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Cavity electrodynamics offers a unique avenue for tailoring ground-state material properties, excited-state engineering, and versatile control of quantum matter. Merging these concepts with high-field physics in the terahertz (THz) spectral range opens the door to explore low-energy, field-driven cavity electrodynamics, emerging from fundamental resonances or order parameters. Despite this demand, leveraging the full potential of field-driven material control in cavities is hindered by the lack of direct access to the intra-cavity fields. Here, we demonstrate a new concept of active cavities, consisting of electro-optic Fabry-Perot resonators, which measure their intra-cavity electric fields on sub-cycle timescales. We thereby demonstrate quantitative retrieval of the cavity modes in amplitude and phase, over a broad THz frequency range. To enable simultaneous intra-cavity sampling alongside excited-state material control, we design a tunable multi-layer cavity, enabling deterministic design of hybrid cavities for polaritonic systems. Our theoretical models reveal the origin of the avoided crossings embedded in the intricate mode dispersion, and will enable fully-switchable polaritonic effects within arbitrary materials hosted by the hybrid cavity. Electro-optic cavities (EOCs) will therefore serve as integrated probes of light-matter interactions across all coupling regimes, laying the foundation for field-resolved intra-cavity quantum electrodynamics., Comment: main: 7 pages, 4 figurs; total: 34 pages, 20 figures

Quantum chemical calculations of the ground-state properties of positron-molecule complexes are challenging. The main difficulty lies in employing an appropriate basis set for representing the coalescence between electrons and a positron. Here, we tackle this problem with the recently developed Fermionic neural network (FermiNet) wavefunction, which does not depend on a basis set. We find that FermiNet produces highly accurate, in some cases state-of-the-art, ground-state energies across a range of atoms and small molecules with a wide variety of qualitatively distinct positron binding characteristics. We calculate the binding energy of the challenging non-polar benzene molecule, finding good agreement with the experimental value, and obtain annihilation rates which compare favourably with those obtained with explicitly correlated Gaussian wavefunctions. Our results demonstrate a generic advantage of neural network wavefunction-based methods and broaden their applicability to systems beyond the standard molecular Hamiltonian., Comment: 14 pages, 3 figures

The advent of high-field THz sources has opened the field of nonlinear THz physics and unlocked access to fundamental low energy excitations for ultrafast material control. Recent advances towards controlling and employing chiral excitations, or generally angular momentum of light, not only rely on the measurement of undistorted intense THz fields, but also on the precise knowledge about sophisticated THz helicity states. A recently reported and promising detector material is $\alpha$-quartz. However, its electrooptic response function and contributing nonlinear effects have remained elusive. Here, we establish z-cut $\alpha$-quartz as a precise electrooptic THz detector for full amplitude, phase and polarization measurement of intense THz fields, all at a fraction of costs of conventional THz detectors. We experimentally determine its complex detector response function, which is in good agreement with our model based on predominantly known literature values. It also explains previously observed thickness-dependent waveforms. These insights allow us to develop a swift and reliable protocol to precisely measure arbitrary THz polarization and helicity states. This two-dimensional electrooptic sampling (2D-EOS) in $\alpha$-quartz fosters rapid and cost-efficient THz time-domain ellipsometry, and enables the characterization of polarization-tailored fields for driving chiral or other helicity-sensitive quasiparticles and topologies., Comment: 26 pages, 9 figures, 1 table

We present a variational Monte Carlo algorithm for estimating the lowest excited states of a quantum system which is a natural generalization of the estimation of ground states. The method has no free parameters and requires no explicit orthogonalization of the different states, instead transforming the problem of finding excited states of a given system into that of finding the ground state of an expanded system. Expected values of arbitrary observables can be calculated, including off-diagonal expectations between different states such as the transition dipole moment. Although the method is entirely general, it works particularly well in conjunction with recent work on using neural networks as variational Ans\"atze for many-electron systems, and we show that by combining this method with the FermiNet and Psiformer Ans\"atze we can accurately recover vertical excitation energies and oscillator strengths on a range of molecules. Our method is the first deep learning approach to achieve accurate vertical excitation energies, including challenging double excitations, on benzene-scale molecules. Beyond the chemistry examples here, we expect this technique will be of great interest for applications to atomic, nuclear and condensed matter physics., Comment: The content of this version is identical to the manuscript draft which was sent to Science on May 17th 2024

Understanding superfluidity remains a major goal of condensed matter physics. Here we tackle this challenge utilizing the recently developed Fermionic neural network (FermiNet) wave function Ansatz [D. Pfau et al., Phys. Rev. Res. 2, 033429 (2020).] for variational Monte Carlo calculations. We study the unitary Fermi gas, a system with strong, short-range, two-body interactions known to possess a superfluid ground state but difficult to describe quantitatively. We demonstrate key limitations of the FermiNet Ansatz in studying the unitary Fermi gas and propose a simple modification based on the idea of an antisymmetric geminal power singlet (AGPs) wave function. The new AGPs FermiNet outperforms the original FermiNet significantly in paired systems, giving results which are more accurate than fixed-node diffusion Monte Carlo and are consistent with experiment. We prove mathematically that the new Ansatz, which only differs from the original Ansatz by the method of antisymmetrization, is a strict generalization of the original FermiNet architecture, despite the use of fewer parameters. Our approach shares several advantages with the original FermiNet: the use of a neural network removes the need for an underlying basis set; and the flexibility of the network yields extremely accurate results within a variational quantum Monte Carlo framework that provides access to unbiased estimates of arbitrary ground-state expectation values. We discuss how the method can be extended to study other superfluids., Comment: 19 pages, 8 figures. Talk presented at the 2023 APS March Meeting, March 5-10, 2023, Las Vegas, Nevada, United States

We present a novel neural network architecture using self-attention, the Wavefunction Transformer (Psiformer), which can be used as an approximation (or Ansatz) for solving the many-electron Schr\"odinger equation, the fundamental equation for quantum chemistry and material science. This equation can be solved from first principles, requiring no external training data. In recent years, deep neural networks like the FermiNet and PauliNet have been used to significantly improve the accuracy of these first-principle calculations, but they lack an attention-like mechanism for gating interactions between electrons. Here we show that the Psiformer can be used as a drop-in replacement for these other neural networks, often dramatically improving the accuracy of the calculations. On larger molecules especially, the ground state energy can be improved by dozens of kcal/mol, a qualitative leap over previous methods. This demonstrates that self-attention networks can learn complex quantum mechanical correlations between electrons, and are a promising route to reaching unprecedented accuracy in chemical calculations on larger systems.

We present evidence that learned density functional theory (``DFT'') force fields are ready for ground state catalyst discovery. Our key finding is that relaxation using forces from a learned potential yields structures with similar or lower energy to those relaxed using the RPBE functional in over 50\% of evaluated systems, despite the fact that the predicted forces differ significantly from the ground truth. This has the surprising implication that learned potentials may be ready for replacing DFT in challenging catalytic systems such as those found in the Open Catalyst 2020 dataset. Furthermore, we show that a force field trained on a locally harmonic energy surface with the same minima as a target DFT energy is also able to find lower or similar energy structures in over 50\% of cases. This ``Easy Potential'' converges in fewer steps than a standard model trained on true energies and forces, which further accelerates calculations. Its success illustrates a key point: learned potentials can locate energy minima even when the model has high force errors. The main requirement for structure optimisation is simply that the learned potential has the correct minima. Since learned potentials are fast and scale linearly with system size, our results open the possibility of quickly finding ground states for large systems.

We report the development of a python-based auxiliary-field quantum Monte Carlo (AFQMC) program, ipie, with preliminary timing benchmarks and new AFQMC results on the isomerization of [Cu$_2$O$_2$$]^{2+}$. We demonstrate how implementations for both central and graphical processing units (CPUs and GPUs) are achieved in ipie. We show an interface of ipie with PySCF as well as a straightforward template for adding new estimators to ipie. Our timing benchmarks against other C++ codes, QMCPACK and Dice, suggest that ipie is faster or similarly performing for all chemical systems considered on both CPUs and GPUs. Our results on [Cu$_2$O$_2$$]^{2+}$ using selected configuration interaction trials show that it is possible to converge the ph-AFQMC isomerization energy between bis($\mu$-oxo) and $\mu$-$\eta^2$:$\eta^2$ peroxo configurations to the exact known results for small basis sets with $10^5$ to $10^6$ determinants. We also report the isomerization energy with a quadruple-zeta basis set with an estimated error less than a kcal/mol, which involved 52 electrons and 290 orbitals with $10^6$ determinants in the trial wavefunction. These results highlight the utility of ph-AFQMC and ipie for systems with modest strong correlation and large-scale dynamic correlation.

Deep neural networks have been extremely successful as highly accurate wave function ans\"atze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network is given no \emph{a priori} knowledge that a phase transition exists, but converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density., Comment: 12 pages, 3 figures

Spin-orbit coupling (SOC) is responsible for a range of spintronic and topological processes in condensed matter. Here we show photonic analogs of SOCs in exciton-polaritons and their condensates in microcavities composed of birefringent lead halide perovskite single crystals. The presence of crystalline anisotropy coupled with splitting in the optical cavity of the transverse electric (TE) and transverse magnetic (TM) modes gives rise to a non-Abelian gauge field, which can be described by the Rashba-Dresselhaus Hamiltonian near the degenerate points of the two polarization modes. With increasing density, the exciton polaritons with pseudospin textures undergo phase transitions to competing condensates with orthogonal polarizations. Unlike their pure photonic counterparts, these exciton polaritons and condensates inherit nonlinearity from their excitonic components and may serve as quantum simulators of many-body SOC processes., Comment: 17 pages, 4 figures, 29 pages Supporting Information

The Fermionic Neural Network (FermiNet) is a recently-developed neural network architecture that can be used as a wavefunction Ansatz for many-electron systems, and has already demonstrated high accuracy on small systems. Here we present several improvements to the FermiNet that allow us to set new records for speed and accuracy on challenging systems. We find that increasing the size of the network is sufficient to reach chemical accuracy on atoms as large as argon. Through a combination of implementing FermiNet in JAX and simplifying several parts of the network, we are able to reduce the number of GPU hours needed to train the FermiNet on large systems by an order of magnitude. This enables us to run the FermiNet on the challenging transition of bicyclobutane to butadiene and compare against the PauliNet on the automerization of cyclobutadiene, and we achieve results near the state of the art for both., Comment: To appear at the 3rd NeurIPS Workshop on Machine Learning and Physical Science

Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially-scaling algorithms. The key challenge for many of these algorithms is the choice of wavefunction approximation, or Ansatz, which must trade off between efficiency and accuracy. Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wavefunction Ansatz for spin systems, but problems in electronic structure require wavefunctions that obey Fermi-Dirac statistics. Here we introduce a novel deep learning architecture, the Fermionic Neural Network, as a powerful wavefunction Ansatz for many-electron systems. The Fermionic Neural Network is able to achieve accuracy beyond other variational quantum Monte Carlo Ans\"atze on a variety of atoms and small molecules. Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly-correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry. This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab-initio quantum chemistry methods, opening the possibility of accurate direct optimization of wavefunctions for previously intractable many-electron systems., Comment: Final proof for Physical Review Research

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the last decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this article we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semi-stochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.

Coupled cluster theory is a vital cornerstone of electronic structure theory and is being applied to ever-larger systems. Stochastic approaches to quantum chemistry have grown in importance and offer compelling advantages over traditional deterministic algorithms in terms of computational demands, theoretical flexibility or lower scaling with system size. We present a highly parallelizable algorithm of the coupled cluster Monte Carlo method involving sampling of clusters of excitors over multiple time steps. The behaviour of the algorithm is investigated on the uniform electron gas and the water dimer at CCSD, CCSDT and CCSDTQ levels. We also describe two improvements to the original sampling algorithm, full non-composite and multi-spawn sampling. A stochastic approach to coupled cluster results in an efficient and scalable implementation at arbitrary truncation levels in the coupled cluster expansion., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in "Spencer, J.S. et al., J. Chem. Phys. 149, 204103 (2018)", and may be found at https://doi.org/10.1063/1.5047420. Data and further info can be accessed at https://doi.org/10.17863/CAM.30359

Epitaxial films of the B20-structure alloy Fe$_{1-y}$Co$_y$Ge were grown by molecular beam epitaxy on Si (111) substrates. The magnetization varied smoothly from the bulk-like values of one Bohr magneton per Fe atom for FeGe to zero for non-magnetic CoGe. The chiral lattice structure leads to a Dzyaloshinskii-Moriya interaction (DMI), and the films' helical magnetic ground state was confirmed using polarized neutron reflectometry measurements. The pitch of the spin helix, measured by this method, varies with Co content $y$ and diverges at $y \sim 0.45$. This indicates a zero-crossing of the DMI, which we reproduced in calculations using first principle methods. We also measured the longitudinal and Hall resistivity of our films as a function of magnetic field, temperature, and Co content $y$. The Hall resistivity is expected to contain contributions from the ordinary, anomalous, and topological Hall effects. Both the anomalous and topological Hall resistivities show peaks around $y \sim 0.5$. Our first principles calculations show a peak in the topological Hall constant at this value of $y$, related to the strong spin-polarisation predicted for intermediate values of $y$. Half-metallicity is predicted for $y = 0.6$, consistent with the experimentally observed linear magnetoresistance at this composition. Whilst it is possible to reconcile theory with experiment for the various Hall effects for FeGe, the large topological Hall resistivities for $y \sim 0.5$ are much larger then expected when the very small emergent fields associated with the divergence in the DMI are taken into account.

In confined helimagnetic nanostructures, skyrmionic states in the form of incomplete and isolated skyrmion states can emerge as the ground state in absence of both external magnetic field and magnetocrystalline anisotropy. In this work, we study the dynamic properties (resonance frequencies and corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples. We employ two different methods in finite-element based micromagnetic simulation: eigenvalue and ringdown method. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system. However, using a particular experimentally feasible excitation can excite only a limited set of eigenmodes. Because of that, we perform ringdown simulations that resemble the experimental setup using both in-plane and out-of-plane excitations. In addition, we report the nonlinear dependence of resonance frequencies on the external magnetic bias field and disk sample diameter and discuss the possible reversal mode of skyrmionic states. We compare the power spectral densities of incomplete skyrmion and isolated skyrmion states and observe several key differences that can contribute to the experimental identification of the state present in the sample. We measure the FeGe Gilbert damping, and using its value we determine what eigenmodes can be expected to be observed in experiments. Finally, we show that neglecting the demagnetisation energy contribution or ignoring the magnetisation variation in the out-of-film direction - although not changing the eigenmode's magnetisation dynamics significantly - changes their resonance frequencies substantially. Apart from contributing to the understanding of skyrmionic states physics, this systematic work can be used as a guide for the experimental identification of skyrmionic states in confined helimagnetic nanostructures., Comment: manuscript: 17 pages, 9 figures; supplementary information: 10 pages, 8 figures

Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average $N$-body density matrices for uniform electron gas systems of up to 10$^{124}$ matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the $k$-space configuration path-integral formalism disagree by up to $\sim$$10$\% at certain reduced temperatures $T/T_F \le 0.5$ and densities $r_s \le 1$. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that DMQMC can calculate free energies directly and present exact free energies for $T/T_F \ge 1$ and $r_s \le 2$., Comment: Accepted version: added free energy data and restructured text. Now includes supplementary material

Within Full Configuration Interaction Quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per timestep and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree--Fock molecular orbitals, suggesting that the choice of basis impacts the method beyond that of the sign problem., Comment: 7 pages, 4 figures, Supplementary material available as 'Ancillary Files'

We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the critical population required to correctly sample the wavefunction for a range of systems and excitation levels and hence leads to a substantial reduction in the computational cost. This development has the potential to substantially extend the range of the method, enabling it to be used to treat larger systems with excitation levels not easily accessible with conventional deterministic methods.

We describe further details of the Stochastic Coupled Cluster method and a diagnostic of such calculations, the shoulder height, akin to the plateau found in Full Configuration Interaction Quantum Monte Carlo. We describe an initiator modification to Stochastic Coupled Cluster Theory and show that initiator calculations can be extrapolated to the unbiased limit. We apply this method to the 3D 14-electron uniform electron gas and present complete basis set limit values of the CCSD and previously unattainable CCSDT correlation energies for up to rs = 2, showing a requirement to include triple excitations to accurately calculate energies at high densities., Comment: 14 pages, 12 figures

Hubbard-like Hamiltonians are widely used to describe on-site Coulomb interactions in magnetic and strongly-correlated solids, but there is much confusion in the literature about the form these Hamiltonians should take for shells of p and d orbitals. This paper derives the most general s, p and d orbital Hubbard-like Hamiltonians consistent with the relevant symmetries, and presents them in ways convenient for practical calculations. We use the full configuration interaction method to study p and d orbital dimers and compare results obtained using the correct Hamiltonian and the collinear and vector Stoner Hamiltonians. The Stoner Hamiltonians can fail to describe properly the nature of the ground state, the time evolution of excited states, and the electronic heat capacity., Comment: Updated the paper to make some clarifications and include colour figures

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N -body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible., Comment: Minor text modifications and added deviation subplot to Fig. 9 following referee's review comments. Include link to supplementary material in references

Magnetic materials without structural inversion symmetry can display the Dzyaloshinskii-Moriya interaction, which manifests itself as chiral magnetic ground states. These chiral states can interact in complex ways with applied fields and boundary conditions provided by finite sample sizes that are of the order of the lengthscale of the chiral states. Here we study epitaxial thin films of FeGe with a thickness close to the helix pitch of the helimagnetic ground state, which is about 70 nm, by conventional magnetometry and polarized neutron reflectometry. We show that the helix in an FeGe film reverses under the application of a field by deforming into a helicoidal form, with twists in the helicoid being forced out of the film surfaces on the way to saturation. An additional boundary condition was imposed by exchange coupling a ferromagnetic Fe layer to one of the interfaces of an FeGe layer. This forces the FeGe spins at the interface to point in the same direction as the Fe, preventing node expulsion and giving a handle by which the reversal of the helical magnet may be controlled.

We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the Beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable., Comment: 10 pages, 7 figures

The HANDE quantum Monte Carlo project offers accessible stochastic algorithms for general use for scientists in the field of quantum chemistry. HANDE is an ambitious and general high-performance code developed by a geographically-dispersed team with a variety of backgrounds in computational science. In the course of preparing a public, open-source release, we have taken this opportunity to step back and look at what we have done and what we hope to do in the future. We pay particular attention to development processes, the approach taken to train students joining the project, and how a flat hierarchical structure aids communication, Comment: 6 pages. Submission to WSSSPE2

We investigate the sign problem for full configuration interaction quantum Monte Carlo (FCIQMC), a stochastic algorithm for finding the ground state solution of the Schr\"odinger equation with substantially reduced computational cost compared with exact diagonalisation. We find $k$-space Hubbard models for which the solution is yielded with storage that grows sub-linearly in the size of the many-body Hilbert space, in spite of using a wave function that is simply linear combination of states. The FCIQMC algorithm is able to find this sub-linear scaling regime without bias and with only a choice of Hamiltonian basis. By means of a demonstration we solve for the energy of a 70-site half-filled system (with a space of $10^{38}$ determinants) in 250 core hours, substantially quicker than the $\sim$10$^{36}$ core hours that would be required by exact diagonalisation. This is the largest space that has been sampled in an unbiased fashion. The challenge for the recently-developed FCIQMC method is made clear: expand the sub-linear scaling regime whilst retaining exact on average accuracy. This result rationalizes the success of the initiator adaptation (i-FCIQMC) and offers clues to improve it. We argue that our results changes the landscape for development of FCIQMC and related methods., Comment: 6 pages, 4 figures. The mentioned supplementary material is included as "Ancillary files". Comments welcome

We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov Chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to in general minimise the bias. We show a reweighting scheme to remove the bias caused by population control commonly used in Diffusion Monte Carlo [J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step., Comment: Supplementary material available as 'Ancillary Files'

We present a quantum Monte Carlo method capable of sampling the full density matrix of a many-particle system at finite temperature. This allows arbitrary reduced density matrix elements and expectation values of complicated non-local observables to be evaluated easily. The method resembles full configuration interaction quantum Monte Carlo but works in the space of many-particle operators instead of the space of many-particle wave functions. One simulation provides the density matrix at all temperatures simultaneously, from $T=\infty$ to $T=0$, allowing the temperature dependence of expectation values to be studied. The direct sampling of the density matrix also allows the calculation of some previously inaccessible entanglement measures. We explain the theory underlying the method, describe the algorithm, and introduce an importance-sampling procedure to improve the stochastic efficiency. To demonstrate the potential of our approach, the energy and staggered magnetization of the isotropic antiferromagnetic Heisenberg model on small lattices, the concurrence of one-dimensional spin rings, and the Renyi $S_2$ entanglement entropy of various sublattices of the $6 \times 6$ Heisenberg model are calculated. The nature of the sign problem in the method is also investigated., Comment: 13 pages, 6 figures

We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids any explicit reference to canonical representations of either occupied or virtual Kohn-Sham states and thus achieves linear-scaling computational effort with system size. In contrast to conventional localised orbital formulations, where a single set of localised functions is used to span the occupied and unoccupied state manifold, we make use of two sets of in situ optimised localised orbitals, one for the occupied and one for the unoccupied space. This double representation approach avoids known problems of spanning the space of unoccupied Kohn-Sham states with a minimal set of localised orbitals optimised for the occupied space, while the in situ optimisation procedure allows for efficient calculations with a minimal number of functions. The method is applied to a number of medium sized organic molecules and a good agreement with traditional TDDFT methods is observed. Furthermore, linear scaling of computational cost with system size is demonstrated on a system of carbon nanotubes.

The sign problem in Full Configuration Interaction Quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not., Comment: 4 pages w/ 2 page appendix, 2 figures, 1 table

The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of the nodal structure of the ground-state wave function. We investigate the nature of the sign problem in this method and how its severity depends on the system studied. We explain how cancelation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations., Comment: 11 pages. 6 figures