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To understand the dynamics of quantum many-body systems, it is essential to study excited eigenstates. While tensor network states have become a standard tool for computing ground states in computational many-body physics, obtaining accurate excited eigenstates remains a significant challenge. In this work, we develop an approach that combines the inexact Lanczos method, which is designed for efficient computations of excited states, with tree tensor network states (TTNSs). We demonstrate our approach by computing excited vibrational states for three challenging problems: (1) 122 states in two different energy intervals of acetonitrile (12-dimensional), (2) Fermi resonance states of the fluxional Zundel ion (15-dimensional), and (3) selected excited states of the fluxional and very correlated Eigen ion (33-dimensional). The proposed TTNS inexact Lanczos method is directly applicable to other quantum many-body systems.
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This content will become publicly available on December 1, 2025
Mass-Energy Compensation Effect of 3$$\alpha$$ Hamiltonian
The 3α phenomenological model describes the structure of the carbon-12 nucleus as a cluster of three alpha particles. This model includes a pairwise α–α interaction and a three-body force. To fit the three-body potential, the 12C data are used, while ensuring that the pair potential reproduces the α–α scattering data. Alternatively, the mass-energy compensation (MEC) effect can be used to simulate the effect of the three-body potential by adjusting the mass of the α particle within the effective-mass approach. We demonstrate the MEC effect for the 3α ground state by numerically solving the differential Faddeev equation, in which the α–α interaction is described by the Ali-Bodmer potential. The effective masses of α particles are evaluated for the ground and excited 0+ and bound 2+ states. We demonstrate a coupling between the ground and first excited 0+ states, indicated by an anti-crossing of these energy levels in the energy–mass coordinates. A correspondence between the effective mass and a three-body potential is demonstrated. We discuss the results of the 0+2 calculations for various models of the α–α interaction.
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- Award ID(s):
- 2101041
- PAR ID:
- 10642164
- Publisher / Repository:
- Physics of Atomic Nuclei
- Date Published:
- Journal Name:
- Physics of Atomic Nuclei
- Volume:
- 87
- Issue:
- S2
- ISSN:
- 1063-7788
- Page Range / eLocation ID:
- S274 to S283
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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