Realistic Hamiltonian Research Articles

Emergent Glassy Behavior in a Kagome Rydberg Atom Array.

We present large-scale quantum MonteCarlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.

Anharmonic phonon behavior via irreducible derivatives: Self-consistent perturbation theory and molecular dynamics

Cubic phonon interactions are now regularly computed from first principles, and the quartic interactions have begun to receive more attention. Given this realistic anharmonic vibrational Hamiltonian, the classical phonon Green's function can be precisely measured using molecular dynamics, which can then be used to rigorously assess the range of validity for self-consistent diagrammatic approaches in the classical limit. Here we use the bundled irreducible derivative approach to efficiently and precisely compute the cubic and quartic phonon interactions of CaF$_2$, systematically obtaining the vibrational Hamiltonian purely in terms of irreducible derivatives. non frequency shifts and linewidths, We demonstrate that the 4-phonon sunset diagram has an important contribution to the optical phonon linewidths beyond $T=500$ K. Reasonable results are obtained even at $T=900$ K when performing self-consistency using the 4-phonon loop diagram and evaluating the 3-phonon bubble and 4-phonon sunset diagrams post self-consistency. Further improvements are obtained by performing quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Our irreducible derivative approach to self-consistent perturbation theory is a robust tool for studying anharmonic phonons in both the quantum and classical regimes.

Sub Coulomb barrier d+ 208Pb scattering in the time-dependent basis function approach

We employ the non-perturbative time-dependent basis function (tBF) approach to study the scattering of the deuteron on 208Pb below the Coulomb barrier. We obtain the bound and discretized scattering states of the projectile, which form the basis representation of the tBF approach, by diagonalizing a realistic Hamiltonian in a large harmonic oscillator basis. We find that the higher-order inelastic scattering effects are noticeable for sub barrier scatterings with the tBF method. We have successfully reproduced experimental sub Coulomb barrier elastic cross section ratios with the tBF approach by considering only the electric dipole (E1) component of the Coulomb interaction between the projectile and the target during scatterings. We find that the correction of the polarization potential to the Rutherford trajectory is dominant in reproducing the data at very low bombarding energies, whereas the role of internal transitions of the deuteron projectile induced by the E1 interaction during the scattering becomes increasingly significant at higher bombarding energies.

Nuclear physics uncertainties in light hypernuclei

The energy levels of light hypernuclei are experimentally accessible observables that contain valuable information about the interaction between hyperons and nucleons. In this work we study strangeness $S = -1$ systems $^{3,4}_\Lambda$H and $^{4,5}_\Lambda$He using the ab initio no-core shell model (NCSM) with realistic interactions obtained from chiral effective field theory ($\chi$EFT). In particular, we quantify the finite precision of theoretical predictions that can be attributed to nuclear physics uncertainties. We study both the convergence of the solution of the many-body problem (method uncertainty) and the regulator- and calibration data-dependence of the nuclear $\chi$EFT Hamiltonian (model uncertainty). For the former, we implement infrared correction formulas and extrapolate finite-space NCSM results to infinite model space. We then use Bayesian parameter estimation to quantify the resulting method uncertainties. For the latter, we employ a family of 42 realistic Hamiltonians and measure the standard deviation of predictions while keeping the leading-order hyperon-nucleon interaction fixed. Following this procedure we find that model uncertainties of ground-state $\Lambda$ separation energies amount to $\sim 20(100)$ keV in $^3_\Lambda$H($^4_\Lambda$H,He) and $\sim 400$ keV in $^5_\Lambda$He. Method uncertainties are comparable in magnitude for the $^4_\Lambda$H,He $1^+$ excited states and $^5_\Lambda$He, which are computed in limited model spaces, but otherwise much smaller. This knowledge of expected theoretical precision is crucial for the use of binding energies of light hypernuclei to infer the elusive hyperon-nucleon interaction.

Constraints on the two-dimensional pseudospin- 12 Mott insulator description of Sr2IrO4

${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ has often been described via a simple, one-band pseudospin-$\frac{1}{2}$ model subject to electron-electron interactions on a square lattice, fostering analogies with cuprate superconductors believed to be well described by a similar model. In this work we argue---based on a detailed study of the low-energy electronic structure by circularly polarized spin and angle-resolved photoemission spectroscopy combined with dynamical mean-field theory calculations---that a pseudospin-$\frac{1}{2}$ model fails to capture the full complexity of the system. We show instead that a realistic multiband Hubbard Hamiltonian, accounting for the full correlated ${t}_{2g}$ manifold, provides a detailed description of the interplay between spin-orbital entanglement and electron-electron interactions and yields quantitative agreement with experiments. Our analysis establishes that the ${j}_{3/2}$ states make up a substantial percentage of the low-energy spectral weight, i.e., approximately 74% as determined from the integration of the $j$-resolved spectral function in the 0 to $\ensuremath{-}1.64\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ energy range. The results in our work are of relevance not only to Ir-based materials but also more generally to multiorbital materials with closely spaced energy scales.

Benchmark calculations of infinite neutron matter with realistic two- and three-nucleon potentials

We present the equation of state of infinite neutron matter as obtained from highly realistic Hamiltonians that include nucleon-nucleon and three-nucleon coordinate-space potentials. We benchmark three independent many-body methods: Brueckner-Bethe-Goldstone (BBG), Fermi hypernetted chain/single-operator chain (FHNC/SOC), and auxiliary-field diffusion Monte Carlo (AFDMC). We find them to provide similar equations of state when the Argonne ${v}_{18}$ and the Argonne ${v}_{6}^{\ensuremath{'}}$ nucleon-nucleon potentials are used in combination with the Urbana IX three-body force. Only at densities larger than about 1.5 the nuclear saturation density (${\ensuremath{\rho}}_{0}=0.16\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$) the FHNC/SOC energies are appreciably lower than the other two approaches. The AFDMC calculations carried out with all of the Norfolk potentials fitted to reproduce the experimental trinucleon ground-state energies and $nd$ doublet scattering length yield unphysically bound neutron matter, associated with the formation of neutron droplets. Including tritium $\ensuremath{\beta}$ decay in the fitting procedure, as in the second family of Norfolk potentials, mitigates but does not completely resolve this problem. An excellent agreement between the BBG and AFDMC results is found for the subset of Norfolk interactions that do not make neutron-matter collapse, while the FHNC/SOC equations of state are moderately softer.

The 1S0 Pairing Gap in Neutron Matter

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.

Non-trivial impurity and field effects in topological Kondo insulator SmB6

Topological Kondo Insulator SmB6 is a strongly correlated material where a spin–orbit interaction between the localized odd-parity f-electron and even parity d-electron levels lead to a band inversion and opening of an insulating gap. The non-trivial topology (Z2 = -1) leads to the formation of a topologically protected conducting surface state due to the presence of strong correlation physics. Although the bulk material is known to form a topological Kondo gap, recent magnetic quantum oscillation experiments on SmB6 find an unconventional Fermi surface whose origin remains a matter of intense debate, and the possible role of topological surfacestate and impurity induced in-gap states have been proposed. By utilizing a realistic multi-orbital tight-binding Hamiltonian, this work aims to develop a microscopic model to study the effects of perturbations like external magnetic fields, and impurities on the low energy bulk and topological surface state properties of SmB6. We further examine the role of an external electric field in tuning the non-trivial topological surface state in SmB6 and provide experimentally observable signatures in the local density of state (LDOS) near non-magnetic and magnetic impurities. Additionally, we study the surface Ferromagnetism that arises in SmB6 as observed by magnetoresistance experiments.

Classical spin dynamics based on SU(N) coherent states

We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of $\mathrm{SU}(N)$, where $N$ is the dimension of the local Hilbert space. This approach, which generalizes the well-known Landau-Lifshitz dynamics from SU(2) to $\mathrm{SU}(N)$, provides a better approximation to the exact quantum dynamics for a large class of realistic spin Hamiltonians, including $S\ensuremath{\ge}1$ systems with large single-ion anisotropy and weakly coupled multispin units, such as dimers or trimers. We illustrate this idea by comparing the spin structure factors of a single-ion $S=1$ model that are obtained with the SU(2) and SU(3) classical spin dynamics against the exact solution.

Antiferromagnetic skyrmions and skyrmion density wave in a Rashba-coupled Hund insulator

We discover magnetic phases hosting highly elusive and technologically important antiferromagnetic skyrmion quasiparticles in a model for a Rashba-coupled Hund insulator. The results are based on unbiased simulations of a classical superexchange model derived, in this work, from a realistic microscopic electronic Hamiltonian. We also discover a skyrmion density wave ground state characterized by a $(Q,Q)$ modulation in the local skyrmion density map. A unique inhomogeneous state characterized by a circular pattern in the spin structure factor and filamentary real-space textures is identified as the parent of sparse antiferromagnetic skyrmions. We predict that the magnetic states reported here can be realized in thin films of multiorbital systems involving $4d$ or $5d$ transition metals.

Correlation holes and slow dynamics induced by fractional statistics in gapped quantum spin liquids

Realistic model Hamiltonians for quantum spin liquids frequently exhibit a large separation of energy scales between their elementary excitations. At intermediate, experimentally relevant temperatures, some excitations are sparse and hop coherently, whereas others are thermally incoherent and dense. Here, we study the interplay of two such species of quasiparticle, dubbed spinons and visons, which are subject to nontrivial mutual statistics – one of the hallmarks of quantum spin liquid behaviour. Our results for {{mathbb{Z}}}_{2} quantum spin liquids show an intriguing feedback mechanism, akin to the Nagaoka effect, whereby spinons become localised on temperature-dependent patches of expelled visons. This phenomenon has important consequences for the thermodynamic and transport properties of the system, as well as for its response to quenches in temperature. We argue that these effects can be measured in experiments and may provide viable avenues for obtaining signatures of quantum spin liquid behaviour.

Many-body scar state intrinsic to periodically driven system

The violation of the Floquet version of eigenstate thermalization hypothesis is systematically discussed with realistic Hamiltonians. Our model is based on the PXP type interactions without disorder. We exactly prove the existence of many-body scar states in the Floquet eigenstates, by showing the explicit expressions of the wave functions. Using the underlying physical mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered.

Field evolution of the spin-liquid candidate YbMgGaO4

We report magnetization, heat capacity, thermal expansion, and magnetostriction measurements down to millikelvin temperatures on the triangular antiferromagnet YbMgGaO$_4$. Our data exclude the formation of the distinct $\frac13$ plateau phase observed in other triangular antiferromagnets, but reveal plateaulike features in second derivatives of the free energy, magnetic susceptibility and specific heat, at $\mu_0H$ = 1.0 - 2.5 T for $H\parallel{}c$ and 2 - 5 T for $H\perp{}c$. Using Monte-Carlo simulations of a realistic spin Hamiltonian, we ascribe these features to nonmonotonic changes in the magnetization and the $\frac12$ plateau that is smeared out by the random distribution of exchange couplings in YbMgGaO$_4$.

Constructing realistic effective spin Hamiltonians with machine learning approaches

The effective Hamiltonian method has recently received considerable attention due to its power to deal with finite-temperature problems and large-scale systems. In this work, we put forward a machine learning (ML) approach to generate realistic effective Hamiltonians. In order to find out the important interactions among many possible terms, we propose some new techniques. In particular, we suggest a new criterion to select models with less parameters using a penalty factor instead of the commonly-adopted additional penalty term, and we improve the efficiency of variable selection algorithms by estimating the importance of each possible parameter by its relative uncertainty and the error induced in the parameter reduction. We also employ a testing set and optionally a validation set to help prevent over-fitting problems. To verify the reliability and usefulness of our approach, we take two-dimensional MnO and three-dimensional TbMnO3 as examples. In the case of TbMnO3, our approach not only reproduces the known results that the Heisenberg, biquadratic, and ring exchange interactions are the major spin interactions, but also finds out that the next most important spin interactions are three-body fourth-order interactions. In both cases, we obtain effective spin Hamiltonians with high fitting accuracy. These tests suggest that our ML approach is powerful for identifying the effective spin Hamiltonians. Our ML approach is general so that it can be adopted to construct other effective Hamiltonians.

Legendre-spectral Dyson equation solver with super-exponential convergence.

Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab initio problems with a fully realistic Hamiltonian in large basis sets is hampered by the storage of the Green's function and the precision of the solution of the Dyson equation. We present a Legendre-spectral algorithm for solving the Dyson equation that addresses both of these issues. By formulating the algorithm in Legendre coefficient space, our method inherits the known faster-than-exponential convergence of the Green's function's Legendre series expansion. In this basis, the fast recursive method for Legendre polynomial convolution enables us to develop a Dyson equation solver with quadratic scaling. We present benchmarks of the algorithm by computing the dissociation energy of the helium dimer He2 within dressed second-order perturbation theory. For this system, the application of the Legendre spectral algorithm allows us to achieve an energy accuracy of 10-9Eh with only a few hundred expansion coefficients.

Direct Comparison of Many-Body Methods for Realistic Electronic Hamiltonians

A large collaboration carefully benchmarks 20 first principles many-body electronic structure methods on a test set of 7 transition metal atoms, and their ions and monoxides. Good agreement is attained between the 3 systematically converged methods, resulting in experiment-free reference values. These reference values are used to assess the accuracy of modern emerging and scalable approaches to the many-electron problem. The most accurate methods obtain energies indistinguishable from experimental results, with the agreement mainly limited by the experimental uncertainties. Comparison between methods enables a unique perspective on calculations of many-body systems of electrons.

Description of Four- and Five-Nucleon Systems by Solving Faddeev-Yakubovsky Equations in Configuration Space

The Faddeev Yakubovsky equations constitute a rigorous formulation of the quantum mechanical N body problem in the framework of non relativistic dynamics. They allow the exact solutions of the Schrodinger equation for bound and scattering states to be obtained. In this review, we will present the general formalism as well as the numerical tools we use to solve Faddeev Yakubovsky equations in configuration space. We will consider in detail the description of the four and five nucleon systems based on modern realistic nuclear Hamiltonians. Recent achievements in this domain will be summarized. Some of the still controversial issues related with the nuclear Hamiltonians as well as the numerical methods traditionally employed to solve few nucleon problems will be highlighted.

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

We numerically investigate the properties of the quasihole excitations above the bosonic fractional Chern insulator state at filling $\nu = 1/2$, in the specific case of the Harper-Hofstadter Hamiltonian with hard-core interactions. For this purpose we employ a Tree Tensor Network technique, which allows us to study systems with up to $N=18$ particles on a $16 \times 16$ lattice and experiencing an additional harmonic confinement. First, we observe the quantization of the quasihole charge at fractional values and its robustness against the shape and strength of the impurity potentials used to create and localize such excitations. Then, we numerically characterize quasihole anyonic statistics by applying a discretized version of the relation connecting the statistics of quasiholes in the lowest Landau level to the depletions they create in the density profile [Macaluso et al., arXiv:1903.03011]. Our results give a direct proof of the anyonic statistics for quasiholes of fractional Chern insulators, starting from a realistic Hamiltonian. Moreover, they provide strong indications that this property can be experimentally probed through local density measurements, making our scheme readily applicable in state-of-the-art experiments with ultracold atoms and superconducting qubits.

Purification of the atom-field interaction Hamiltonian

We study the Jaynes-Cummings model with initial mixed states, for the atom or the field, are considered. The evolved mixed field density matrix is purified to a wavefunction that describes the interaction between a quantised field and an artificial four-level atom. This allows us to use the Araki-Lieb inequality to calculate the field entropy from the atomic entropy. We then suggest Hamiltonians that reproduce the field entropy dynamics. We finally show that more realistic Hamiltonians may be considered by using two entangled two-level atoms.

Ab initio calculations of 5H resonant states

By solving the 5-body Faddeev-Yakubovsky equations in configuration space with realistic nuclear Hamiltonians we have studied the resonant states of 5H isotope. Two different methods, allowing to bypass the exponentially diverging boundary conditions, have been employed providing consistent results. The existence of 5H broad Jπ=1/2+,3/2+,5/2+ states as S-matrix poles has been confirmed and compared with the, also calculated, resonant states in 4H isotope. We have established that the positions of these resonances only mildly depend on the nuclear interaction model.