is sensitive to the shape-phase transition between spherical and $\ensuremath{\gamma}$-unstable regions in nuclei. The results show that entanglement entropy is a powerful tool for identifying shape phase transitions in nuclei. It is found that the coupling of the single fermion with angular momentum jjj to the even-even system does not change the geometry imposed by the boson core performing the transition and only the entanglement entropy values have been shifted by the addition of the odd particle with respect to the even case.
Bipartite entanglement, entanglement spectrum, and Schmidt gap in S=1 bond-alternative antiferromagnetic Heisenberg chain are investigated by the infinite time-evolving block decimation (iTEBD) method. The quantum phase transition (QPT) from the singlet-dimer phase to the Haldane phase can be detected by the singular behavior of bipartite entanglement, the sudden change of the entanglement spectrum, and the completely vanishing of the Schmidt gap. The critical point is determined to be around r c ≃ 0.587, and the second-order character of the QPT is verified. Doubly degenerate entanglement spectra of both even and odd bonds are observed in the Haldane phase, by which one can distinguish the Haldane phase from the singlet-dimer phase easily. Nearest-neighbor antiferromagnetic correlations and next-nearest-neighbor ferromagnetic correlations are found in the whole parameter region. At the critical massless point, although exponentially decaying antiferromagnetic correlation is observed, it approaches to a constant value finally. Therefore, long-range correlations exist and the correlation length becomes divergent at the critical point.
The spectral degeneracies emerging in the critical region of the interacting boson model are systematically investigated. The results indicate that the level crossings in the transitions from the U(5) to the SU(3) quasidynamical symmetry can induce the approximate spectral degeneracies along the first-order transitional line for large boson number NNN. The remnants of these types of degeneracies in finite-NNN systems have been preliminarily identified from the low-lying spectra of 150Nd^{150}\mathrm{Nd}150Nd. In addition, the similar approximate degeneracies emerging in the phase transition between the U(5) and SO(6) quasidynamical symmetries are parallel emphasized and those in other critical models are also mentioned.