DMRG in nuclear physics

Density matrix renormalization group

First articles

• S. R. White
  Density-matrix algorithms for quantum renormalization groups
  Phys. Rev. B 48, 10345 (1993) article

• S. R. White
  Density matrix formulation for quantum renormalization groups
  Phys. Rev. Lett. 69, 2863 (1992) article

Book and Review

• U. Schollwöck
  The density-matrix renormalization group
  Rev. Mod. Phys. 77, 259 (2005) article

• I. Peschel, X. Wang, M. Kaulke, and K. Hallberg
  Density-Matrix Renormalization - A New Numerical Method in Physics
  Springer-Verlag Berlin Heidelberg, 1st, 1999 book

Density matrix renormalization group in nuclear physics

$m$-scheme shell model formulation

• T. Papenbrock, and D. J. Dean
  Density matrix renormalization group and wavefunction factorization for nuclei
  J. Phys. G 31, S 1377 (2005) article
  • Convergence issue noticed in $m$-scheme
• S. Pittel, and J. Dukelsky
  The density matrix renormalization group in nuclear physics: a status report
  Rev. Mex. Fis. 49 Supl. 4, 82 (2003)
  • Suggest $j$-scheme to solve convergence issues in $m$-scheme

• J. Dukelsky, S. Pittel, S. S. Dimitrova, and M. V. Stoitsov
  Density matrix renormalization group method and large-scale nuclear shell-model calculations
  Phys. Rev. C 65, 054319 (2002) article

• S. Pittel, and J. Dukelsky
  The density matrix renormalization group: a new approach to large-scale nuclear structure calculations
  Rev. Mex. Fis. 47 Supl. 2, 42 (2001)
  • Convergence issue noticed

• J. Dukelsky, and S. Pittel
  New approach to large-scale nuclear structure calculations
  Phys. Rev. C 63, 061303(R) (2001) article

• J. Dukelsky, and G. G. Dussel
  Application of the density matrix renormalization group to the two level pairing model
  Phys. Rev. C 59, R3005(R) (1999) article

Convergence issues in $m$-scheme solved in $j$-scheme shell model

• S. Pittel, and B. Thakur
  The density matrix renormalization group and the nuclear shell model
  Rev. Mex. Fis. 55, 108 (2009)

• B. Thakur, S. Pittel, and N. Sandulescu
  Density matrix renormalization group study of ${ {}^{48}\text{Cr} }$ and ${ {}^{56}\text{Ni} }$
  Phys. Rev. C 78, 041303(R) (2008) article

• S. Pittel, B. Thakur, and N. Sandulescu
  The density matrix renormalization group and the nuclear shell model
  Int. J. Mod. Phys. E 17, 122 (2008) article

• S. Pittel, and N. Sandulescu
  Density matrix renormalization group and the nuclear shell model
  Phys. Rev. C 73, 014301 (2006) article

• J. Dukelsky, and S. Pittel
  The density matrix renormalization group for finite Fermi systems Rep. Prog. Phys. 67, 513 (2004) article

Reordering of states in the medium to reduce the $m$-scheme convergence issue

• Ö. Legeza, L. Veis, A. Poves, and J. Dukelsky
  Advanced density matrix renormalization group method for nuclear structure calculations
  Phys. Rev. C 92, 051303(R) (2015) article

$j$-scheme shell model formulation in the Berggren basis (Gamow-DMRG)

• J. Rotureau, N. Michel, W. Nazarewicz, M. Płoszajczak, and J. Dukelsky
  Density matrix renormalization group approach to two-fluid open many-fermion systems
  Phys. Rev. C 79, 014304 (2009) article

• J. Rotureau, N. Michel, W. Nazarewicz, M. Płoszajczak, and J. Dukelsky
  Density matrix renormalisation group approach for many-body open quantum systems
  Phys. Rev. Lett. 97, 110603 (2006) article

Idea of the Gamow-DMRG emitted in the middle of a paper

• N. Michel, W. Nazarewicz, M. Płoszajczak, and J. Rotureau
  Gamow shell-model description of weakly bound and unbound nuclear states
  Revista Mexicana De Fisica 5 Suplemento 2, 74 (2004)

Density matrix renormalization group applied on nuclear open quantum systems (J. Rotureau)

Ab initio Hamiltonians for systems with ${ A=3-6 }$

• K. Fossez, J. Rotureau, N. Michel, and M. Płoszajczak
  Can tetraneutron be a narrow resonance?
  Phys. Rev. Lett. 119, 032501 (2017) article arXiv

• Ik Jae Shin, Youngman Kim, P. Maris, J. P. Vary, C. Forssén, J. Rotureau, and N. Michel
  Ab initio no-core solutions for ${ {}^{6}\text{Li} }$
  J. Phys. G 44, 075103 (2017) article arXiv

• G. Papadimitriou, J. Rotureau, N. Michel, M. Płoszajczak, and B. R. Barrett
  Ab-initio no-core Gamow shell model calculations with realistic interactions
  Phys. Rev. C 88, 044318 (2013) article arXiv

Effective Hamiltonians with up to 10 valence nucleons

• K. Fossez, J. Rotureau, and W. Nazarewicz
  Energy spectrum of neutron-rich helium isotopes: complex made simple
  Phys. Rev. C 98, 061302(R) (2018) article arXiv

• M. D. Jones, K. Fossez, T. Baumann, P. A. DeYoung, J. E. Finck, N. Frank, A. N. Kuchera, N. Michel, W. Nazarewicz, J. Rotureau, J. K. Smith, S. L. Stephenson, K. Stiefel, M. Thoennessen, and R. G. T. Zegers
  Search for excited states in ${ {}^{25}\mathrm{O} }$
  Phys. Rev. C 96, 054322 (2017) article arXiv

• K. Fossez, J. Rotureau, N. Michel, and W. Nazarewicz
  Continuum effects in neutron-drip-line oxygen isotopes
  Phys. Rev. C 96, 024308 (2017) article arXiv

• K. Fossez, J. Rotureau, N. Michel, Q. Liu, and W. Nazarewicz
  Single-particle and collective motion in unbound deformed ${ {}^{39}\text{Mg} }$
  Phys. Rev. C 94, 054302 (2016) article

• G. Papadimitriou, A. T. Kruppa, N. Michel, W. Nazarewicz, M. Płoszajczak, and J. Rotureau
  Charge radii and neutron correlation in helium halo nuclei
  Phys. Rev. C 84, 051304(R) (2011) article

Introduction of natural orbitals

The introduction of the natural orbitals basis dramatically accelerated the convergence of the energy with the number of iterations and effectively rendered the sweep phases unnecessary. This was introduced in:

• Ik Jae Shin, Youngman Kim, P. Maris, J. P. Vary, C. Forssén, J. Rotureau, and N. Michel
  Ab initio no-core solutions for ${ {}^{6}\text{Li} }$
  J. Phys. G 44, 075103 (2017) article arXiv

Natural orbitals

• L. Brillouin
  Diffraction de la lumière par des ultrasons
  Actualités Scientifiques et Industrielles. No. 59, 71, 159, Hermann et Cie., Paris (1933)