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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Twisted bilayer graphene. VI. An exact diagonalization study at nonzero integer filling

Using exact diagonalization, we research the projected Hamiltonian with the Coulomb interaction in the eight flat bands of first magic angle twisted bilayer graphene. Employing the U(4) [U(4) × U(4)] symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent that allows for study around ν = ±3,±2,±1 fillings. In the first chiral limit w 0 /w 1 = 0, where w 0 (w 1 ) is the A A (AB) stacking hopping, we find that the ground states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable charge ±1 excitations found in Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] are the lowest charge excitations up to system sizes 8 × 8 (for restricted Hilbert space) in the chiral-flat limit. We also find that the flat metric condition (FMC) used by Bernevig et al. [Phys. Rev. B 103, 205411 (2021)], Song et al. [Phys. Rev. B 103, 205412 (2021)], Bernevig et al. [Phys. Rev. B 103, 205413 (2021)], Lian et al. [Phys. Rev. B 103, 205414 (2021)], and Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] for obtaining a series of exact ground states and excitations holds in a large parameter space. For ν = -3, the ground state is the spin and valley polarized Chern insulator with ν C = ±1 at w 0 /w 1 ≲ 0.9 (0.3) with (without) FMC. At ν = -2, we can only numerically access the valley polarized sector, and we find a spin ferromagnetic phase when w 0 /w 1 ≳ 0.5 t where t ϵ [0,1] is the factor of rescaling of the actual TBG bandwidth, and a spin singlet phase otherwise, confirming the perturbative calculation [Lian. et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. The analytic FMC ground state is, however, predicted in the intervalley coherent sector which we cannot access [Lian et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. For ν = -3 with/without FMC, when w 0 /w 1 is large, the finite-size gap Δ to the neutral excitations vanishes, leading to phase transitions. Further analysis of the ground state momentum sectors at ν = -3 suggests a competition among (nematic) metal, momentum M M (π) stripe and K M -CDW orders at large w 0 /w 1 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene

We report on finite-size exact-diagonalization calculations in a Hilbert space defined by the continuum-model flat moiré bands of magic angle twisted bilayer graphene. For moiré band filling 3>|ν|>2, where superconductivity is strongest, we obtain evidence that the ground state is a spin ferromagnet. Near |ν|=3, we find Chern insulator ground states that have spontaneous spin, valley, and sublattice polarization, and demonstrate that the anisotropy energy in this order-parameter space is strongly band-filling-factor dependent. We emphasize that inclusion of the remote band self-energy is necessary for a reliable description of magic angle twisted bilayer graphene flat band correlations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Ground and excited states of even-numbered Hubbard ring at half-filling: comparison of the extended Gutzwiller approach with exact diagonalization

It remains a great challenge in condensed matter physics to develop a method to treat strongly correlated many-body systems with balanced accuracy and efficiency. We introduce an extended Gutzwiller (EG) method incorporating a manifold technique, which builds an effective manifold of the many-body Hilbert space, to describe the ground- and excited-state properties of strongly correlated electrons. Here we systematically apply an EG projector onto the ground and excited states of a non-interacting system. Diagonalization of the true Hamiltonian within the manifold formed by the resulting EG wavefunctions gives the approximate ground and excited states of the correlated system. To validate this technique, we implement it on even-numbered fermionic Hubbard rings at half-filling with periodic boundary conditions, and compare the results with the exact diagonalization (ED) method. The EG method is capable of generating high-quality ground and low-lying excited state wavefunctions, as evidenced by the high overlaps of wavefunctions between the EG and ED methods. Favorable comparisons are also achieved for other quantities including the total energy, the double occupancy, the total spin and the staggered magnetization. With the capability of accessing the excited states, the EG method can capture the essential features of the one-electron removal spectral function that contains contributions from states deep in the excited spectrum. Finally, we provide an outlook on the application of this method on large extended systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method

Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si$_2$H$_6$ which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data

In this work, we present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

First-principles characterization of the magnetic properties of Cu 2 (OH) 3 Br

Low-dimensional spin-1/2 transition metal oxides and oxyhalides continue to be at the forefront of research investigating nonclassical phases such as quantum spin liquids. In this work, we examine the magnetic properties of the oxyhalide Cu 2 (OH) 3 Br in the botallackite structure using first-principles density functional theory, linear spin-wave theory, and exact diagonalization calculations. This quasi-two-dimensional system consists of Cu 2+ S = 1/2 moments arranged on a distorted triangular lattice. Our exact diagonalization calculations, which rely on a first-principles-based magnetic model, generate spectral functions consistent with inelastic neutron scattering data. By performing computational experiments to disentangle the chemical and steric effects of the halide ions, we find that the dominant effect of the halogen ions is steric in the Cu 2 (OH) 3 X series of compounds.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quasiparton distributions in massive QED2: Toward quantum computation

We analyze the quasiparton distributions of the lightest 𝜂′ meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous 𝜂′ state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted 𝜂′ state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the 𝜂′ state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions.

Lattice field theory↗
DOE OSTI2025

More about the lattice Hamiltonian for Adjoint QCD 2

In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD 2 using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge group G. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD 2 for arbitrary G. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6j-symbols of G. For G = SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6j-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies.

confinement↗
DOE OSTI2024

Classical and quantum computing of shear viscosity for ( 2 + 1 ) D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for ( 2 + 1 )-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density η s is consistent with a well-known holographic result 1 4 π at several temperatures on a 4 × 4 honeycomb lattice with the local electric representation truncated at j max = 1 2 . We also find the ratio of the spectral function and frequency ρ x y ( ω ) ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond j max = 1 2 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including j max truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Decay rates of almost strong modes in Floquet spin chains beyond Fermi's Golden Rule

The stability and dynamics of almost strong zero and π modes in weakly nonintegrable Floquet spin chains are investigated. Such modes can also be viewed as localized Majorana modes at the edge of a topological superconductor. Perturbation theory in the strength of integrability breaking interaction J z is employed to estimate the decay rates of these modes, and compared to decay rates obtained from exact diagonalization. Here, the structure of the perturbation theory and thus the lifetime of the modes is governed by the conservation of quasienergy modulo 2π/T, where T is the period of the Floquet system. If there are 4n – 1 bulk excitations whose quasienergies add up to zero (or π/T for a π mode), one obtains a decay channel of the Majorana mode with a decay rate proportional to $J$$^{2n}_{z}$. Thus the lifetime is sensitively controlled by the width of the single-particle Floquet bands. For regimes where the decay rates are quadratic in J z , an analytic expression for the decay rate in terms of an infinite temperature autocorrelation function of the integrable model is derived, and shown to agree well with exact diagonalization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Metal-insulator transition in transition metal dichalcogenide heterobilayer moiré superlattices

Moiré superlattices formed in two-dimensional semiconductor heterobilayers provide a new realization of Hubbard model physics in which the number of electrons per effective atom can be tuned at will. Here we report on an exact diagonalization study of the electronic properties of half-filled narrow moiré bands in which correlation strengths are varied by changing twist angles or interaction strengths. We construct a phase diagram for the bilayer, identifying where the metal-insulator phase transition occurs, estimating the sizes of the charge gaps in the insulating phase, and commenting on the nature of the transition and the importance of subdominant interaction parameters.

2-dimensional systems↗
DOE OSTI2021

J eff = $\frac{3}{2}$ metallic phase and unconventional superconductivity in GaTa 4 Se 8

By means of density functional theory plus dynamical mean-field theory (DFT+DMFT) calculations and resonant inelastic x-ray scattering (RIXS) experiments, we investigate the high-pressure phases of the spin-orbit-coupled Jeff = 3/2 insulator GaTa 4 Se 8 . Its metallic phase, derived from the Mott state by applying pressure, is found to carry J eff = 3/2 moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of J eff at the Ta L2-edge up to 10.4 GPa. Our exact diagonalization based DFT+DMFT calculations including spin-orbit coupling also reveal that the J eff = 3/2 character can be clearly identified under high pressure. These results establish the intriguing nature of the correlated metallic magnetic phase, which represents the first confirmed example of J eff =3/2 moments residing in a metal. They also indicate that the pressure-induced superconductivity is likely unconventional and influenced by these J eff = 3/2 moments. Based on a self-energy analysis, we furthermore propose the possibility of doping-induced superconductivity related to a spin-freezing crossover.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Topology and many-body localization

We discuss the problem of localization in two dimensional electron systems in the quantum Hall (single Landau level) regime. After briefly summarizing the well-studied problem of Anderson localization in the non-interacting case, we concentrate on the problem of disorder induced many-body localization (MBL) in the presence of electron–electron interactions using numerical exact diagonalization and eigenvalue spacing statistics as a function of system size. We provide evidence showing that MBL is not attainable in a single Landau level with short range (white noise) disorder in the thermodynamic limit. We then study the interplay of topology and localization, by contrasting the behavior of topological and nontopological subbands arising from a single Landau level in two models — (i) a pair of extremely flat Hofstadter bands with an optimally chosen periodic potential, and (ii) a Landau level with a split-off nontopological impurity band. Both models provide convincing evidence for the strong effect of topology on the feasibility of many-body localization as well as slow dynamics starting from a nonequilibrium state with charge imbalance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Magnetism and quantum melting in moiré-material Wigner crystals

Recent experiments have established that semiconductor-based moir´e materials can host incompressible states at a series of fractional moir´e-miniband fillings. These states have been identified as generalized Wigner crystals in which electrons localize on a subset of the available triangular-lattice moir´e superlattice sites. In this article, we use momentum-space exact diagonalization to investigate the many-body ground state evolution at rational fillings from the weak-hopping classical lattice gas limit, in which only spin degrees-of-freedom are active at low energies, to the strong-hopping metallic regime where the Wigner crystals melt. We specifically address the nature of the magnetic ground states of the generalized Wigner crystals at fillings ν = 1/3 and ν = 2/3.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Robustness and Eventual Slow Decay of Bound States of Interacting Microwave Photons in the Google Quantum AI Experiment

Integrable models are characterized by the existence of stable excitations that can propagate indefinitely without decaying. This includes multimagnon bound states in the celebrated 𝑋⁢𝑋⁢𝑍 spin-chain model and its integrable Floquet counterpart. A recent Google Quantum AI experiment [A. Morvan et al., Nature 612, 240 (2022)] realizing the Floquet model has demonstrated the persistence of such collective excitations even when the integrability is broken: this observation is at odds with the expectation of ergodic dynamics in generic nonintegrable systems. Here, we study the spectrum of the model realized in the experiment using exact diagonalization and physical arguments. We find that isolated bands corresponding to the descendants of the exact bound states of the integrable model are clearly observable in the spectrum for a large range of system sizes. However, our numerical analysis of the localization properties of the eigenstates suggests that the bound states become unstable in the thermodynamic limit. A perturbative estimate of the decay rate agrees with the prediction of an eventual instability for large system sizes.

Exact diagonalization↗
DOE OSTI2021

Orbitally selective resonant photodoping to enhance superconductivity

Signatures of superconductivity at elevated temperatures above T c in high-temperature superconductors have been observed near 1/8 hole doping for photoexcitation with infrared or optical light polarized either in the CuO 2 plane or along the c axis. While the use of in-plane polarization has been effective for incident energies aligned to specific phonons, c-axis laser excitation in a broad range between 5 μm and 400 nm was found to affect the superconducting dynamics in striped La 1.88 5Ba 0.115 CuO 4 , with a maximum enhancement in the 1/ω dependence to the conductivity observed at 800 nm. This broad energy range, specifically 800 nm, is not resonant with any phonon modes, yet induced electronic excitations appear to be connected to superconductivity at energy scales well above the typical gap energies in the cuprates. A critical question is, What can be responsible for such an effect at 800 nm? Using time-dependent exact diagonalization, we demonstrate that the holes in the CuO 2 plane can be photoexcited into the charge reservoir layers at resonant wavelengths within a multiband Hubbard model. This orbitally selective photoinduced charge transfer effectively changes the in-plane doping level, which can lead to an enhancement of T c near the 1/8 anomaly.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Hamming distance and the onset of quantum criticality

Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight configurations in the sampling, that is, the sign problem (SP). There have been several recent calculations which exploit the SP to locate underlying critical behavior. Here, utilizing a metric that quantifies phase-space ergodicity in such sampling, the Hamming distance, we suggest a significant advance on these ideas to extract the location of quantum critical points in various fermionic models, in spite of the presence of a severe SP. Combined with other methods, exact diagonalization in our case, it elucidates both the nature of the different phases as well as their location, as we demonstrate explicitly for the honeycomb and triangular Hubbard models, in both their U(1) and SU(2) forms. Furthermore, our approach exemplifies a possible path allowing the exploration of the phase diagram of a variety of fermionic quantum models hitherto considered to be impractical via quantum Monte Carlo simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗