September 15, 2014 to October 10, 2014
Nordita, Stockholm
Europe/Stockholm timezone

Tensor methods and entanglement measurements for models with long-range interactions

Sep 19, 2014, 9:40 AM
FP41 (Nordita, Stockholm)


Nordita, Stockholm


Örs Legeza


Strongly correlated materials are typically rather difficult to treat theoretically. They have a complicated band structure, and it is quite difficult to determine which minimal model correctly describes their essential physical properties. Moreover, the value of the model parameters to be used for a given material is often the subject of debate. Unfortunately, analytic approaches often do not provide rigorous conclusions for the interesting parameter sets, therefore, numerical simulations are mandatory. Momentum-space formulations of local models such as the Hubbard model and problems in quantum chemistry are especially hard to treat using matrix- and tensor product-based algorithms because they contain non-local interactions. Quantum entropy-based measures can be used to map the entanglement structure in order to gain physical information and to optimize algorithms. In this tutorial contribution, we present an overview of the real space, momentum space and quantum chemistry versions of the DMRG/MPS and tree-TNS algorithms and their applications to various spin and fermionic lattice models, and to transition metal complexes. Data sparse representation of the wavefunction will be investigated through advances in entanglement localization providing optimized tensor topologies. Entropy generation by the RG procedure, the mutual information leading to a multiply connected network of lattice sites or orbitals, and reduction of entanglement by basis transformation will be discussed. Inclusion of the concepts of entanglement will be used to identify the wave vector of soft modes in critical models, to determine highly correlated molecular orbitals leading to an efficient construction of active spaces and for characterizing the various types of correlation effects relevant for chemical bonding. The state of the art matrix-product-based algorithms is demonstrated on polydiacetylene chains by reproducing experimentally measured quantities with high accuracy. [1] S. R. White, Phys. Rev. Lett. 69, 2863-2866 (1992). [2] S. R. White and R. L. Martin, J. Chem. Phys. 110, 4127-4130 (1999). [3] O. Legeza, R. M. Noack, J. SĂłlyom, and L. Tincani, in Computational Many-Particle Physics, eds. H. Fehske, R. Schneider, and A. Weisse 739, 653-664 (2008). [4] K. H. Marti and M. Reiher, Z. Phys. Chem. 224, 583-599 (2010). [5] G. K.-L. Chan and S. Sharma, Annu. Rev. Phys. Chem. 62, 465-481 (2011). [6] O. Legeza and J. SĂłlyom, Phys. Rev. B 68, 195116 (2003), ibid Phys Rev. B 70, 205118 (2004). [7] J. Rissler, R.M.Noack, and S.R. White, Chemical Physics, 323, 519 (2006). [8] K. Boguslawski, P. Tecmer, O. Legeza, and M. Reiher, J. Phys. Chem. Lett. 3, 3129-3135 (2012). [9] K. Boguslawski, P. Tecmer, G. Barcza, O. Legeza, and M. Reiher, J. Chem. Theory Comp. (2013). [10] F. Verstraete, J.I. Cirac, V. Murg, Adv. Phys. 57 (2), 143 (2008). [11] V. Murg, F. Verstraete, O. Legeza, and R. M. Noack, Phys. Rev. B 82, 205105 (2010). [12] V. Murg, F. Verstraete, R. Schneider, P. Nagy and O. Legeza, arxiv:1403.0981 (2014). [13] G. Barcza, O. Legeza, K. H. Marti, and M. Reiher, Phys. Rev. A 83, 012508 (2011). [14] G. Barcza, R. M. Noack, J. SĂłlyom, O. Legeza, arxiv:1406.6643 (2014)

Presentation materials