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DOE OSTI2020

Measurement and microscopic description of odd–even staggering of charge radii of exotic copper isotopes

Nuclear charge radii globally scale with atomic mass number A as A 1/3 , and isotopes with an odd number of neutrons are usually slightly smaller in size than their even-neutron neighbours. This odd–even staggering, ubiquitous throughout the nuclear landscape1, varies with the number of protons and neutrons, and poses a substantial challenge for nuclear theory. Here, we report measurements of the charge radii of short-lived copper isotopes up to the very exotic 78 Cu (with proton number Z = 29 and neutron number N = 49), produced at only 20 ions s –1 , using the collinear resonance ionization spectroscopy method at the Isotope Mass Separator On-Line Device facility (ISOLDE) at CERN. We observe an unexpected reduction in the odd–even staggering for isotopes approaching the N = 50 shell gap. To describe the data, we applied models based on nuclear density functional theory and A-body valence-space in-medium similarity renormalization group theory. Through these comparisons, we demonstrate a relation between the global behaviour of charge radii and the saturation density of nuclear matter, and show that the local charge radii variations, which reflect the many-body polarization effects, naturally emerge from A-body calculations fitted to properties of A ≤ 4 nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Spinon excitations and spin correlations in the one-dimensional quantum magnet β -VOSO 4 probed by Raman spectroscopy

Fractionalized excitations such as spinons and anyons have emerged as a central theme in condensed matter physics with broad implications for superconductivity, quantum statistics, and quantum computation. The nearly ideal one-dimensional S = 1/2 system β-VOSO 4 without long-range order down to 85 mK provides a promising platform to experimentally explore such fractionalized excitations. Here, we employ Raman spectroscopy to probe magnetic excitations and the evolution of spin correlations in β-VOSO 4 . Spinon signatures are found along the chain direction, evidenced by a broad, gapless scattering continuum at low temperatures. The temperature dependence of the spinon spectral weight aligns considerably with numerical density matrix renormalization group calculations. By comparing the experimental spinon spectral weight with calculated results and evaluating the associated quantum Fisher information (QFI) therefrom, we observe a steep increase in QFI upon cooling, indicating rapidly growing correlation lengths. Our study showcases QFI as a probe of spin correlations in quantum magnets.

Wulferding, Dirk [Sejong Univ., Seoul (Korea, Repu↗

DOE OSTI2022

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Toward DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: Electrons moving at relativistic speeds, close lying states, and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules in which all the three effects are present. These are the heavier transition metal compounds, lanthanides, and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and the density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs as we demonstrate on the system of TlH, AsH, and SbH.

Brandejs, Jan (ORCID:0000000221073095)↗

DOE OSTI2022

On the new universality class in structurally disordered n -vector model with long-range interactions

We study a stability boundary of a region where nontrivial critical behavior of an n-vector model with long-range power-law decaying interactions is induced by the presence of a structural disorder (e.g., weak quenched dilution). This boundary is given by the marginal dimension of the order parameter nc dependent on space dimension, d, and a control parameter of the interaction decay, σ, below which the model belongs to the new dilution-induced universality class. Exploiting the Harris criterion and recent field theoretical renormalization group results for the pure model with long-range interactions, we get nc as a three loop ɛ = 2σ – d-expansion. We provide numerical values for nc applying series resummation methods. Our results show that not only the Ising systems (n = 1) can belong to the new disorder-induced long-range universality class at d = 2 and 3.

Physics↗

DOE OSTI2021

A graphene edge-mediated quantum gate

We propose a quantum gate architecture that allows for the systematic control of the effective exchange interactions between magnetic impurities embedded in nanoscale graphene flakes connected by a gated bridge. The entanglement between the magnetic moment and the edge states of the fragments is used to electrostatically tune the exchange interaction from ferro to antiferromagnetic by merely changing the bridge's carrier density. By characterizing the effects of size and coupling parameters, we explore different operation regimes of this device by means of exact calculations with the density matrix renormalization group. We analyze the results utilizing a simplified model that accounts for the main many-body mechanisms. Finally, we discuss how to use arrays of these devices to build quantum simulators for quantum many-body Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Automatic derivation of many-body theories based on general Fermi vacua

This paper describes Wick&D, an implementation of the algebra of second-quantized operators normal ordered with respect to general correlated references and the corresponding Wick theorem [D. Mukherjee, Chem. Phys. Lett. 274, 561 (1997) and W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997)]. Wick&D employs a compact representation of operators and a backtracking algorithm to efficiently evaluate Wick contractions. Since Wick&D can handle both fully and partially contracted terms, it can be applied to both projective and Fock-space many-body formalisms. To demonstrate the usefulness of Wick&D, here we use it to evaluate the single-reference coupled cluster equations up to octuple excitations and report an automated derivation and implementation of the second-order driven similarity renormalization group multireference perturbation theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Magnetic phases of spatially modulated spin-1 chains in Rydberg excitons: Classical and quantum simulations

Here, in this work, we study the magnetic phases of a spatially modulated chain of spin-1 Rydberg excitons. Using the Density Matrix Renormalization Group (DMRG) technique, we study various magnetic and topologically nontrivial phases using both single-particle properties, such as local magnetization and quantum entropy, and many-body ones, such as pair-wise Néel and long-range string correlations. In particular, we investigate the emergence and robustness of the Haldane phase, a topological phase of anti-ferromagnetic spin-1 chains. Furthermore, we devise a hybrid quantum algorithm employing restricted Boltzmann machine to simulate the ground state of such a system that shows very good agreement with the results of exact diagonalization and DMRG.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Toward more accurate adiabatic connection approach for multireference wavefunctions

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the “fixed-RDM” approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Hilbert space multireference coupled cluster tailored by matrix product states

In the past decade, the quantum chemical version of the density matrix renormalization group method has established itself as the method of choice for strongly correlated molecular systems. However, despite its favorable scaling, in practice, it is not suitable for computations of dynamic correlation. Several approaches to include that in post-DMRG methods exist; in our group, we focused on the tailored coupled cluster (TCC) approach. This method works well in many situations; however, in exactly degenerate cases (with two or more determinants of equal weight), it exhibits a bias toward the reference determinant representing the Fermi vacuum. Although sometimes it is possible to use a compensation scheme to avoid this bias for energy differences, it is certainly a drawback. In order to overcome this bias of the TCC method, we have developed a Hilbert-space multireference version of tailored CC, which can treat several determinants on an equal footing. We have implemented and compared the performance of three Hilbert-space multireference coupled cluster (MRCC) variants—the state universal one and the Brillouin–Wigner and Mukherjee’s state specific ones. We have assessed these approaches on the cyclobutadiene and tetramethyleneethane molecules, which are both diradicals with exactly degenerate determinants at a certain geometry. We have also investigated the sensitivity of the results on the orbital rotation of the highest occupied and lowest unoccupied molecular orbital (HOMO–LUMO) pair, as it is well known that Hilbert-space MRCC methods are not invariant to such transformations.

Chemistry↗

DOE OSTI2024

Efficient simulation of open quantum systems coupled to a reservoir through multiple channels

It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system–bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system–bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system–bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system–bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system–bath couplings using matrix product states, which may further our understanding of nonlocal exciton–phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.

Chemistry↗

DOE OSTI2026

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

Here, we develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

Islam, Shariful [North Carolina State University, ↗

DOE OSTI2020

Murray Gell-Mann

Murray Gell-Mann, the preeminent architect of theoretical elementary-particle physics, died on 24 May 2019 in Santa Fe, New Mexico. He received the 1969 Nobel Prize “for his contributions and discoveries concerning the classification of elementary particles and their interactions.” His contributions to physics include many foundational ideas, such as the renormalization group, which is fundamental to quantum field theory and statistical mechanics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Stripe order enhanced superconductivity in the Hubbard model

Unidirectional (“stripe”) charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of “optimal” inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated—mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi–long-range order with a Luttinger exponent, K sc ~ 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Ground-state phase diagram of the t-t ′ -J model

Significance Theoretical efforts to understand the superconducting cuprates have focused on a few simplified but challenging models: notably the Hubbard and the t - t ′ - J models. Using density matrix renormalization group (DMRG) simulations on width-8 cylinders, we study the ground-state phase diagram of the t - t ′- J model. The next nearest-neighbor hopping t ′ allows one to distinguish between hole ( t ′ < 0 ) and electron doping ( t ′ > 0 ). We find for the magnetic, charge, and single-particle properties that this model roughly captures the differences between the electron- and hole-doped cuprates. However, the superconducting properties differ. For hole doping ( t ′ < 0 ), there is an absence of superconductivity, while for electron doping ( t ′ > 0), we find d -wave superconductivity coexisting with antiferromagnetism and a secondary triplet p -wave pairing component.

Jiang, Shengtao↗

DOE OSTI2024

Quantum Barkhausen noise induced by domain wall cotunneling

Most macroscopic magnetic phenomena (including magnetic hysteresis) are typically understood classically. Here, we examine the dynamics of a uniaxial rare-earth ferromagnet deep within the quantum regime, so that domain wall motion, and the associated hysteresis, is initiated by quantum nucleation, which then grows into large-scale domain wall motion, which is observable as an unusual form of Barkhausen noise. We observe noncritical behavior in the resulting avalanche dynamics that only can be explained by going beyond traditional renormalization group methods or classical domain wall models. We find that this “quantum Barkhausen noise” exhibits two distinct mechanisms for domain wall movement, each of which is quantum-mechanical, but with very different dependences on an external magnetic field applied transverse to the spin (Ising) axis. These observations can be understood in terms of the correlated motion of pairs of domain walls, nucleated by cotunneling of plaquettes (sections of domain wall), with plaquette pairs correlated by dipolar interactions; this correlation is suppressed by the transverse field. Similar macroscopic correlations may be expected to appear in the hysteresis of other systems with long-range interactions.

Science & Technology - Other Topics↗

DOE OSTI2025

Global phase diagram of D-wave superconductivity in the square-lattice t-J model

The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.

Chen, Feng (ORCID:000000018196030X)↗

DOE OSTI2025

Anyon superconductivity from topological criticality in a Hofstadter–Hubbard model

We argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moiré materials, which make large flux per unit cell accessible at laboratory fields, we study the triangular lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette, where previous literature has argued that a chiral spin liquid separates a weak-coupling integer quantum Hall phase and a strong-coupling topologically trivial antiferromagnetic insulator at a density of one electron per site. We argue that topological superconductivity emerges upon doping in the vicinity of the integer quantum Hall to chiral spin liquid transition. We employ exact diagonalization and density matrix renormalization group methods to examine this theoretical scenario and find that electronic pairing indeed occurs on both sides of criticality over a remarkably broad range of interaction strengths. On the chiral spin liquid side, our results provide a concrete model realization of the long-hypothesized mechanism of anyon superconductivity. Our study thus establishes a beyond-Bardeen-Cooper-Schrieffer route to electron pairing in a well-controlled limit, relying crucially on the interplay between electron correlations and band topology.

Hubbard model↗