Tensor network factorization and tailored coupled cluster method in quantum chemistry

Transcription

1 Tensor network factorization and tailored coupled cluster method in quantum chemistry Örs Legeza Strongly Correlated Systems Lendület Research Group Wigner Research Centre for Physics, Hungarian Academy of Sciences and Simen Kvaal Hylleraas Centre for Quantum Molecular Sciences University of Oslo, The Arctic University of Norway in Tromsø Future Research Challenges: Hungarian Norwegian Research Conference & Knowledge Exchange February 2018, Budapest, Hungary

2 Wigner Research Centre for Physics Strongly Correlated Systems Lendu let Research Group Created in 2012 through the centre of excellence programme of the Hungarian Academy of Sciences Strong international collaborations: Austria, Canada, Czech Republic, Germany, Great-Britain, France, Poland, Spain, Switzerland, USA The Budapest-DMRG code is used in more than 15 research institutes and universities around the world. erosen-korrelalt-rendszerek

3 Research at Strongly Correlated Systems Lendület Group Overall goal: Develop scientific softwares based on tensor network state algorithms for simulating strongly correlated quantum systems that are untraceable with present-day conventional software packages. nterdisciplinary research organized into six research themes (RTs): RT1 Material properties of solid state systems RT2 Molecular quantum chemistry RT3 Ultracold atomic systems RT4 Quantum simulation of the information technology RT5 Nuclear structure theory RT6 Rigorous mathematical analysis of the algorithms Supports: European Research Area, Alexander von Humboldt Foundation, Hungarian Academy of Sciences, Hungarian National Research, Development and nnovation Office, DFG, FWF, etc

4 The Hylleraas Centre for Quantum Molecular Sciences Newly created centre of excellence by the Research Council of Norway (no logo yet!) University of Oslo, The Arctic University of Norway in Tromsø

5 Research at Hylleraas Overall goal: Develop and apply computational methods to understand, interpret, and predict new chemistry, physics, and biology of molecules in complex and extreme environments. Organized into six research themes (RTs): RT1 Electronic Structure RT2 Multiscale Modelling RT3 Spectroscopic Processes RT4 Extreme Environments RT5 Chemical Transformations RT6 Multiphase Systems

6 The ERC Starting Grant project BVAQUM Hosted at the Hylleraas Centre Cutting-edge research on wavefunction methods Unconventional formulation of quantum mechanics via the bivariational principle Cross-disciplinary: Chemistry, Physics, Mathematics From multireference quantum chemistry to real-time dynamics in extreme environments Simen Kvaal (Leader) Andre Laestadius (Postdoc) Rolf H. Myhre (Postdoc) Benedicte Ofstad (PhD) Fabian Faulstich (PhD)

7 Coupled cluster method with single and double excitations tailored by matrix product state wave functions L. Veis, A. Antalik, F. Neese, O. Legeza, J. Pittner, J. Chem. Phys. Lett. (2016) Quantum information measures of correlations Efficient treatment of static and dynamic correlations based on TCCSD method

8 Brief theoretical overview Formally single reference theory, Fermi vacuum is a single determinant Split-amplitude ansatz Ψ TCC = e T Ψ ref = e T ext +T CAS Ψ ref T CAS amplitudes extracted from DMRG (CASC) calculation frozen during CC calculation account for static correlation Ψ TCCSD = e e T ext ( ) T1 ext +T2 ext ) ( T1 ext +T2 ext determined through the usual CC account for dynamic correlation ( ) T e 1 CAS +T2 CAS Ψ ref Ψ CASC Requires only small modifications of the CC code

9 CCSD tailored by MPS wave functions 1. Small active space DMRG calculation 2. Acquisition of C coefficients by efficient contraction of MPS w.f. (in two-site form) Ψ MPS = {α} A α1 A α2 W α i α i+1 A αn α 1 α 2 α n, 3. Calculation of CAS amplitudes T CAS 1 = C 1 T CAS 2 = C (C 1) 2 4. CCSD calculation for T1 ext and T2 ext Cost of the MPS T 12 conversion: O(M 2 n 4 ) with a small prefactor, using techniques from Zgid and Nooijen, JCP 128,

10 State-of-the-art results: correlation energies Single-point calculation for Chromium dimer at 1.5 Å Extrapolated DMRG by Olivares-Amaya et al. JCP 142, , 2015 serves as a FC benchmark Recently established largescale project: Migration of the Budapest-DMRG into the NWChem commercial program package through massive parallelization (Pacific North National Laboratory, USA).

11 First analytic results for the DMRG-TCC method The mathematical analysis of coupled-cluster schemes is far from being complete and does not cover the DMRG-TCCSD method. We aspires to close the gap between theory and applications in the case of DMRG-TCCSD, presenting a sound mathematical framework and first analytic results for the TCC method built on tensor network state (TNS) reference wave functions. Analysis of The Coupled-Cluster Method Tailored by Tensor-Network States in Quantum Chemistry, F. M. Faulstich, A. Laestadius, S. Kvaal, Ö. Legeza and R. Schneider (2018) submitted to SAM Journal on Numerical Analysis (SNUM). Our work is of utmost importance to provide further impetus to the TNS-TCC scheme to become the black-box method used on a daily basis in order to efficiently treat strongly correlated systems. We seek for financial support for our future joint projects