arXiv subjects

Garnet Kin-Lic Chan

Publications and source records attributed to Garnet Kin-Lic Chan.

At least 181 records · Page 10Linked to original sources

arXiv2014

Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer

We combine explicit correlation via the canonical transcorrelation approach with the density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer curve, {\it without} the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of $D_e$=931.2 cm$^{-1}$ which agrees very well with recent experimentally derived estimates $D_e$=929.7$\pm 2$~cm$^{-1}$ [Science, 324, 1548 (2009)] and $D_e$=934.6~cm$^{-1}$ [Science, 326, 1382 (2009)]], as well the best composite theoretical estimates, $D_e$=938$\pm 15$~cm$^{-1}$ [J. Phys. Chem. A, 111, 12822 (2007)] and $D_e$=935.1$\pm 10$~cm$^{-1}$ [Phys. Chem. Chem. Phys., 13, 20311 (2011)]. Our results suggest possible inaccuracies in the functional form of the potential used at shorter bond lengths to fit the experimental data [Science, 324, 1548 (2009)]. With the density matrix renormalization group we also compute near-exact vertical excitation energies at the equilibrium geometry. These provide non-trivial benchmarks for quantum chemical methods for excited states, and illustrate the surprisingly large error that remains for 1$^1Σ^-_g$ state with approximate multi-reference configuration interaction and equation-of-motion coupled cluster methods. Overall, we demonstrate that explicitly correlated density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods allow us to fully converge to the basis set and correlation limit of the non-relativistic Schrödinger equation in small molecules.

physics.chem-ph↗

arXiv2014

A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states

We describe a formulation of multi-reference perturbation theory that obtains a rigorous upper bound to the second order energy by minimizing the Hylleraas functional in the space of matrix product states (MPS). The first order wavefunctions so obtained can also be used to compute the third order energy with little overhead. Our formulation has several advantages including (i) flexibility with respect to the choice of zeroth order Hamiltonian, (ii) recovery of the exact uncontracted multi-reference perturbation theory energies in the limit of large MPS bond dimension, (iii) no requirement to compute high body density matrices, (iv) an embarrassingly parallel algorithm (scaling up to the number of virtual orbitals, squared, processors). Preliminary numerical examples show that the MPS bond dimension required for accurate first order wavefunctions scales sub-linearly with the size of the basis.

physics.chem-ph↗

arXiv2014

Projector quantum Monte Carlo with matrix product states

We marry tensor network states (TNS) and projector quantum Monte Carlo (PMC) to overcome the high computational scaling of TNS and the sign problem of PMC. Using TNS as trial wavefunctions provides a route to systematically improve the sign structure and to eliminate the bias in fixed-node and constrained-path PMC. As a specific example, we describe phaseless auxiliary-field quantum Monte Carlo with matrix product states (MPS-AFQMC). MPS-AFQMC improves significantly on the DMRG ground-state energy. For the J1-J2 model on two-dimensional square lattices, we observe with MPS-AFQMC an order of magnitude reduction in the error for all couplings, compared to DMRG. The improvement is independent of walker bond dimension, and we therefore use bond dimension one for the walkers. The computational cost of MPS-AFQMC is then quadratic in the bond dimension of the trial wavefunction, which is lower than the cubic scaling of DMRG. The error due to the constrained-path bias is proportional to the variational error of the trial wavefunction. We show that for the J1-J2 model on two-dimensional square lattices, a linear extrapolation of the MPS-AFQMC energy with the discarded weight from the DMRG calculation allows to remove the constrained-path bias. Extensions to other tensor networks are briefly discussed.

cond-mat.str-el↗

arXiv2014

The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model

We obtain the phase-diagram of the half-filled honeycomb Hubbard model with density matrix embedding theory, to address recent controversy at intermediate couplings. We use clusters from 2-12 sites and lattices at the thermodynamic limit. We identify a paramagnetic insulating state, with possible hexagonal cluster order, competitive with the antiferromagnetic phase at intermediate coupling. However, its stability is strongly cluster and lattice size dependent, explaining controver- sies in earlier work. Our results support the paramagnetic insulator as being a metastable, rather than a true, intermediate phase, in the thermodynamic limit.

cond-mat.str-el↗

arXiv2013

Linear Response Theory for the Density Matrix Renormalization Group: Efficient Algorithms for Strongly Correlated Excited States

Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [Dorando et al., J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [Haegeman et al., Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.

cond-mat.str-el↗

arXiv2013

The Thouless theorem for matrix product states and subsequent post-density matrix renormalization group methods

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.

cond-mat.str-el↗

arXiv2013

Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an ilustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

cond-mat.str-el↗

arXiv2012

Density matrix embedding: A strong-coupling quantum embedding theory

We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett. 109 186404 (2012)] from lattice models to the full chemical Hamiltonian. DMET allows the many-body embedding of arbitrary fragments of a quantum system, even when such fragments are open systems and strongly coupled to their environment (e.g., by covalent bonds). In DMET, empirical approaches to strong coupling, such as link atoms or boundary regions, are replaced by a small, rigorous quantum bath designed to reproduce the entanglement between a fragment and its environment. We describe the theory and demonstrate its feasibility in strongly correlated hydrogen ring and grid models; these are not only beyond the scope of traditional embeddings, but even challenge conventional quantum chemistry methods themselves. We find that DMET correctly describes the notoriously difficult symmetric dissociation of a 4x3 hydrogen atom grid, even when the treated fragments are as small as single hydrogen atoms. We expect that DMET will open up new ways of treating of complex strongly coupled, strongly correlated systems in terms of their individual fragments.

cond-mat.str-el↗

arXiv2012

Excited States, Dynamic Correlation Functions and Spectral Properties from Full Configuration Interaction Quantum Monte Carlo

In this communication, we propose a method for obtaining isolated excited states within the Full Configuration Interaction Quantum Monte Carlo framework. This method allows for stable sampling with respect to collapse to lower energy states and requires no uncontrolled approximations. In contrast with most previous methods to extract excited state information from Quantum Monte Carlo methods, this results from a modification to the underlying propagator, and does not require explicit orthogonalization, analytic continuation, transient estimators or restriction of the Hilbert space via a trial wavefunction. Furthermore, we show that the propagator can directly yield frequency-domain correlation functions and spectral functions such as the density of states which are difficult to obtain within a traditional Quantum Monte Carlo framework. We demonstrate this approach with pilot applications to the neon atom and beryllium dimer.

cond-mat.str-el↗

arXiv2012

Striped spin liquid crystal ground state instability of kagome antiferromagnets

The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome antiferromagnet has potential instabilities[1-4]. This has been suggested as the reason why it is not strongly supported in large-scale numerical calculations[5]. However, previous attempts to observe these instabilities have failed. We report on the discovery of a projected BCS state with lower energy than the projected Dirac spin liquid state which provides new insight into the stability of the ground state of the kagome antiferromagnet. The new state has three remarkable features. First, it breaks both spatial symmetry in an unusual way that may leave spinons deconfined along one direction. Second, it breaks the U(1) gauge symmetry down to $Z_2$. Third, it has the spatial symmetry of a previously proposed "monopole" suggesting that it is an instability of the Dirac spin liquid. The state described herein also shares a remarkable similarity to the distortion of the kagome lattice observed at low Zn concentrations in Zn-Paratacamite suggesting it may already be realized in these materials.

cond-mat.str-el↗

arXiv2012

Density matrix embedding: A simple alternative to dynamical mean-field theory

We introduce DMET, a new quantum embedding theory for predicting ground-state properties of infinite systems. Like dynamical mean-field theory (DMFT), DMET maps the the bulk interacting system to a simpler impurity model and is exact in the non-interacting and atomic limits. Unlike DMFT, DMET is formulated in terms of the frequency-independent local density matrix, rather than the local Green's function. In addition, it features a finite, algebraically constructible bath of only one bath site per impurity site, which exactly embeds ground-states at a mean-field level with no bath discretization error. Frequency independence and the minimal bath make DMET a computationally simple and very efficient method. We test the theory in the 1D and 2D Hubbard models at and away from half-filling, and we find that compared to benchmark data, total energies, correlation functions, and paramagnetic metal-insulator transitions are well reproduced, at a tiny computational cost.

cond-mat.str-el↗

arXiv2012

A correlator product state study of molecular magnetism in the giant Keplerate Mo72Fe30

We have studied the properties of the giant Keplerate molecular magnet Mo72Fe30, as a function of applied magnetic field, using the correlator product state (CPS) tensor network ansatz. The magnet is modeled with an S = 5/2 antiferromagnetic Heisenberg Hamiltonian on the 30-site icosidodecahedron lattice, a model for which exact diagonalization is infeasible. The CPS ansatz produces significant improvements in variational energies relative to previous studies using the density matrix renormalization group, a result of its superior ability to handle strong correlation in two dimensional spin systems. The CPS results reaffirm that the ground state energies adhere qualitatively to the parabolic progression of the rotational band model (RBM), but show important deviations near 1/3 of the saturation field. These deviations predict anomalous behavior in the differential magnetization and heat capacity that cannot be explained by the RBM alone. Finally, we show that these energetic deviations originate from a qualitative change in the ground state that resembles a finite size analogue of a phase transition.

cond-mat.str-el↗

arXiv2011

Optimizing large parameter sets in variational quantum Monte Carlo

We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they are sampled, we remove the need to construct and store these matrices and thus bypass the most expensive steps of the stochastic reconfiguration and linear method optimization techniques. We demonstrate the effectiveness of this approach by using stochastic reconfiguration to optimize a correlator product state wavefunction with a pfaffian reference for four example systems. In two examples on the two dimensional Hubbard model, we study 16 and 64 site lattices, recovering energies accurate to 1% in the smaller lattice and predicting particle-hole phase separation in the larger. In two examples involving an ab initio Hamiltonian, we investigate the potential energy curve of a symmetrically dissociated 4x4 hydrogen lattice as well as the singlet-triplet gap in free base porphin. In the hydrogen system we recover 98% or more of the correlation energy at all geometries, while for porphin we compute the gap in a 24 orbital active space to within 0.02eV of the exact result. The numbers of variational parameters in these examples range from 4x10^3 to 5x10^5, demonstrating an ability to go far beyond the reach of previous formulations of stochastic reconfiguration.

cond-mat.str-el↗

arXiv2011

Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States

Drawing on similarities in Hartree-Fock theory and the theory of matrix product states (MPS), we explore extensions to time evolution, response theory, and Green functions. We derive analytic equations of motion for MPS from the least action principle, which describe optimal evolution in the small time-step limit. We further show how linearized equations of motion yield a MPS random phase approximation, from which one obtains response functions and excitations. Finally we analyze the structure of site-based Green functions associated with MPS, as well as the structure of correlations introduced via the fluctuation-dissipation theorem.

cond-mat.str-el↗

arXiv2011

Uniform Peak Optical Conductivity in Single-Walled Carbon Nanotubes

Recent measurements in single-walled carbon nanotubes show that, on resonance, all nanotubes display the same peak optical conductivity of approximately 8 $e^2/h$, independent of radius or chirality [Joh \emph{et al.}, \emph{Nature Nanotechnology} \textbf{6}, 51 (2011)]. We show that this uniform peak conductivity is a consequence of the relativistic band structure and strength of the Coulomb interaction in carbon nanotubes. We further construct a minimalist model of exciton dynamics that describes the general phenomenology and provides an accurate prediction of the numerical value of the peak optical conductivity. The work illustrates the need for careful treatment of relaxation mechanisms in modeling the optoelectronic properties of carbon nanotubes.

cond-mat.mes-hall↗

arXiv2010

Dynamical mean-field theory from a quantum chemical perspective

We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab-initio Hamiltonians and impurity solvers for DMFT. Here we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next we describe an implementation of dynamical mean-field theory where we start from an ab-initio Hartree- Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally we finish with some conclusions for future directions.

cond-mat.str-el↗

arXiv2010

Further developments in correlator product states: deterministic optimization and energy evaluation

Correlator product states (CPS) are a class of tensor network wavefunctions applicable to strongly correlated problems in arbitrary dimensions. Here, we present a method for optimizing and evaluating the energy of the CPS wavefunction that is non-variational but entirely deterministic. The fundamental assumption underlying our technique is that the CPS wavefunction is an exact eigenstate of the Hamiltonian, allowing the energy to be obtained approximately through a projection of the Schrödinger equation. The validity of this approximation is tested on two dimensional lattices for the spin-1/2 antiferromagnetic Heisenberg model, the spinless Hubbard model, and the full Hubbard model. In each of these models, the projected method reproduces the variational CPS energy to within 1%. For fermionic systems, we also demonstrate the incorporation of a Slater determinant reference into the ansatz, which allows CPS to act as a generalization of the Jastrow-Slater wavefunction.

cond-mat.str-el↗

arXiv2010

Embedding theory for excited states with inclusion of self-consistent environment screening

We present a general embedding theory of electronic excitations of a relatively small, localized system in contact with an extended, chemically complex environment. We demonstrate how to include the screening response of the environment into highly accurate electronic structure calculation of the localized system by means of an effective interaction between the electrons, which contains only screening processes occurring in the environment. For the common case of a localized system which constitutes an inhomogeneity in an otherwise homogeneous system, such as a defect in a crystal, we show how matrix elements of the environment-screened interaction can be calculated from density-functional calculations of the homogeneous system only. We apply our embedding theory to the calculation of excitation energies in crystalline ethylene.

cond-mat.mtrl-sci↗