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Register a new userImproved parallelization techniques for the density matrix renormalization group
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A distributed-memory parallelization strategy for the density matrix renormalization group is proposed for cases where correlation functions are required. This new strategy has substantial improvements with respect to previous works. A scalability analysis shows an overall serial fraction of 9.4% and an efficiency of around 60% considering up to eight nodes. Sources of possible parallel slowdown are pointed out and solutions to circumvent these issues are brought forward in order to achieve a better performance.
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We introduce the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory for the efficient approximation of the energy for strongly correlated systems. tcDMRG encodes the wave function as a product of a fixed Jastrow or Gutzwiller correlator and a matrix product state. The latter is optimized by applying the imaginary-time variant of time-dependent (TD) DMRG to the non-Hermitian transcorrelated Hamiltonian. We demonstrate the efficiency of tcDMRG at the example of the two-dimensional Fermi-Hubbard Hamiltonian, a notoriously difficult target for the DMRG algorithm, for different sizes, occupation numbers, and interaction strengths. We demonstrate fast energy convergence of tcDMRG, which indicates that tcDMRG could increase the efficiency of standard DMRG beyond quasi-monodimensional systems and provides a generally powerful approach toward the dynamic correlation problem of DMRG.
Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. However, the unfavorable scaling and the resulting high computational cost of standard variational approaches limit their application to small molecules with only few vibrational modes. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. We study the convergence of these calculations with respect to the size of the local basis of each mode, the number of renormalized block states, and the number of DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for small molecules that were intensively studied in the literature. We then proceed to show that the complete fingerprint region of the sarcosyn-glycin dipeptide can be calculated with vDMRG.
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some non-trivial cases, this approach can even be exact for finite bond dimensions.
The similarities between Hartree-Fock (HF) theory and the density-matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the non-redundant parametrization of the matrix product state (MPS) tangent space [J. Haegeman et al., Phys. Rev. Lett. 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e. an explicit non-redundant parametrization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.
The density-matrix renormalization group (DMRG) method, which can deal with a large active space composed of tens of orbitals, is nowadays widely used as an efficient addition to traditional complete active space (CAS)-based approaches. In this paper, we present the DMRG algorithm with a multi-level (ML) control of the active space based on chemical intuition-based hierarchical orbital ordering, which is called as ML-DMRG with its self-consistent field variant ML-DMRG-SCF. Ground and excited state calculations of H2O, N2, indole, and Cr2 with comparisons to DMRG references using fixed number of kept states (M) illustrate that MLtype DMRG calculations can obtain noticeable efficiency gains. It is also shown that the orbital re-ordering based on hierarchical multiple active subspaces may be beneficial for reducing computational time for not only ML-DMRG calculations but also DMRG ones with fixed M values.
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