For electronic structure calculations of periodic extended systems based on many-body wave functions, we investigate the utility of a similarity transformation of the Hamiltonian in the thermodynamic limit, followed by a treatment of the resulting transcorrelated Hamiltonian within a supercell approximation. Using a correlation factor fulfilling the long-range asymptotic condition of the uniform electron gas, the effective potential of the transcorrelated Hamiltonian decays much faster than the original Coulomb potential. This is found to significantly speed up the convergence of the supercell energies towards the thermodynamic limit.

Transcorrelated methods provide an efficient way of partially transferring the description of electronic correlations from the ground state wavefunction directly into the underlying Hamiltonian. In particular, Dobrautz et al. [Phys. Rev. B, 99(7), 075119, (2019)] have demonstrated that the use of momentum-space representation, combined with a non-unitary similarity transformation, results in a Hubbard Hamiltonian that possesses a significantly more compact ground state wavefunction, dominated by a single Slater determinant. This compactness/single-reference character greatly facilitates electronic structure calculations. As a consequence, however, the Hamiltonian becomes non-Hermitian, posing problems for quantum algorithms based on the variational principle. We overcome these limitations with the ansatz-based quantum imaginary time evolution algorithm and apply the transcorrelated method in the context of digital quantum computing. We demonstrate that this approach enables up to 4 orders of magnitude more accurate and compact solutions in various instances of the Hubbard model at intermediate interaction strength (U/t=4), enabling the use of shallower quantum circuits for wavefunction ansatzes. In addition, we propose a more efficient implementation of the quantum imaginary time evolution algorithm in quantum circuits that is tailored to non-Hermitian problems. To validate our approach, we perform hardware experiments on the ibmq_lima quantum computer. Our work paves the way for the use of exact transcorrelated methods for the simulations of ab initio systems on quantum computers.

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or $\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.

With a transcorrelated Hamiltonian, we perform a many body perturbation calculation on the uniform electron gas in the high density regime. By using a correlation factor optimized for a single determinant Jastrow ansatz, the second order correlation energy is calculated as 1-ln⁡2π2ln(rs)-0.05075. This already reproduces the exact logarithmic term of the random phase approximation (RPA) result, while the constant term is roughly 7% larger than the RPA one. The close agreement with the RPA method demonstrates that the transcorrelated method offers a viable and potentially efficient method for treating metallic systems.

We demonstrate how similarity-transformed full configuration interaction quantum Monte Carlo (FCIQMC) based on the transcorrelated Hamiltonian can be applied to make highly accurate predictions for the binding curve of the beryllium dimer, marking the first case study of a molecular system with this method. In this context, the non-Hermitian transcorrelated Hamiltonian, resulting from a similarity transformation with a Jastrow factor, serves the purpose to effectively address dynamic correlation beyond the used basis set and thus allows for obtaining energies close to the complete basis set limit from FCIQMC already with moderate basis sets and computational effort. Building on results from other explicitly correlated methods, we discuss the role of the Jastrow factor and its functional form, as well as potential sources for size consistency errors, and arrive at Jastrow forms that allow for high accuracy calculations of the vibrational spectrum of the beryllium dimer.

We propose a streamlined combination scheme of the transcorrelation (TC) and coupled cluster (CC) theory, which not only increases the convergence rate with respect to the basis set, but also extends the applicability of the lowest order CC approximations to strongly correlated regimes in the three dimensional uniform electron gas (3D UEG). With the correct physical insights built into the correlator used in TC, highly accurate ground state energies with errors ≤ 0.001 a.u./electron relative to the state-of-the-art quantum Monte Carlo results can be obtained across a wide range of densities. The greatly improved efficiency and accuracy of our methods hold great promise for strongly correlated solids where many other methods fail.

We investigate Nagaoka ferromagnetism in the two-dimensional Hubbard model with one hole using the spin-adapted (SU(2) conserving) full configuration interaction quantum Monte Carlo method. This methodology gives us access to the ground state energies of all possible spin states S of finite Hubbard lattices, here obtained for lattices up to 24 sites, for various interaction strengths (U). The critical interaction strength, U_c, at which the Nagaoka transition occurs is determined for each lattice and is found to be proportional to the lattice size for the larger lattices. Below U_c the overall ground states are found to favour the minimal total spin (S=1/2), and no intermediate spin state is found to be the overall ground state on lattices larger than 16 sites. However, at U_c, the energies of all the spin states are found to be nearly degenerate, implying that large fluctuations in total spin can be expected in the vicinity of the Nagaoka transition.

A hyperbolic singularity in the wave function of s-wave interacting atoms is the root problem for any accurate numerical simulation. Here, we apply the transcorrelated method, whereby the wave-function singularity is explicitly described by a two-body Jastrow factor, and then folded into the Hamiltonian via a similarity transformation. The resulting nonsingular eigenfunctions are approximated by stochastic Fock-space diagonalization with energy errors scaling with 1/M in the number M of single-particle basis functions. The performance of the transcorrelated method is demonstrated on the example of strongly correlated fermions with unitary interactions. The current method provides the most accurate ground-state energies so far for three and four fermions in a rectangular box with periodic boundary conditions.

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0.

Similarity transformation of the Hubbard Hamiltonian using a Gutzwiller correlator leads to a non-Hermitian effective Hamiltonian, which can be expressed exactly in momentum-space representation, and contains three-body interactions. We apply this methodology to study the two-dimensional Hubbard model with repulsive interactions near half-filling in the intermediate interaction strength regime ($U/t=4$). We show that at optimal or near optimal strength of the Gutzwiller correlator, the similarity transformed Hamiltonian has extremely compact right eigenvectors, which can be sampled to high accuracy using the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method, and its initiator approximation. Near-optimal correlators can be obtained using a simple projective equation, thus obviating the need for a numerical optimisation of the correlator. The FCIQMC method, as a projective technique, is well-suited for such non-Hermitian problems, and its stochastic nature can handle the 3-body interactions exactly without undue increase in computational cost. The highly compact nature of the right eigenvectors means that the initiator approximation in FCIQMC is not severe, and that large lattices can be simulated, well beyond the reach of the method applied to the original Hubbard Hamiltonian. Results are provided in lattice sizes upto 50 sites and compared to auxiliary-field QMC. New benchmark results are provided in the off half-filling regime, with no severe sign-problem being encountered. In addition, we show that methodology can be used to calculate excited states of the Hubbard model and lay the groundwork for the calculation of observables other than the energy.

By expressing the electronic wavefunction in an explicitly correlated (Jastrow-factorized) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions. The resulting ground-state eigenvalue problem can be solved projectively using a stochastic configuration-interaction formalism. Our approach permits the use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets. Results are presented for the total energies and ionization potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort.

We suggest an efficient method to resolve electronic cusps in electronic structure calculations through the use of an effective transcorrelated Hamiltonian. This effective Hamiltonian takes a simple form for plane wave bases, containing up to two-body operators only, and its use incurs almost no additional computational overhead compared to that of the original Hamiltonian. We apply this method in combination with the full configuration interaction quantum Monte Carlo (FCIQMC) method to the homogeneous electron gas. As a projection technique, the non-Hermitian nature of the transcorrelated Hamiltonian does not cause complications or numerical difficulties for FCIQMC. The rate of convergence of the total energy to the complete basis set limit is improved from [Formula: see text] to [Formula: see text], where M is the total number of orbital basis functions.

Exact diagonalization expansions of Bose or Fermi gases with contact interactions converge very slowly due to a nonanalytic cusp in the wave function. Here we develop a transcorrelated approach where the cusp is treated exactly and folded into the many-body Hamiltonian with a similarity transformation that removes the leading-order singularity. The resulting transcorrelated Hamiltonian is not Hermitian but can be treated numerically with a standard projection approach. The smoothness of the wave function improves by at least one order and thus the convergence rate for the ground-state energy improves. By numerical investigation of a one-dimensional gas of spin-1/2 fermions we find the error in the transcorrelated energy to scale as M-3 with a single-particle basis of M plane waves compared to M-1 for the expansion of the original Hamiltonian and M-2 using conventional lattice renormalization.

Three-dimensional (3D) hierarchical CNTs/GO/S ternary composites were prepared by solution-based reaction-deposition, using graphene oxide (GO) and carbon nanotubes (CNTs) as precursors. Scanning electron microscopy (SEM) and transmission electron microscope (TEM) indicated a uniform S coating on CNTs/GO which arose because of the large GO specific surface area. CNTs interspersed between the GO layers to form a 3D porous structure. Constant current charge-discharge tests showed that CNTs/GO/S composites had a high discharge capacity and excellent cycling stability, and delivered a high initial discharge capacity of 904 mAh . g(-1) at 1C rate. After 50 cycles at the same rate, the reversible capacity remained at 578 mAh . g(-1).

In this paper, hierarchical Li4Ti5O12 microspheres were successfully synthesized in a large scale via a facile hydrothermal route. X-ray diffraction, field emission scanning electron microscopy and transmission electron microscopy were used to characterize the obtained Li4Ti5O12 microspheres and the results indicate that the monodispersed Li4Ti5O12 microspheres with ca. 2 μm in diameter was assembled by well-crystalline nanoparticles. Electrochemical analysis indicated that the Li4Ti5O12 microspheres have superior rate capability and cycling performance. At the charge–discharge rate of 0.2, 1, 2, 5, 10 and 20 C, the discharge capacities of Li4Ti5O12 microspheres are 169.2, 163.5, 158.3, 136.4, 117.6 and 94.3 mAh g−1, respectively. Excellent capacity retention of 98.7% was achieved after 100 cycles at 1 C rate and it can still maintained 91% even at high rate of 10 C.

We describe a novel approach for the synthesis of carbon coated Li4Ti5O12 (Li4Ti5O12/C) nanorods for high rate lithium ion batteries. The carbon coated TiO2 nanotubes using the glucose as carbon source are first synthesized by hydrothermal treatment. The commercial anatase TiO2 powder is immersed in KOH sulotion and subsequently transforms into Li4Ti5O12/C in LiOH solution under hydrothermal condition. Field-emission scanning electron microscopy, transmission electron microscopy, X-ray diffraction, nitrogen adsorption/desorption and Raman spectra are performed to characterize their morphologies and structures. Compared with the pristine Li4Ti5O12, one-dimensional (1D) Li4Ti5O12/C nanostructures show much better rate capability and cycling stability. The 1D Li4Ti5O12/C architectures effectively restrict the particle growth and enhance their electronic conductivity, enabling fast ion and electron transport. (c) 2013 Elsevier B.V. All rights reserved.

We present a direct comparison of the exchange-only optimized effective potential ($x$-OEP) method, originating from density functional theory, with Hartree-Fock (HF) results for jellium slabs of finite width, based on fully self-consistent calculations. The nonlocal character of the HF exchange potential causes a coupling of the momentum parallel to the slab surface with the perpendicular component of the orbitals. This results in an entirely different energy-band structure close to the Fermi surface and in terms of bandwidth, as compared with the $x$-OEP energy-band structure. Good agreement between $x$-OEP and HF calculations for jellium slabs has been observed for Friedel oscillations of the electron density, surface energies, and dipole barriers, as well as for electrostatic and averaged exchange potentials. However, marked differences appear between $x$-OEP and HF work functions for narrow slabs, which is in contrast to the good agreement of ionization energies reported for finite systems. On the other hand, we present evidence that both work functions are very similar in the limit of very wide slabs.