Analytical approach to quantum many body systems

PD 24/2020), financed by UEFISCDI.


Team: Dr. Virgil V. Baran (Director), Dr. Peter Schuck (Mentor)



A large amount of effort has been devoted to the understanding of the proton-neutron correlations responsible for the appearance of the quartet degrees of freedom in nuclear systems. Despite significant advances in the field, several computational shortcomings still prevent the quartet models for achieving their full potential. However, with the recent introduction of new analytical techniques by the project leader, these may finally be addressed.

As such, this project aims to provide a highly efficient approach for the description of the nuclear properties within an analytically upgraded quartet model and to study its new physical implications. In order to achieve this, multiple issues need to be addressed, in particular regarding the generalization of the quartet models to the description of excited states of nuclei.

The first objective of the project is related to fixing the last remaining broken symmetry of the quartet models, the rotational symmetry. This enables the following two objectives, that of developing a description of nuclear electromagnetic transitions and beta decay based on quartets and that of relating quartet condensation and alpha decay in heavy nuclei. The final objective is an attempt at cross-fertilization between various fields, i.e. to apply a quartet-BCS theory recently proposed by the project leader for nuclear systems to the study of quartet correlation in neutron stars and condensed matter systems like cold atomic gases.

Beside providing the nuclear physics community with a physically transparent alternative to the weighty shell model approach operating at the same level of precision, the work done within this project brings unique theoretical contributions to the understanding of physical phenomena of interest at top facilities, like ELI-NP. Also, new physical insight may be obtained regarding long standing open problems, for example why clustering occurs in the ground states of some nuclei but only in the excited states of others.



The most significant result obtained within the project has been the unification of two theoretical approaches for the description of the proton-neutron pairing correlations in nuclear systems, the Quartet Condensation Model (QCM) and the symmetry-restored BCS theory (PNTBCS), initially considered to be distinct in the literature [Phys. Rev. C 85, 061303(R), 2012]. The equivalence QCM=PNTBCS is significant both from the physical point of view (it links the structure of the states of the proton-neutron system to its fundamental symmetry properties), and from the computational point of view (the numerical calculations within the PNTBCS approach are more efficient than within QCM). This result, not initially foreseen in the original project proposal, has allowed the development of theoretical tools for the description of quantum many-body systems with applicability beyond nuclear physics, e.g. to quantum chemistry and condensed matter physics.


Scientific Report


Main Results

  • Within the project's first stage, an efficient technique for the angular momentum projection within the Quartet Condensation Model (QCM) has been developed. It is based on the remarkable equivalence between the QCM picture and the symmetry restored BCS picture for the nuclear correlations induced by the proton-neutron pairing interaction, established in [1] and further explored in [2].
  • Within the second stage of the project: an upgraded model based on quartetting was formulated and validated for the precise description of the correlations induced by the pairing interaction in atomic nuclei: the quartet correlations are incorporated through a set of coupled-cluster doubles excitations on top of a symmetry restored mean field BCS ansatz, as detailed in [3]. A framework for investigating alpha condensation in atomic nuclei has been formulated based on the annihilation operators of an alpha coherent state; a framework based on the the structurally similar annihilation operators of the number-projected BCS has been developed and validated for describing the properties of odd nuclear systems.
  • Within the third stage of the project, a combined theoretical approach based on the Density Matrix Renormalization Group + the Eigenvector Continuation techniques has been developed for the simultaneous efficient description of pairing, quartetting and many body correlations in nuclear systems. It has then been generalized for the description of condensed matter systems like hybrid quantum devices based on superconducting islands coupled to quantum dots, where it can be used as a tool to efficiently model realistic configurations of technological interest.



[1]  Bridging the quartet and pair pictures of isovector proton-neutron pairing,  V. V. Baran, D. R. Nichita, D. Negrea, D. S. Delion, N. Sandulescu, P. Schuck, Physical Review C 102, 061301(R) (2020).

[2] Structure of the quartetting ground state of N=Z nuclei, A. G. Serban, D. R. Nichita, D. Negrea, V. V. Baran, The European Physical Journal A 57 (1), 1-7 (2021).

[3] Variational theory combining number-projected BCS and coupled-cluster doubles, V.V. Baran, J. Dukelsky, Physical Review C 103, 054317 (2021).

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