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Register a new userTracking excited states in wave function optimization using density matrices and variational principles
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We present a method for finding individual excited states energy stationary points in complete active space self-consistent field theory that is compatible with standard optimization methods and highly effective at overcoming difficulties due to root flipping and near-degeneracies. Inspired by both the maximum overlap method and recent progress in excited state variational principles, our approach combines these ideas in order to track individual excited states throughout the orbital optimization process. In a series of tests involving root flipping, near-degeneracies, charge transfers, and double excitations, we show that this approach is more effective for state-specific optimization than either the naive selection of roots based on energy ordering or a more direct generalization of the maximum overlap method. Furthermore, we provide evidence that this state-specific approach improves the performance of complete active space perturbation theory. With a simple implementation, a low cost, and compatibility with large active space methods, the approach is designed to be useful in a wide range of excited state investigations.
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Representing a target quantum state by a compact, efficient variational wave-function is an important approach to the quantum many-body problem. In this approach, the main challenges include the design of a suitable variational ansatz and optimization of its parameters. In this work, we address both of these challenges. First, we define the variational class of Computational Graph States (CGS) which gives a uniform framework for describing all computable variational ansatz. Secondly, we develop a novel optimization scheme, supervised wave-function optimization (SWO), which systematically improves the optimized wave-function by drawing on ideas from supervised learning. While SWO can be used independently of CGS, utilizing them together provides a flexible framework for the rapid design, prototyping and optimization of variational wave-functions. We demonstrate CGS and SWO by optimizing for the ground state wave-function of 1D and 2D Heisenberg models on nine different variational architectures including architectures not previously used to represent quantum many-body wave-functions and find they are energetically competitive to other approaches. One interesting application of this architectural exploration is that we show that fully convolution neural network wave-functions can be optimized for one system size and, using identical parameters, produce accurate energies for a range of system sizes. We expect these methods to increase the rate of discovery of novel variational ansatz and bring further insights to the quantum many body problem.
We extend our recently-developed heat-bath configuration interaction (HCI) algorithm, and our semistochastic algorithm for performing multireference perturbation theory, to the calculation of excited-state wavefunctions and energies. We employ time-reversal symmetry, which reduces the memory requirements by more than a factor of two. An extrapolation technique is introduced to reliably extrapolate HCI energies to the Full CI limit. The resulting algorithm is used to compute the twelve lowest-lying potential energy surfaces of the carbon dimer using the cc-pV5Z basis set, with an estimated error in energy of 30-50 {mu}Ha compared to Full CI. The excitation energies obtained using our algorithm have a mean absolute deviation of 0.02 eV compared to experimental values. We also calculate the complete active-space (CAS) energies of the S0, S1, and T0 states of tetracene, which are of relevance to singlet fission, by fully correlating active spaces as large as 18 electrons in 36 orbitals.
A method is developed that allows analysis of quantum Monte Carlo simulations to identify errors in trial wave functions. The purpose of this method is to allow for the systematic improvement of variational wave functions by identifying degrees of freedom that are not well-described by an initial trial state. We provide proof of concept implementations of this method by identifying the need for a Jastrow correlation factor, and implementing a selected multi-determinant wave function algorithm for small dimers that systematically decreases the variational energy. Selection of the two-particle excitations is done using quantum Monte Carlo within the presence of a Jastrow correlation factor, and without the need to explicitly construct the determinants. We also show how this technique can be used to design compact wave functions for transition metal systems. This method may provide a route to analyze and systematically improve descriptions of complex quantum systems in a scalable way.
We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state of a local Hamiltonian. The method is based on a systematic summation of Hamiltonian contributions using the corner transfer-matrix method. Benchmark results for challenging problems are presented, including the 2D Heisenberg model, the Shastry-Sutherland model, and the t-J model, which show that the variational scheme yields considerably more accurate results than the previously best imaginary time evolution algorithm, with a similar computational cost and with a faster convergence towards the ground state.
The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry makes it practical to evaluate static correlation in a large active space, while dynamic correlation provides a critical correction to the DMRG reference for strong-correlated systems and is usually obtained using multi-reference perturbation (MRPT) or configuration interaction (MRCI) methods with internal contraction (ic) approximation. These methods can use active space scalable to relatively larger size references than has previously been possible. However, they are still hardly applicable to systems with active space larger than 30 orbitals because of high computation and storage costs of high-order reduced density matrices (RDMs) and the number of virtual orbitals are normally limited to few hundreds. In this work, we propose a new effective implementation of DMRG-MRCI, in which we use re-constructed CASCI-type configurations from DMRG wave function via the entropy-driving genetic algorithm (EDGA), and integrate with MRCI by an external contraction (ec) scheme. This bypasses the bottleneck of computing high-order RDMs in traditional DMRG dynamic correlation methods with ic approximation and the number of MRCI configurations is not dependent on the number of virtual orbitals. Therefore, DMRG-ec-MRCI method is promising for dealing with larger active space than 30 orbitals and large basis sets. We demonstrate the capability of our DMRG-ec-MRCI method in several benchmark applications, including the evaluation of potential energy curve of Cr$_{2}$, single-triplet gaps of higher n-acene molecules and the energy of Eu-BTBP(NO$_3$)$_3$ complex.
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