arXiv subjects

Örs Legeza

Publications and source records attributed to Örs Legeza.

At least 55 records · Page 3Linked to original sources

arXiv2020

Massively parallel quantum chemical density matrix renormalization group method

We present, to the best of our knowlegde, the first attempt to exploit the supercomputer platform for quantum chemical density matrix renormalization group (QC-DMRG) calculations. We have developed the parallel scheme based on the in-house MPI global memory library, which combines operator and symmetry sector parallelisms, and tested its performance on three different molecules, all typical candidates for QC-DMRG calculations. In case of the largest calculation, which is the nitrogenase FeMo cofactor cluster with the active space comprising 113 electrons in 76 orbitals and bond dimension equal to 6000, our parallel approach scales up to approximately 2000 CPU cores.

physics.chem-ph↗

arXiv2020

Ground State of the Fe(II)-porphyrin Model System Corresponds to the Quintet State: A DFT and DMRG-based Tailored CC Study

Fe(II)-porphyrins (FeP) play an important role in many reactions relevant to material science and biological processes, due to their closely lying spin states. However, this small energetic separation also makes it challenging to establish the correct spin state ordering. Although the prevalent opinion is that these systems posses the triplet ground state, the recent experiment on Fe(II)-phthalocyanine under conditions matching those of an isolated molecule points toward the quintet ground state. We present a thorough study of FeP model by means of the density functional theory and density matrix renormalization group based tailored coupled clusters, in which we address all previously discussed correlation effects. We examine the importance of geometrical parameters, the Fe-N distances in particular, and conclude that the system possesses the quintet ground state, which is in our calculations well-separated from the triplet state.

physics.chem-ph↗

arXiv2020

DMRG on top of plane-wave Kohn-Sham orbitals: case study of defected boron nitride

In this paper, we analyze the numerical aspects of the inherently multi-reference density matrix renormalization group (DMRG) calculations on top of the periodic Kohn-Sham density functional theory (DFT) using the complete active space (CAS) approach. Following the technical outline related to the computation of the Hamiltonian matrix elements and to the construction of the active space, we illustrate the potential of the framework by studying the vertical many-body energy spectrum of hexagonal boron nitride (hBN) nano-flakes embedding a single boron vacancy point defect with prominent multi-reference character. We investigate the consistency of the DMRG energy spectrum from the perspective of sample size, basis size, and active space selection protocol. Results obtained from standard quantum chemical atom-centered basis calculations and plane-wave based counterparts show excellent agreement. Furthermore, we also discuss the spectrum of the periodic sheet which is in good agreement with extrapolated data of finite clusters. These results pave the way toward applying DMRG method in extended correlated solid state systems, such as point qubit in wide band gap semiconductors.

cond-mat.str-el↗

arXiv2020

Towards DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: electrons moving at relativistic speeds, close lying states and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules, in which all the three effects are present. These are the heavier transition metal compounds, lanthanides and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs, as we demonstrate on the system of TlH, AsH and SbH.

physics.chem-ph↗

arXiv2020

Near-linear Scaling in DMRG-based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T)

We present a new implementation of DMRG-based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO-TCCSD). Compared to the previous LPNO version of the method, the new implementation is more accurate, offers more favorable scaling and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen) and Iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8-99.9% of the total canonical correlation energy which is the improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for Iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.

physics.chem-ph↗

arXiv2019

Symmetric single-impurity Kondo model on a tight-binding chain: a comparison of analytical and numerical ground-state approaches

We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurity-induced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model on a tight-binding chain with bandwidth $W=2{\cal D}$ and coupling strength $J_{\rm K}$. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact data obtained from the Density-Matrix Renormalization Group (DMRG) and from the Numerical Renormalization Group (NRG) methods. The Gutzwiller variational approach becomes exact in the strong-coupling limit and reproduces the ground-state properties from DMRG and NRG for large couplings. We calculate the impurity spin polarization and its susceptibility in the presence of magnetic fields that are applied globally/locally to the impurity spin. The Yosida wave function provides qualitatively correct results in the weak-coupling limit. In DMRG, chains with about $10^3$ sites are large enough to describe the susceptibilities down to $J_{\rm K}/{\cal D}\approx 0.5$. For smaller Kondo couplings, only the NRG provides reliable results for a general host-electron density of states $ρ_0(ε)$. To compare with results from Bethe Ansatz, we study the impurity-induced magnetization and zero-field susceptibility. For small Kondo couplings, the zero-field susceptibilities at zero temperature approach $χ_0(J_{\rm K}\ll {\cal D})/(gμ_{\rm B})^2\approx \exp[1/(ρ_0(0)J_{\rm K})]/(2C{\cal D}\sqrt{πe ρ_0(0)J_{\rm K}})$, where $\ln(C)$ is the regularized first inverse moment of the density of states. Using NRG, we determine the universal sub-leading corrections up to second order in $ρ_0(0)J_{\rm K}$.

cond-mat.str-el↗

arXiv2019

Ab initio theory of negatively charged boron vacancy qubit in hBN

Highly correlated orbitals coupled with phonons in two-dimension are identified for paramagnetic and optically active boron vacancy in hexagonal boron nitride by first principles methods which are responsible for recently observed optically detected magnetic resonance signal. We report ab initio analysis of the correlated electronic structure of this center by density matrix renormalization group and Kohn-Sham density functional theory methods. By establishing the nature of the bright and dark states as well as the position of the energy levels, we provide a complete description of the magneto-optical properties and corresponding radiative and non-radiative routes which are responsible for the optical spin polarization and spin dependent luminescence of the defect. Our findings pave the way toward advancing the identification and characterization of room temperature quantum bits in two-dimensional solids.

cond-mat.mes-hall↗

arXiv2019

Analysis of The Tailored Coupled-Cluster Method in Quantum Chemistry

In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the Born--Oppenheimer approximation. In this article, we analyze the tailored coupled-cluster method (TCC), one particular and promising method for treating molecular electronic-structure problems with static correlation. The TCC method combines the single-reference coupled-cluster (CC) approach with an approximate reference calculation in a subspace [complete active space (CAS)] of the considered Hilbert space that covers the static correlation. A one-particle spectral gap assumption is introduced, separating the CAS from the remaining Hilbert space. This replaces the nonexisting or nearly nonexisting gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital usually encountered in standard single-reference quantum chemistry. The analysis covers, in particular, CC methods tailored by tensor-network states (TNS-TCC methods). The problem is formulated in a nonlinear functional analysis framework, and, under certain conditions such as the aforementioned gap, local uniqueness and existence are proved using Zarantonello's lemma. From the Aubin--Nitsche-duality method, a quadratic error bound valid for TNS-TCC methods is derived, e.g., for linear-tensor-network TCC schemes using the density matrix renormalization group method.

math.NA↗

arXiv2019

Towards the Efficient Local Tailored Coupled Cluster Approximation and the Peculiar Case of Oxo-Mn(Salen)

We introduce a new implementation of the coupled cluster method tailored by matrix product states wave functions (DMRG-TCCSD), which employs the local pair natural orbital approach (LPNO). By exploiting locality in the coupled cluster stage of the calculation, we were able to remove some of the limitations that hindered the application of the canonical version of the method to larger systems and/or with larger basis sets. We assessed the accuracy of the approximation using two systems: tetramethyleneethane (TME) and oxo-Mn(Salen). Using the default cut-off parameters, we were able to recover over 99.7% and 99.8% of canonical correlation energy for the triplet and singlet state of TME respectively. In case of oxo-Mn(Salen), we found out that the amount of retrieved canonical correlation energy depends on the size of the active space (CAS) - we retrieved over 99.6% for the larger 27 orbital CAS and over 99.8% for the smaller 22 orbital CAS. The use of LPNO-TCCSD allowed us to perform these calculations up to quadruple-$ζ$ basis set amounting to 1178 basis functions. Moreover, we examined dependance of the ground state of oxo-Mn(Salen) on CAS composition. We found out that the inclusion of 4d$_{xy}$ orbital plays an important role in stabilizing the singlet state at the DMRG-CASSCF level via double-shell effect. However, by including dynamic correlation the ground state was found to be triplet regardless of the size of the basis set or composition of CAS, which is in agreement with previous findings by canonical DMRG-TCCSD in smaller basis.

physics.chem-ph↗

arXiv2019

Ground-state properties of the symmetric single-impurity Anderson model on a ring from Density-Matrix Renormalization Group, Hartree-Fock, and Gutzwiller theory

We analyze the ground-state energy, magnetization, magnetic susceptibility, and Kondo screening cloud of the symmetric single-impurity Anderson model (SIAM) that is characterized by the band width $W$, the impurity interaction strength $U$, and the local hybridization $V$. We compare Gutzwiller variational and magnetic Hartree-Fock results in the thermodynamic limit with numerically exact data from the Density-Matrix Renormalization Group (DMRG) method on large rings. To improve the DMRG performance, we use a canonical transformation to map the SIAM onto a chain with half the system size and open boundary conditions. We compare to Bethe-Ansatz results for the ground-state energy, magnetization, and spin susceptibility that become exact in the wide-band limit. Our detailed comparison shows that the field-theoretical description is applicable to the SIAM on a ring for a broad parameter range. Hartree-Fock theory gives an excellent ground-state energy and local moment for intermediate and strong interactions. However, it lacks spin fluctuations and thus cannot screen the impurity spin. The Gutzwiller variational energy bound becomes very poor for large interactions because it does not describe properly the charge fluctuations. Nevertheless, the Gutzwiller approach provides a qualitatively correct description of the zero-field susceptibility and the Kondo screening cloud. The DMRG provides excellent data for the ground-state energy and the magnetization for finite external fields. At strong interactions, finite-size effects make it extremely difficult to recover the exponentially large zero-field susceptibility and the mesoscopically large Kondo screening cloud.

cond-mat.str-el↗

arXiv2019

Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory

We study quantum quenches in the $S=1$ Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum mechanically. We analyze the non-equilibrium time evolution of the distribution of the total spin in half of the system and compare the predictions of the semi-semiclassical theory with those of a non-Abelian time evolving block decimation (TEBD) algorithm which exploits the SU(2) symmetry. We show that while the standard semiclassical approach using the universal low energy scattering matrix cannot describe the dynamics, the hybrid semiclassical method based on the full scattering matrix gives excellent agreement with the first principles TEBD simulation.

cond-mat.stat-mech↗

arXiv2019

Quantum information-based analysis of electron-deficient bonds

Recently, the correlation theory of the chemical bond was developed, which applies concepts of quantum information theory for the characterization of chemical bonds, based on the multiorbital correlations within the molecule. Here for the first time, we extend the use of this mathematical toolbox for the description of electron-deficient bonds. We start by verifying the theory on the textbook example of a molecule with three-center two-electron bonds, namely the diborane(6). We then show that the correlation theory of the chemical bond is able to properly describe bonding situation in more exotic molecules which have been synthetized and characterized only recently, in particular the diborane molecule with four hydrogen atoms [diborane(4)] and neutral zerovalent s-block beryllium complex, whose surprising stability was attributed to a strong three-center two-electron $π$ bond stretching across the C-Be-C core. Our approach is of a high importance especially in the light of a constant chase after novel compounds with extraordinary properties where the bonding is expected to be unusual.

physics.chem-ph↗

arXiv2018

Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer

In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate chemical properties of the used method, such as energy size extensivity and the equivalence of linked and unlinked formulation. The existing mathematical analysis is here elaborated in a quantum chemical framework. In particular, we highlight the use of a so-called CAS-ext gap describing the basis splitting between the complete active space and the external part. Moreover, the behavior of the energy error as a function of the optimal basis splitting is discussed. We show numerical investigations on the robustness with respect to the bond dimensions of the single orbital entropy and the mutual information, which are quantities that are used to choose the complete active space. Furthermore, we extend the mathematical analysis with a numerical study on the complete active space dependence of the error.

physics.chem-ph↗

arXiv2018

Role of the pair potential for the saturation of generalized Pauli constraints

The dependence of the (quasi-)saturation of the generalized Pauli constraints on the pair potential is studied for ground states of few-fermion systems. For this, we consider spinless fermions in one dimension which are harmonically confined and interact by pair potentials of the form $|x_i-x_j|^s$ with $-1 \leq s\leq 5$. We use the Density Matrix Renormalization Group approach and large orbital basis to achieve the convergence on more than ten digits of both the variational energy and the natural occupation numbers. Our results confirm that the conflict between energy minimization and fermionic exchange symmetry results in a universal and non-trivial quasi-saturation of the generalized Pauli constraints (\emph{quasipinning}), implying tremendous structural simplifications of the fermionic ground state for all $s$. Those numerically exact results are complemented by an analytical study based on a self-consistent perturbation theory which we develop for this purpose. The respective results for the weak coupling regime eventually elucidate the singular behaviour found for the specific values $s=2,4,\ldots$, resulting in an extremely strong quasipinning.

quant-ph↗

arXiv2018

Imaging the Wigner Crystal of Electrons in One Dimension

The quantum crystal of electrons, predicted more than eighty years ago by Eugene Wigner, is still one of the most elusive states of matter. Here, we present experiments that observe the one-dimensional Wigner crystal directly, by imaging its charge density in real-space. To measure this fragile state without perturbing it, we developed a new scanning probe platform that utilizes a pristine carbon nanotube as a scanning charge perturbation to image, with minimal invasiveness, the many-body electronic density within another nanotube. The obtained images, of few electrons confined in one-dimension, match those of strongly interacting crystals, with electrons ordered like pearls on a necklace. Comparison to theoretical modeling demonstrates the dominance of Coulomb interactions over kinetic energy and the weakness of exchange interactions. Our experiments provide direct evidence for this long-sought electronic state, and open the way for studying other fragile interacting states by imaging their many-body density in real-space.

cond-mat.mes-hall↗

arXiv2018

T3NS: three-legged tree tensor network states

We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two virtual indices, as in the matrix product state (MPS) ansatz of the density matrix renormalization group (DMRG). Branching tensors have no physical index, but up to three virtual indices. In this way, advantages of DMRG, in particular a low computational cost and a simple implementation of symmetries, are combined with advantages of TTNS, namely incorporating more entanglement. Our code is capable of simulating quantum chemical Hamiltonians, and we present several proof-of-principle calculations on LiF, N$_2$ and the bis($μ$-oxo) and $μ- η^2 : η^2$ peroxo isomers of $[\mathrm{Cu}_2\mathrm{O}_2]^{2+}$.

cond-mat.str-el↗

arXiv2018

Full configuration interaction quantum Monte Carlo benchmark and multireference coupled cluster studies of tetramethyleneethane diradical

We have performed a FCI-quality benchmark calculation for the tetramethyleneethane molecule in cc-pVTZ basis set employing a subset of CASPT2(6,6) natural orbitals for the FCIQMC calculation. The results are in an excellent agreement with the previous large scale diffusion Monte Carlo calculations by Pozun et al. and available experimental results. Our computations verified that there is a maximum on PES of the ground singlet state ($^1\text{A}$) $45^{\circ}$ torsional angle and the corresponding vertical singlet-triplet energy gap is $0.01$ eV. We have employed this benchmark for assessment of the accuracy of MkCCSDT and DMRG-tailored CCSD (TCCSD) methods. MR MkCCSDT with CAS(2,2) model space, though giving good values for the singlet-triplet energy gap, is not able to properly describe the shape of the multireference singlet PES. Similarly, DMRG(24,25) is not able to correctly capture the shape of the singlet surface, due to the missing dynamic correlation. On the other hand, the DMRG-tailored CCSD method describes the shape of the ground singlet state with an excellent accuracy, but for the correct ordering requires computation of the zero-spin-projection component of the triplet state ($^3\text{B}_1$).

physics.chem-ph↗

arXiv2017

Analysis of Electron Correlation Effects in Strongly Correlated Systems ($\rm N_2$ and $\rm N_2^+$) by applying DMRG and Quantum Information Theory

The dissociation of $\rm N_2$ and $\rm N_2^+$ has been studied by using the \emph{ab initio} Density Matrix Renormalization Group (DMRG) method. Accurate Potential Energy Surfaces (PES) have been obtained for the electronic ground states of $\rm N_2$ ($\rm X^1Σ_g^+$) and $\rm N_2^+$ ($\rm X^2Σ_g^+$) as well as for the $\rm N_2^+$ excited state $\rm B^2Σ_u^+$. Inherently to the DMRG approach, the eigenvalues of the reduced density matrix ($ρ$) and their correlation functions are at hand. Thus we can apply Quantum Information Theory (QIT) directly, and investigate how the wave function changes along the PES and depict differences between the different states. Moreover by characterizing quantum entanglement between different pairs of orbitals and analyzing the reduced density matrix, we achieved a better understanding of the multi-reference character featured by these systems.

physics.chem-ph↗