Numerical studies of correlated electron systems

• Applicant: Professor Dr. Fakher Fakhry Assaad
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2003 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5403159

• Final Report Year: 2014

Final Report Abstract

Approximation free numerical simulations of models of many fermion systems generically scale exponentially with system size on classical computers. There is however no fundamental theorem which states that it is impossible to come up with clever algorithms to solve in polynomial time a set of outstanding issues. During the funding period of this DFG grant proposal, we have enlarging the class of problems which can be solved in polynomial time. This includes numerical simulations of correlated topological insulators, as summarized above, or simulations of SU(N)-symmetric model Hamiltonians. We have also developed and tested novel algorithms. The Gaussian QMC approach had the potential of circumventing the minus sign problem inherent to QMC methods for a large class of problems including the Hubbard model on arbitrary lattice topologies. Extensive work has shown that although the sign problem can be avoided, the probability distribution one has to sample turns out to ill defined (i.e. fat tails). We have further developed the so called weak coupling continuous time QMC algorithm (CT-INT) introduced by Rubtsov et al. Here our contributions are two-fold. On one hand we have extended the approach to include bosonic baths (e.g. phonons) and on the other hand we have tested projective T = 0 schemes. This development has lead to a number of applications and insights in the domain of electron phonon systems. The combination of modern high performance massively parallel computers and algorithmic developments provides constant advance in our understanding of correlated electron systems. The progress we have achieved during this grant proposal will and has allowed us to tackle a number of fascinating issues. Here we can mention the interplay between spin-orbit coupling and correlations, concepts in entanglement entropy and entanglement spectra, and finally the understanding of the quantum criticality between semi-metals and anti-ferromagnetic Mott insulators. Let us finally mention that this project has been awarded the ”NIC-Exzellenzprojekte” prize in 2012. We have equally done our best to communicate our research to a wider audience by accepting an invitation for a contribution in the Innovatives Supercomputing in Deutschland (inSiDe) magazine in 2013.

Publications

• Diagrammatic determinantal quantum monte carlo methods: Projective schemes and applications to the hubbard-holstein model Phys. Rev. B 76, 035116, (2007)
  F. F. Assaad and T. C. Lang
  
• Spin gap and string order parameter in the ferromagnetic spiral staircase heisenberg ladder: A quantum Monte Carlo study Phys. Rev. Lett. 100, 017202, (2008)
  C. Brunger, F. F. Assaad, S. Capponi, F. Alet, D. N. Aristov, and M. N. Kiselev
  
• Spin, charge, and single-particle spectral functions of the one-dimensional quarter filled holstein model Phys. Rev. B 78, 155124, (2008)
  F. F. Assaad
  
• Magnetic field induced semimetal-to-canted-antiferromagnet transition on the honeycomb lattice Phys. Rev. B 80, 045412, (2009)
  M. Bercx, T. C. Lang, and F. F. Assaad
  
• Fermi surface topology of the two-dimensional kondo lattice model: Dynamical cluster approximation approach Phys. Rev. B 82, 245105, (2010)
  L. C. Martin, M. Bercx, and F. F. Assaad
  
• Quantum spin-liquid emerging in two-dimensional correlated dirac fermions Nature 464, 847, (2010)
  Z. Y. Meng, T. C. Lang, S. Wessel, F. F. Assaad, and A. Muramatsu
  
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study Phys. Rev. Lett. 106, 100403 (2011)
  M. Hohenadler, T. C. Lang, and F. F. Assaad
  
• Dynamical signatures of edge-state magnetism on graphene nanoribbons Phys. Rev. Lett. 106, 226401, (2011)
  H. Feldner, Z. Y. Meng, T. C. Lang, F. F. Assaad, S. Wessel, and A. Honecker
  
• Time and spatially resolved quench of the fermionic hubbard model showing restricted equilibration Phys. Rev. B 85, 085129, (2012)
  F. Goth and F. F. Assaad
  
• Dimerized solids and resonating plaquette order in SU(N)-dirac fermions Phys. Rev. Lett. 111, 066401,(2013)
  T. C. Lang, Z. Y. Meng, A. Muramatsu, S. Wessel, and F. F. Assaad
  
• Magnetic impurities in the Kane-Mele model Phys. Rev. B 88, 075110, (2013)
  F. Goth, D. J. Luitz, and F. F. Assaad
  
• Topological invariant and quantum spin models from magnetic π fluxes in correlated topological insulators Phys. Rev. X 3, 011015, (2013)
  F. F. Assaad, M. Bercx, and M. Hohenadler