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In this paper we develop quantum dynamical methods capable of treating the dynamics of chemically reacting systems in an optical cavity in the vibrationally strong-coupling (VSC) limit at finite temperatures and in the presence of a dissipative solvent in both the few and many molecule limits. In the context of two simple models we demonstrate how reactivity in the {\em collective} VSC regime does not exhibit altered rate behavior in equilibrium, but may exhibit resonant cavity modification of reactivity when the system is explicitly out of equilibrium. Our results suggest experimental protocols that may be used to modify reactivity in the collective regime and point to features not included in the models studied which demand further scrutiny.

Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, particularly for glass-forming materials at low temperatures. The so-called thermodynamic scaling relation, validated for many molecular systems through experiments, offers an efficient means to explore a vast range of time scales along a one-dimensional phase diagram. Isomorph theory provides a theoretical framework for thermodynamic scaling based on strong virial-potential energy correlations, but this approach is most successful for simple point particles. In particular, isomorph theory has resisted extension to complex molecular liquids due to the existence of high-frequency intramolecular interactions. To elucidate the microscopic origin of density scaling for molecular systems, we employ two distinct approaches for coarse-graining in space or in time. The former eliminates fast degrees of freedom by reducing a molecule to a center-of-mass-level description, while the latter involves temporally averaged fluctuations or correlation functions over the characteristic time scale. We show that both approaches yield a consistent density scaling coefficient for ortho-terphenyl, which is moreover in agreement with the experimental value. Building upon these findings, we derive the density scaling relationship exhibiting a single-parameter phase diagram from fully atomistic simulations. Our results unravel the microscopic nature underlying thermodynamic scaling and shed light on the role of coarse-graining for assessing the slow fluctuations in molecular systems, ultimately enabling the extension of systematic bottom-up approaches to larger and more complex molecular liquids that are experimentally challenging to probe., Comment: 24 pages, 18 figures

We describe two developments of tensor network influence functionals (in particular, influence functional matrix product states (IF-MPS)) for quantum impurity dynamics within the fermionic setting of the Anderson impurity model. The first provides the correct extension of the IF-MPS to continuous time by introducing a related mathematical object, the boundary influence functional MPS. The second connects the dynamics described by a compressed IF-MPS to that of a quantum embedding method with a time-dependent effective bath undergoing non-unitary dynamics. Using these concepts, we implement higher-order time propagators for the quench dynamics of the Anderson impurity model within the boundary IF-MPS formalism. The calculations illustrate the ability of the current formulation to efficiently remove the time-step error in standard discrete-time IF-MPS implementations as well as to interface with state-vector propagation techniques. They also show the advantages of IF-MPS dynamics, with its associated highly compact effective bath dynamics, over state-vector propagation with a static bath discretization.

Convincing evidence of domain growth in the heating of ultrastable glasses suggests that the equilibration dynamics of super-cooled liquids could be driven by a nucleation and growth mechanism. We investigate this possibility by simulating the equilibration dynamics of a model glass during both heating and cooling between poorly and well-annealed states. Though we do observe the growth of domains during heating, we find that domains are absent during cooling. This absence is inconsistent with classical nucleation theory. By comparing the equilibration dynamics of our glass with that of two models with kinetic constraints, we demonstrate that dynamical facilitation generically leads to heating driven by domain growth and cooling without domains. Our results provide strong evidence that dynamical facilitation, not nucleation and interfacial-tension-driven domain growth, is the driving mechanism for the equilibration dynamics of glass-formers., Comment: 21 pages, 16 figures. Supplemental Movies too large for arXiv. Will provide download link once available. Available on request until then

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system., Comment: 36 pages, 6 figures

We apply the Lang-Firsov (LF) transformation to electron-boson coupled Hamiltonians and variationally optimize the transformation parameters and molecular orbital coefficients to determine the ground state. M\o{}ller-Plesset (MP-$n$, with $n = 2$ and $4$) perturbation theory is then performed on top of the optimized LF mean-field state to improve the description of electron-electron and electron-boson correlations. The method (LF-MP) is applied to several electron-boson coupled systems, including the Hubbard-Holstein model, diatomic molecule dissociation ($\text{H}_2$, $\text{HF}$), and the modification of proton transfer reactions (malonaldehyde and aminopropenal) via the formation of polaritons in an optical cavity. We show that with a correction for the electron-electron correlation, the method gives quantitatively accurate energies comparable to exact diagonalization or coupled-cluster theory. The effect of multiple photon modes, spin polarization, and the comparison to the coherent state MP theory are also discussed., Comment: 16 pages, 8 figures

Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained approaches in $\textit{k}$-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher-order contributions. We propose a systematic framework for constructing a faithful Fourier space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular coarse-grained models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parametrization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems., Comment: 54 pages, 11 figures

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo (AFQMC) through the application of automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices (RDMs) with the same computational cost scaling as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations., Comment: 10 pages, 6 figures

We present a comprehensive study of generalized Wigner crystals across various filling factors for system sizes up to 162 holes employing Hartree-Fock theory and explicitly correlated wave function approaches. While we find broad agreement with the behavior observed in experiments and classical Monte Carlo simulations, we highlight the fact that the Hartree-Fock energy landscape appears to be remarkably complex, exhibiting many competing states, both ordered and disordered, separated by energies of a fraction of $\sim$ 1 meV/hole. We demonstrate which of the located states are metastable by performing a stability analysis at the Hartree-Fock level. Correlated wave function methods furthermore reveal small correlation energies that are nevertheless large enough to tip the balance of state ordering found within Hartree-Fock theory., Comment: 17 pages, 12 figures

We formulate and characterize a new constraint for Auxiliary Field Quantum Monte Carlo (AFQMC) applicable for general fermionic systems, which allows for the accumulation of phase in the random walk but disallows walkers with a magnitude of phase greater than $\pi$ with respect to the trial wave function. For short imaginary times, before walkers accumulate sizable phase values, this approach is equivalent to exact free projection, allowing one to observe the accumulation of bias associated with the constraint and thus estimate its magnitude \textit{a priori}. We demonstrate the stability of this constraint over arbitrary imaginary times and system sizes, highlighting the removal of noise due to the fermionic sign problem. Benchmark total energies for a variety of weakly and strongly correlated molecular systems reveal a distinct bias with respect to standard phaseless AFQMC, with a comparative increase in accuracy given a sufficient quality of trial wave function for the set of studied cases. We then take this constraint, referred to as linecut (lc-) AFQMC, and systematically release it (lcR-AFQMC), providing a route to obtain a smooth bridge between constrained AFQMC and the exact free projection results., Comment: 26 pages, 11 figures, 3 tables

Halide pervoskites are an important class of semiconducting materials which hold great promise for optoelectronic applications. In this work we investigate the relationship between vibrational anharmonicity and dynamic disorder in this class of solids. Via a multi-scale model parameterized from first-principles calculations, we demonstrate that the non-Gaussian lattice motion in halide perovskites is microscopically connected to the dynamic disorder of overlap fluctuations among electronic states. This connection allows us to rationalize the emergent differences in temperature-dependent mobilities of prototypical MAPbI$_3$ and MAPbBr$_3$ compounds across structural phase-transitions, in agreement with experimental findings. Our analysis suggests that the details of vibrational anharmonicity and dynamic disorder can complement known predictors of electronic conductivity and can provide structure-property guidelines for the tuning of carrier transport characteristics in anharmonic semiconductors.

We develop a microscopic theory for the multimode polariton dispersion in materials coupled to cavity radiation modes. Starting from a microscopic light-matter Hamiltonian, we devise a general strategy for obtaining simple matrix models of polariton dispersion curves based on the structure and spatial location of multi-layered 2D materials inside the optical cavity. Our theory exposes the connections between seemingly distinct models that have been employed in the literature and resolves an ambiguity that has arisen concerning the experimental description of the polaritonic band structure. We demonstrate the applicability of our theoretical formalism by fabricating various geometries of multi-layered perovskite materials coupled to cavities and demonstrating that our theoretical predictions agree with the experimental results presented here.

We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of $O(N_{\rm e}^3$), where $N_{\rm e}$ is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals (ERI). To improve the time-propagation and the spectral resolution, we adopt the dynamic mode decomposition (DMD) technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective, we celebrate his work at these frontiers.

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the $k$-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage., Comment: 31 pages, 2 tables, 1 figure

We investigate why the Lyapunov exponents $\lambda$ of out-of-time-ordered correlators (OTOCs) satisfy a universal bound $\lambda < 2 \pi k_B T/{\hbar}$ by probing imaginary-time path-integral space using ring-polymer molecular dynamics (RPMD) for a barrier-crossing model. We find that the RPMD OTOC satisfies the same bound as the quantum OTOC, which is caused by the stability of quantum thermal fluctuations around the instanton on the barrier. We expect that similar instantons (or other delocalised structures) will be found in many other systems with exponentially growing OTOCs.

Structural defects control the kinetic, thermodynamic and mechanical properties of glasses. For instance, rare quantum tunneling two-level systems (TLS) govern the physics of glasses at very low temperature. Because of their extremely low density, it is very hard to directly identify them in computer simulations. We introduce a machine learning approach to efficiently explore the potential energy landscape of glass models and identify desired classes of defects. We focus in particular on TLS and we design an algorithm that is able to rapidly predict the quantum splitting between any two amorphous configurations produced by classical simulations. This in turn allows us to shift the computational effort towards the collection and identification of a larger number of TLS, rather than the useless characterization of non-tunneling defects which are much more abundant. Finally, we interpret our machine learning model to understand how TLS are identified and characterized, thus giving direct physical insight into their microscopic nature.

Obtaining the atomistic structure and dynamics of disordered condensed phase systems from first principles remains one of the forefront challenges of chemical theory. Here we exploit recent advances in periodic electronic structure to show that, by leveraging transfer learning starting from lower tier electronic structure methods, one can obtain machine learned potential energy surfaces for liquid water from the higher tier AFQMC, CCSD, and CCSD(T) approaches using $\le$200 energies. By performing both classical and path integral molecular dynamics simulations on these machine learned potential energy surfaces we uncover the interplay of dynamical electron correlation and nuclear quantum effects across the entire liquid range of water while providing a general strategy for efficiently utilizing periodic correlated electronic structure methods to explore disordered condensed phase systems.

In this work we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time non-equilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

We present an efficient implementation of the Generalized Green's function Cluster Expansion (GGCE), which is a new method for computing the ground-state properties and dynamics of polarons (single electrons coupled to lattice vibrations) in model electron-phonon systems. The GGCE works at arbitrary temperature and is well suited for a variety of electron-phonon couplings, including, but not limited to, site and bond Holstein and Peierls (Su-Schrieffer-Heeger) couplings, and couplings to multiple phonon modes with different energy scales and coupling strengths. Quick calculations can be performed efficiently on a laptop using solvers from NumPy and SciPy, or in parallel at scale using the PETSc sparse linear solver engine., Comment: 3 pages, software can be found open source under the BSD-3-clause license at github.com/x94carbone/GGCE

We employ an exact quantum mechanical simulation technique to investigate a model of cavity-modified chemical reactions in the condensed phase. The model contains the coupling of the reaction coordinate to a generic solvent, cavity coupling to either the reaction coordinate or a non-reactive mode, and the coupling of the cavity to lossy modes. Thus, many of the most important features needed for realistic modeling of the cavity modification of chemical reactions are included. We find that when a molecule is coupled to an optical cavity it is essential to treat the problem quantum mechanically in order to obtain a quantitative account of alterations to reactivity. We find sizable and sharp changes in the rate constant that are associated with quantum mechanical state splittings and resonances. The features that emerge from our simulations are closer to those observed in experiments than are previous calculations, even for realistically small values of coupling and cavity loss. This work highlights the importance of a fully quantum treatment of vibrational polariton chemistry.

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially-localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements., Comment: 17 pages, 12 figures

We review the phenomena of dynamical heterogeneity in glass-forming systems and its description within replica and mean-field theories of the glass transition., Comment: To appear as a chapter in the book "Spin Glass Theory and Far Beyond - Replica Symmetry Breaking after 40 years"

The physics of the glass transition and amorphous materials continues to attract the attention of a wide research community after decades of effort. Supercooled liquids and glasses have been studied numerically since the advent of molecular dynamics and Monte Carlo simulations in the last century. Computer studies have greatly enhanced both experimental discoveries and theoretical developments and constitute an active and continually expanding research field. Our goal in this review is to provide a modern perspective on this area. We describe the need to go beyond canonical methods to attack a problem that is notoriously difficult in terms of time scales, length scales, and physical observables. We first summarise recent algorithmic developments to achieve enhanced sampling and faster equilibration using replica exchange methods, cluster and swap Monte Carlo algorithms, and other techniques. We then review some major recent advances afforded by these novel tools regarding the statistical mechanical description of the liquid-to-glass transition as well as the mechanical, vibrational and thermal properties of the glassy solid. We finally describe some important challenges for future research., Comment: 17 pages, 5 figures, to be published in Nature Reviews Physics

The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through quantum computation, as a potential ``killer application''. Indications of potential exponential quantum advantage in artificial tasks have increased interest in this application, thus, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation. We conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for quantum chemistry, it may be prudent to assume exponential speedups are not generically available for this problem.

In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph- AFQMC) approach from a computational quantum chemistry perspective, and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multi-reference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.

A recent preprint by Mazzola and Carleo numerically investigates exponential challenges that can arise for the QC-QMC algorithm introduced in our work, "Unbiasing fermionic quantum Monte Carlo with a quantum computer." As discussed in our original paper, we agree with this general concern. However, here we provide further details and numerics to emphasize that the prospects for practical quantum advantage in QC-QMC remain open. The exponential challenges in QC-QMC are dependent on (1) the choice of QMC methods, (2) the underlying system, and (3) the form of trial and walker wavefunctions. While one can find difficult examples with a specific method, a specific system, and a specific walker/trial form, for some combinations of these choices, the approach is potentially more scalable than other near-term quantum algorithms. Future research should aim to identify examples for which QC-QMC enables practical quantum advantage.

In this work we provide an exact and efficient numerical approach to simulate multi-time correlation functions in the Mahan-Nozi\`{e}res-De Dominicis model, which crudely mimics the spectral properties of doped two-dimensional semiconductors such as monolayer transition metal dichalcogenides. We apply this approach to study the coherent two-dimensional electronic spectra of the model. We show that several experimentally observed phenomena, such as peak asymmetry and coherent oscillations in the waiting-time dependence of the trion-exciton cross peaks of the two-dimensional rephasing spectrum, emerge naturally in our approach. Additional features are also present which find no correspondence with experimentally expected behavior. We trace these features to the infinite hole mass property of the model. We use this understanding to construct an efficient approach which filters out configurations associated with the lack of exciton recoil, enabling the connection to previous work and providing a route to the construction of realistic two-dimensional spectra over a broad doping range in two-dimensional semiconductors., Comment: 8 Pages, 6 Figures

Recent experiments have suggested that ground state chemical kinetics can be suppressed or enhanced by coupling the vibrational degrees of freedom of a molecular system with a radiation mode inside an optical cavity. Experiments show that the chemical rate is strongly modified when the photon frequency is close to characteristic vibrational frequencies. The origin of this remarkable effect remains unknown. In this work, we develop an analytical rate theory for cavity-modified ground state chemical kinetics based on the Pollak-Grabert-H\"anggi rate theory. Unlike previous work, our theory covers the complete range of solvent friction values, from the energy-diffusion limited to the spatial-diffusion limited regimes. We show that the chemical reaction rate can either be enhanced or suppressed depending on the bath friction; when bath friction is weak chemical kinetics is enhanced as opposed to the case of strong bath friction, where chemical kinetics is suppressed. Further, we show that the photon frequency at which maximum modification of chemical rate is achieved is close to the reactant well, and hence resonant rate modification occurs. In the strong friction limit the {\it resonant} photon frequency is instead close to the barrier frequency, as obtained using the Grote-Hynes rate theory. Finally, we observe that the rate changes (as a function of photon frequency) are much sharper and more sizable in the weak friction limit than in the strong friction limit, and become increasingly sharp with decreasing well frequency.

Semiconductor excitations can hybridize with cavity photons to form exciton-polaritons (EPs) with remarkable properties, including light-like energy flow combined with matter-like interactions. To fully harness these properties, EPs must retain ballistic, coherent transport despite matter-mediated interactions with lattice phonons. Here we develop a nonlinear momentum-resolved optical approach that directly images EPs in real space on femtosecond scales in a range of polaritonic architectures. We focus our analysis on EP propagation in layered halide perovskite microcavities. We reveal that EP-phonon interactions lead to a large renormalization of EP velocities at high excitonic fractions at room temperature. Despite these strong EP-phonon interactions, ballistic transport is maintained for up to half-exciton EPs, in agreement with quantum simulations of dynamic disorder shielding through light-matter hybridization. Above 50% excitonic character, rapid decoherence leads to diffusive transport. Our work provides a general framework to precisely balance EP coherence, velocity, and nonlinear interactions.

In this work we present a self-consistent cumulant expansion (SC-CE) and investigate its accuracy for the one-dimensional Holstein model with and without phonon dispersion. We show that for finite lattices sizes, the numerical integration of the SC-CE equations becomes unstable at long times. This defect is partially ameliorated when studying systems in the thermodynamic limit, enabling the demonstration that the SC-CE corrects many deficits of the standard perturbative CE in the (non-dispersive) Holstein model. The natural phonon damping that arises in the more realistic dispersed Holstein model renders the SC-CE stable, allowing for a complete assessment of the method. Here we find that self-consistency dramatically corrects many of the failures found in the perturbative CE, but also introduces some unphysical features. Finally, we comment on the potential use of SC-CE as a tool for calculating Green's functions in generic many-body problems., Comment: 11 pages, 4 figures

In this work we investigate the ability of the cumulant expansion (CE) to capture one-particle spectral information in electron-phonon coupled systems at both zero and finite temperatures. In particular, we present a comprehensive study of the second- and fourth-order CE for the one-dimensional Holstein model as compared with numerically exact methods. We investigate both finite sized systems as well as the approach to the thermodynamic limit, drawing distinctions and connections between the behavior of systems in and away from the thermodynamic limit that enable a greater understanding of the ability of the CE to capture real-frequency information across the full range of wave vectors. We find that for zero electronic momentum, the spectral function is well described by the second-order CE at low and high temperatures. However, for non-zero electronic momenta, the CE is only accurate at high temperature. We analyze the fourth-order cumulant, and find that while it improves the description of the short-time dynamics encoded in the one-particle Green's function, it can introduce divergences in the time domain as well as unphysical negative spectral weight in the spectral function. When well-behaved, the fourth-order CE does provide notable accurate corrections to the second-order CE. Finally, we use our results to comment on the use of the CE as a tool for calculating transport behavior in the realistic ab initio modeling of materials., Comment: 16 pages, 7 figures

Phaseless Auxiliary-Field Quantum Monte Carlo (ph-AFQMC) has recently emerged as a promising method for the production of benchmark-level simulations of medium to large-sized molecules, due to its accuracy and favorable polynomial scaling with system size. Unfortunately the memory footprint of standard energy evaluation algorithms are non-trivial, which can significantly impact timings on graphical processing units (GPUs) where memory is limited. Previous attempts to reduce scaling by taking advantage of the low rank structure of the Coulombic integrals have been successful, but are significantly limited by high prefactors, rendering the utility limited to very large systems. Here, we present a complementary, cubic scaling route to reduce memory and computational scaling based on the low rank of the Coulombic interactions between localized orbitals, focusing on the application to phaseless AFQMC. We show that the error due to this approximation, which we term Localized Orbital AFQMC (LO-AFQMC), is systematic and controllable via a single variable, and is computationally favorable even for small systems. We present results demonstrating a robust retention of accuracy versus both experiment and full ph-AFQMC for a variety of test cases chosen for their potential difficulty for localized orbital based methods, including the singlet-triplet gaps of polyacenes benzene through pentacene, the heats of formation for a set of platonic hydrocarbon cages, and the total energy of ferrocene (Fe(Cp)$_2$). Finally, we reproduce our previous result of the gas phase ionization energy of Ni(Cp)$_2$, agreeing with full ph-AFQMC to within statistical error while using less than a fifteenth of the computer time., Comment: 36 pages, 8 figures; Supplemental Info, 11 pages, 1 figure

The multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach suffers from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of a regularization parameter. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to $10^6$ bath modes, and find that for these problems the PSI requires roughly 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH, and 2-3/1-2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to $\sim 1.3\times 10^9$ parameters to obtain accurate dynamics., Comment: Main paper: 17 pages, 7 figures. Supplemental information (for paper I and paper II of the series): 22 pages, 2 figures

We derive a family of equations of motion (EOMs) for evolving multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) wavefunctions that, unlike the standard ML-MCTDH EOMs, never require the evaluation of the inverse of singular matrices. All members of this family of EOMs make use of alternative static gauge conditions than that used for standard ML-MCTDH. These alternative conditions result in an expansion of the wavefunction in terms of a set of potentially arbitrary orthonormal functions, rather than in terms of a set of non-orthonormal and potentially linearly dependent functions, as is the case for standard ML-MCTDH. We show that the EOMs used in the projector splitting integrator (PSI) and the invariant EOMs approaches are two special cases of this family obtained from different choices for the dynamic gauge condition, with the invariant EOMs making use of a choice that introduces potentially unbounded operators into the EOMs. As a consequence, all arguments for the existence of parallelizable integration schemes for the invariant EOMs can also be applied to the PSI EOMs., Comment: 10 + $\epsilon$ pages, 2 figures

Potassium-doped terphenyl has recently attracted attention as a potential host for high-transition-temperature superconductivity. Here, we elucidate the many-body electronic structure of recently synthesized potassium-doped terphenyl crystals. We show that this system may be understood as a set of weakly coupled one-dimensional ladders. Depending on the strength of the inter-ladder coupling the system may exhibit spin-gapped valence-bond solid or antiferromagnetic phases, both of which upon hole doping may give rise to superconductivity. This terphenyl-based ladder material serves as a new platform for investigating the fate of ladder phases in presence of three-dimensional coupling as well as for novel superconductivity., Comment: 6 pages main text + 3 pages supplementary information, 4 figures main text