Many-body Wave Function Research Articles

Nuclear spectroscopy with heavy ion nucleon knockout and (p,2p) reactions

Knockout reactions with heavy ion targets in inverse kinematics, as well as "quasi-free" (p,2p) and (p,pn) reactions are useful tools for nuclear spectroscopy. We report calculations on \textit{ab-initio} many-body wavefunctions based on the no-core shell model to study the nucleon removal reactions in light nuclei, including beryllium, carbon, and oxygen isotopic chains, and explore the importance of using an \textit{ab-initio} method. Our study helps clarifying how the extraction of spectroscopic factors from the experiments depend on the details of the many-body wavefunctions being probed. We show that recent advances with the ab-initio method can provide more insights on the spectroscopy information extracted from experiments.

Caustics in quantum many-body dynamics

We describe a new class of nonequilibrium quantum many-body phenomena in the form of networks of caustics that dominate the many-body wave function in the semiclassical regime following a sudden quench. It includes the light cone-like propagation of correlations as a particular case. Caustics are singularities formed by the birth and death of waves and form a hierarchy of universal patterns whose natural mathematical description is via catastrophe theory. Examples in classical waves range from rainbows and gravitational lensing in optics to tidal bores and rogue waves in hydrodynamics. Quantum many-body caustics are discretized by second quantization (``quantum catastrophes'') and live in Fock space, which can potentially have many dimensions. We illustrate these ideas using the Bose Hubbard dimer and trimer models, which are simple enough that the caustic structure can be elucidated from first principles and yet run the full range from integrable to nonintegrable dynamics. The dimer gives rise to discretized versions of fold and cusp catastrophes whereas the trimer allows for higher catastrophes including the codimension-3 hyperbolic and elliptic umbilics, which are organized by, and projections of, an 8-dimensional corank-2 catastrophe known as ${X}_{9}$. These results describe a hitherto unrecognized form of universality in quantum dynamics organized by singularities that manifest as strong fluctuations in mode population probabilities.

Charge ordering in Ir dimers in the ground state of Ba5AlIr2O11

It has been well established experimentally that the interplay of electronic correlations and spin-orbit interactions in ${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ir}}^{5+}$ oxides results in insulating ${J}_{\mathrm{eff}}=1/2$ and ${J}_{\mathrm{eff}}=0$ ground states, respectively. However, in compounds where the structural dimerization of iridium ions is favorable, the direct Ir $d\text{\ensuremath{-}}d$ hybridization can be significant and takes a key role. Here, we investigate the effects of direct Ir $d\text{\ensuremath{-}}d$ hybridization in comparison with electronic correlations and spin-orbit coupling in ${\mathrm{Ba}}_{5}{\mathrm{AlIr}}_{2}{\mathrm{O}}_{11}$, a compound with Ir dimers. Using a combination of ab initio many-body wave-function quantum chemistry calculations and resonant inelastic x-ray scattering experiments, we elucidate the electronic structure of ${\mathrm{Ba}}_{5}{\mathrm{AlIr}}_{2}{\mathrm{O}}_{11}$. We find excellent agreement between the calculated and the measured spin-orbit excitations. Contrary to expectations, the analysis of the many-body wave function shows that the two Ir (${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ir}}^{5+}$) ions in the ${\mathrm{Ir}}_{2}{\mathrm{O}}_{9}$ dimer unit in this compound preserve their local ${J}_{\mathrm{eff}}$ character close to 1/2 and 0, respectively. The local point group symmetry at each of the Ir ions plays an important role, significantly limiting the direct $d\text{\ensuremath{-}}d$ hybridization. Our results emphasize that minute details in the local crystal field environment can lead to dramatic differences in the electronic states in iridates and $5d$ oxides in general.

Ground state of asymmetric tops with DMRG: Water in one dimension.

We propose an approach to compute the ground state properties of collections of interacting asymmetric top molecules based on the density matrix renormalization group method. Linear chains of rigid water molecules of varying sizes and density are used to illustrate the method. A primitive computational basis of asymmetric top eigenstates with nuclear spin symmetry is used, and the many-body wave function is represented as a matrix product state. We introduce a singular value decomposition approach in order to represent general interaction potentials as matrix product operators. The method can be used to describe linear chains containing up to 50 water molecules. Properties such as the ground state energy, the von-Neumann entanglement entropy, and orientational correlation functions are computed. The effect of basis set truncation on the convergence of ground state properties is assessed. It is shown that specific intermolecular distance regions can be grouped by their von-Neumann entanglement entropy, which in turn can be associated with electric dipole-dipole alignment and hydrogen bond formation. Additionally, by assuming conservation of local spin states, we present our approach to be capable of calculating chains with different arrangements of the para and ortho spin isomers of water and demonstrate that for the water dimer.

Space-warp coordinate transformation for efficient ionic force calculations in quantum Monte Carlo.

Ab initio quantum Monte Carlo (QMC) methods are a state-of-the-art computational approach to obtaining highly accurate many-body wave functions. Although QMC methods are widely used in physics and chemistry to compute ground-state energies, calculation of atomic forces is still under technical/algorithmic development. Very recently, force evaluation has started to become of paramount importance for the generation of machine-learning force-field potentials. Nevertheless, there is no consensus regarding whether an efficient algorithm is available for the QMC force evaluation, namely, one that scales well with the number of electrons and the atomic numbers. In this study, we benchmark the accuracy of all-electron variational Monte Carlo (VMC) and lattice-regularized diffusion Monte Carlo (LRDMC) forces for various mono- and heteronuclear dimers (1 ≤ Z ≤ 35, where Z is the atomic number). The VMC and LRDMC forces were calculated with and without the so-called space-warp coordinate transformation (SWCT) and appropriate regularization techniques to remove the infinite variance problem. The LRDMC forces were computed with the Reynolds (RE) and variational-drift (VD) approximations. The potential energy surfaces obtained from the LRDMC energies give equilibrium bond lengths (req) and harmonic frequencies (ω) very close to the experimental values for all dimers, improving the corresponding VMC results. The LRDMC forces with the RE approximation improve the VMC forces, implying that it is worth computing the DMC forces beyond VMC despite the higher computational cost. The LRDMC forces with the VD approximations also show improvement, which unfortunately comes at a much higher computational cost in all-electron calculations. We find that the ratio of computational costs between QMC energy and forces scales as Z∼2.5 without the SWCT. In contrast, the application of the SWCT makes the ratio independent of Z. As such, the accessible QMC system size is not affected by the evaluation of ionic forces but governed by the same scaling as the total energy one.

Regularized second-order correlation methods for extended systems.

Second-order Møller-Plesset perturbation theory (MP2) constitutes the simplest form of many-body wavefunction theory and often provides a good compromise between efficiency and accuracy. There are, however, well-known limitations to this approach. In particular, MP2 is known to fail or diverge for some prototypical condensed matter systems like the homogeneous electron gas (HEG) and to overestimate dispersion-driven interactions in strongly polarizable systems. In this paper, we explore how the issues of MP2 for metallic, polarizable, and strongly correlated periodic systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillouin-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model, and the graphene-water interaction. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for the various systems.

Gaussian trajectory description of fragmentation in an isolated spinor condensate

Spin-1 Bose gases quenched to spin degeneracy exhibit fragmentation: the appearance of a condensate in more than one single-particle state. Due to its highly entangled nature, the dynamics leading to this collective state are beyond the scope of a Gaussian variational approximation of the many-body wave function. Here, we improve the performance of the Gaussian variational ansatz by considering dissipation into a fictitious environment, effectively suppressing entanglement within individual quantum trajectories at the expense of introducing a classical mixture of states. We find that this quantum trajectory approach captures the dynamical formation of a fragmented condensate and analyze how much dissipation should be added to the experiment in order to keep a single realization in a nonfragmented state.

Observing the loss and revival of long-range phase coherence through disorder quenches

Relaxation of quantum systems is a central problem in nonequilibrium physics. In contrast to classical systems, the underlying quantum dynamics results not only from atomic interactions but also from the long-range coherence of the many-body wave function. Experimentally, nonequilibrium states of quantum fluids are usually created using moving objects or laser potentials, directly perturbing and detecting the system's density. However, the fate of long-range phase coherence for hydrodynamic motion of disordered quantum systems is less explored, especially in three dimensions. Here, we unravel how the density and phase coherence of a Bose-Einstein condensate of 6Li2 molecules respond upon quenching on or off an optical speckle potential. We find that, as the disorder is switched on, long-range phase coherence breaks down one order of magnitude faster than the density of the quantum gas responds. After removing it, the system needs two orders of magnitude longer times to reestablish quantum coherence, compared to the density response. We compare our results with numerical simulations of the Gross-Pitaevskii equation on large three-dimensional grids, finding an overall good agreement. Our results shed light on the importance of long-range coherence and possibly long-lived phase excitations for the relaxation of nonequilibrium quantum many-body systems.

Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We review how matrix product states and projected entangled pair states describe many-body wavefunctions in terms of local tensors. These tensors express how the entanglement is routed, act as a novel type of non-local order parameter, and we describe how their symmetries are reflections of the global entanglement patterns in the full system. We will discuss how tensor networks enable the construction of real-space renormalization group flows and fixed points, and examine the entanglement structure of states exhibiting topological quantum order. Finally, we provide a summary of the mathematical results of matrix product states and projected entangled pair states, highlighting the fundamental theorem of matrix product vectors and its applications.

Excited-State DMRG Made Simple with FEAST

We introduce DMRG[FEAST], a new method for optimizing excited-state many-body wave functions with the density matrix renormalization group (DMRG) algorithm. Our approach applies the FEAST algorithm, originally designed for large-scale diagonalization problems, to matrix product state wave functions. We show that DMRG[FEAST] enables the stable optimization of both low- and high-energy eigenstates, therefore overcoming the limitations of state-of-the-art excited-state DMRG algorithms. We demonstrate the reliability of DMRG[FEAST] by calculating anharmonic vibrational excitation energies of molecules with up to 30 fully coupled degrees of freedom.

Breakdown of quantum-classical correspondence and dynamical generation of entanglement

The {\it exchange} interaction arising from the particle indistinguishability is of central importance to physics of many-particle quantum systems. Here we study analytically the dynamical generation of quantum entanglement induced by this interaction in an isolated system, namely, an ideal Fermi gas confined in a chaotic cavity, which evolves unitarily from a non-Gaussian pure state. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure. Furthermore, for a class of initial states, such change leads to the approach to thermal equilibrium everywhere in the cavity, with the well-known Ehrenfest time in quantum chaos as the thermalization time. Specifically, the quantum expectation values of various correlation functions at different spatial scales are all determined by the Fermi-Dirac distribution. In addition, by using the reduced density matrix (RDM) and the entanglement entropy (EE) as local probes, we find that the gas inside a subsystem is at equilibrium with that outside, and its thermal entropy is the EE, even though the whole system is in a pure state. As a by-product of this work, we provide an analytical solution supporting an important conjecture on thermalization, made and numerically studied by Garrison and Grover in: Phys. Rev. X \textbf{8}, 021026 (2018), and strengthen its statement.

Conditional Wave Function Theory: A Unified Treatment of Molecular Structure and Nonadiabatic Dynamics.

We demonstrate that a conditional wave function theory enables a unified and efficient treatment of the equilibrium structure and nonadiabatic dynamics of correlated electron–ion systems. The conditional decomposition of the many-body wave function formally recasts the full interacting wave function of a closed system as a set of lower-dimensional (conditional) coupled “slices”. We formulate a variational wave function ansatz based on a set of conditional wave function slices and demonstrate its accuracy by determining the structural and time-dependent response properties of the hydrogen molecule. We then extend this approach to include time-dependent conditional wave functions and address paradigmatic nonequilibrium processes including strong-field molecular ionization, laser-driven proton transfer, and nuclear quantum effects induced by a conical intersection. This work paves the road for the application of conditional wave function theory in equilibrium and out-of-equilibrium ab initio molecular simulations of finite and extended systems.

Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model

Variational quantum algorithms (VQA) are considered as some of the most promising methods to determine the properties of complex strongly correlated quantum many-body systems, especially from the perspective of devices available in the near term. In this context, the development of efficient quantum circuit ansatze to encode a many-body wavefunction is one of the keys for the success of a VQA. Great efforts have been invested to study the potential of current quantum devices to encode the eigenstates of fermionic systems, but little is known about the encoding of bosonic systems. In this work, we investigate the encoding of the ground state of the (simple but rich) attractive Bose-Hubbard model using a Continuous-Variable (CV) photonic-based quantum circuit. We introduce two different ansatz architectures and demonstrate that the proposed continuous variable quantum circuits can efficiently encode (with a fidelity higher than 99%) the strongly correlated many-boson wavefunction with just a few layers, in all many-body regimes and for different number of bosons and initial states. Beyond the study of the suitability of the ansatz to approximate the ground states of many-boson systems, we also perform initial evaluations of the use of the ansatz in a variational quantum eigensolver algorithm to find it through energy minimization. To this end we also introduce a scheme to measure the Hamiltonian energy in an experimental system, and study the effect of sampling noise.

The NUMEN Technical Design Report

NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross-section measurements of heavy-ion induced Double Charge Exchange (DCE) reactions. Despite the fact that the two processes, namely neutrinoless double beta decay and DCE reactions, are triggered by the weak and strong interaction respectively, important analogies are suggested. The basic point is the coincidence of the initial and final state many-body wave functions in the two types of processes and the formal similarity of the transition operators. The main experimental tools for this project are the K800 Superconducting Cyclotron and MAGNEX spectrometer at the INFN-LNS laboratory. However, the tiny values of DCE cross-sections and the resolution requirements demand beam intensities much higher than those manageable with the present facility. The on-going upgrade of the INFN-LNS facilities promoted by the POTLNS a project in this perspective is intimately connected to the NUMEN project. This paper describes the solutions proposed as a result of the R&D activity performed during the recent years. The goal is to develop suitable technologies allowing for the measurements of DCE cross-section under extremely high beam intensities. a PIR01_00005 — potenziamento dell’infrastruttura di ricerca Laboratori Nazionali del Sud per la produzione di fasci di ioni ad alta intensitá.

Exploration of doped quantum magnets with ultracold atoms

In the last decade, quantum simulators, and in particular cold atoms in optical lattices, have emerged as a valuable tool to study strongly correlated quantum matter. These experiments are now reaching regimes that are numerically difficult or impossible to access. In particular they have started to fulfill a promise which has contributed significantly to defining and shaping the field of cold atom quantum simulations, namely the exploration of doped and frustrated quantum magnets and the search for the origins of high-temperature superconductivity in the fermionic Hubbard model. Despite many future challenges lying ahead, such as the need to further lower the experimentally accessible temperatures, remarkable studies have already been conducted. Among them, spin-charge separation in one-dimensional systems has been demonstrated, extended-range antiferromagnetism in two-dimensional systems has been observed, connections to modern day large-scale numerical simulations were made, and unprecedented comparisons with microscopic trial wavefunctions have been carried out at finite doping. In many regards, the field has acquired new realms, putting old ideas to a new test and producing new insights and inspiration for the next generation of physicists.In the first part of this paper, we review the results achieved in cold atom realizations of the Fermi–Hubbard model in recent years. We put special emphasis on the new probes available in quantum gas microscopes, such as higher-order correlation functions, full counting statistics, the ability to study far-from-equilibrium dynamics, machine learning and pattern recognition of instantaneous snapshots of the many-body wavefunction, and access to non-local correlators. Our review is written from a theoretical perspective, but aims to provide basic understanding of the experimental procedures. We cover one-dimensional systems, where the phenomenon of spin-charge separation is ubiquitous, and two-dimensional systems where we distinguish between situations with and without doping. Throughout, we focus on the strong coupling regime where the Hubbard interactions U dominate and connections to t−J models can be justified.In the second part of this paper, with the stage set and the current state of the field in mind, we propose a new direction for cold atoms to explore: namely mixed-dimensional bilayer systems, where the charge motion is restricted to individual layers which remain coupled through spin-exchange. These systems can be directly realized experimentally and we argue that they have a rich phase diagram, potentially including a strongly correlated BEC-to-BCS cross-over and regimes with different superconducting order parameters, as well as complex parton phases and possibly even analogs of tetraquark states. In particular, we propose a novel, strong pairing mechanism in these systems, which puts the formation of hole pairs at experimentally accessible, elevated temperatures within reach. Ultimately we propose to explore how the physics of the mixed-dimensional bilayer system can be connected to the rich phenomenology of the single-layer Hubbard model.

Berry Connection from Many-Body Wave Functions and Superconductivity: Calculations by the Particle Number Conserving Bogoliubov-De Gennes Equations

A fundamentally revised version of superconductivity theory has been put forward since the standard theory of superconductivity based on the BCS theory cannot explain superconductivity in cuprates discovered in 1986, and reexaminations on several experimental results on the conventional superconductors indicate the necessity for a fundamental revision. The revision is made on the origin of the superconducting phase variable, which is attributed to a Berry connection arising from many-body wave functions. With this revision, the theory can be cast into a particle number conserving formalism. We have developed a method to calculate superconducting states with the Berry connection using the particle number conserving version of the Bogoliubov-de Gennes equations.

Fock-Space Embedding Theory: Application to Strongly Correlated Topological Phases.

A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schrödinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce the topological phase diagram of a multiband Hubbard model as a function of crystal field and Hubbard parameters. The roles of band filling and interband fluctuations are elucidated.

Kinetic samplers for neural quantum states

Neural quantum states are a recently introduced class of variational many-body wave functions that are very flexible in approximating diverse quantum states. Optimization of an NQS ansatz requires sampling from the corresponding probability distribution defined by squared wave function amplitude. For this purpose, we propose to use kinetic sampling protocols and demonstrate that in many important cases such methods lead to much smaller autocorrelation times than the Metropolis-Hastings sampling algorithm while still allowing to easily implement lattice symmetries (unlike autoregressive models). We also use uniform manifold approximation and projection algorithm to construct two-dimensional isometric embedding of Markov chains and show that kinetic sampling helps attain a more homogeneous and ergodic coverage of the Hilbert space basis.

Vacuum anomalous Hall effect in gyrotropic cavity

We consider the ground state of an electron gas embedded in a quantum gyrotropic cavity. We show that the light-matter interaction leads to a nontrivial topology of the many-body electron-photon wave function characterized by a nonzero Berry curvature. Physically, the latter manifests as the anomalous Hall effect, appearance of equilibrium edge/surface currents and orbital magnetization induced by vacuum fluctuations. Remarkably, closed analytical expressions for the anomalous Hall conductivity and macroscopic magnetization are obtained for the interacting many-body case.

Mott transition in a cavity-boson system: A quantitative comparison between theory and experiment

The competition between short-range and cavity-mediated infinite-range interactions in a cavity-boson system leads to the existence of a superfluid phase and a Mott-insulator phase within the self-organized regime. In this work, we quantitatively compare the steady-state phase boundaries of this transition measured in experiments and simulated using the Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles. To make the problem computationally feasible, we represent the full system by the exact many-body wave function of a two-dimensional four-well potential. We argue that the validity of this representation comes from the nature of both the cavity-atomic system and the Bose-Hubbard physics. Additionally, we show that the chosen representation only induces small systematic errors, and that the experimentally measured and theoretically predicted phase boundaries agree reasonably well. We thus demonstrate a new approach for the quantitative numerical modeling for the physics of the superfluid--Mott-insulator phase boundary.