Renormalization Group Calculations Research Articles

Ab initio calculations of anomalous seniority breaking in the πg9/2 shell for the N = 50 isotones

We performed ab initio valence-space in-medium similarity renormalization group (VS-IMSRG) calculations based on chiral two-nucleon and three-nucleon interactions to investigate the anomalous seniority breaking in the neutron number N=50 isotones: 92Mo, 94Ru, 96Pd, and 98Cd. Our calculations well reproduced the measured low-lying spectra and electromagnetic E2 transitions in these nuclei, supporting partial seniority conservation in the first πg9/2 shell. Recent experiments have revealed that, compared to the symmetric patterns predicted under the conserved seniority symmetry, the 41+→21+E2 transition strength in 94Ru is significantly enhanced and that in 96Pd is suppressed. In contrast, the 61+→41+ and 81+→61+ transitions exhibit the opposite trend. We found that this anomalous asymmetry is sensitive to subtle seniority breaking effects, providing a stringent test for state-of-the-art nucleon-nucleon interactions and nuclear models. We analyzed the anomalous asymmetry using VS-IMSRG calculations across various valence spaces. Our ab initio results suggest that core excitations of both proton and neutron across the Z=50 shell are ascribed to the observed anomalous seniority breaking in the N=50 isotones.

The quantum transition of the two-dimensional Ising spin glass

Quantum annealers are commercial devices that aim to solve very hard computational problems1, typically those involving spin glasses2,3. Just as in metallurgic annealing, in which a ferrous metal is slowly cooled4, quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. Removing the field diminishes the quantum fluctuations but forces the system to traverse the critical point that separates the disordered phase (at large fields) from the spin-glass phase (at small fields). A full understanding of this phase transition is still missing. A debated, crucial question regards the closing of the energy gap separating the ground state from the first excited state. All hopes of achieving an exponential speed-up, compared to classical computers, rest on the assumption that the gap will close algebraically with the number of spins5–9. However, renormalization group calculations predict instead that there is an infinite-randomness fixed point10. Here we solve this debate through extreme-scale numerical simulations, finding that both parties have grasped parts of the truth. Although the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. As this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the quantum annealing paradigm11–13.

Reduced Tensor Network Formulation for Non-Abelian Gauge Theories in Arbitrary Dimensions

Abstract Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to “trace out” these degrees of freedom with the use of character expansion, giving a reduced tensor network where the degeneracy associated with the internal symmetry is eliminated. In this work, we show that such an index loop also exists in higher dimensions in the form of a closed tensor network that we call the “armillary sphere”. This allows us to completely eliminate the matrix indices and reduce the overall size of the tensors in the same way as is possible in two dimensions. This formulation allows us to include significantly more representations with the same tensor size, thus making it possible to reach a greater level of numerical accuracy in the tensor renormalization group computations.

Antiferromagnetic Bosonic t-J Models and Their Quantum Simulation in Tweezer Arrays.

The combination of optical tweezer arrays with strong interactions-via dipole exchange of molecules and Van der Waals interactions of Rydberg atoms-has opened the door for the exploration of a wide variety of quantum spin models. A next significant step will be the combination of such settings with mobile dopants. This will enable one to simulate the physics believed to underlie many strongly correlated quantum materials. Here, we propose an experimental scheme to realize bosonic t-J models via encoding the local Hilbert space in a set of three internal atomic or molecular states. By engineering antiferromagnetic (AFM) couplings between spins, competition between charge motion and magnetic order similar to that in high-T_{c} cuprates can be realized. Since the ground states of the 2D bosonic AFM t-J model we propose to realize have not been studied extensively before, we start by analyzing the case of two dopants-the simplest instance in which their bosonic statistics plays a role-and compare our results to the fermionic case. We perform large-scale density matrix renormalization group calculations on six-legged cylinders, and find a strong tendency for bosonic holes to form stripes. This demonstrates that bosonic, AFM t-J models may contain similar physics as the collective phases in strongly correlated electrons.

Ab initio valence-space in-medium similarity renormalization group calculations for neutron-rich P, Cl, and K isotopes* *Supported by the National Key R&D Program of China (2023YFA1606403), the National Natural Science Foundation of China (12205340, 12175281, 12347106, 12121005), the Natural Science Foundation of Gansu Province, China (22JR5RA123, 23JRRA614), the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000), the Key Research

Neutron-rich P, Cl, and K isotopes, particularly those with neutron numbers of approximately , have attracted extensive experimental and theoretical interest. We utilize the ab initio valence-space in-medium similarity renormalization group approach, based on chiral nucleon-nucleon and three-nucleon forces, to investigate the exotic properties of these isotopes. Systematic calculations of the low-lying spectra are performed. A key finding is the level inversion between and states in odd-A isotopes, attributed to the inversion of and single-particle states. The ab initio calculations, which incorporate the three-nucleon forces, correlate closely with existing experimental data. Further calculations of effective proton single-particle energies provide deeper insights into the shell evolution for and sub-shells. Our results indicate that the three-body force plays important roles in the shell evolution for and sub-shells with neutron numbers ranging from 20 to 28. Additionally, systematic ab initio calculations are conducted for the low-lying spectra of odd-odd nuclei. The results correspond with experimental data and provide new insights for future research into these isotopes up to and beyond the drip line.

Extracting correlation length in Mott insulators by strong-field driving

The breakdown of a Mott-insulator when subjected to intense laser fields is characterized by the formation of doublon-hole pairs. This breakdown is furthermore evidenced by the production of high harmonics that can be experimentally measured. Here, we present an approach for extracting the doublon-hole correlation length of a Mott insulator. The method is based on a dynamical calculation of the Mott insulator’s rate of charge production in response to an applied strong-field laser pulse. We find that coupling the Mott insulator to a metal drastically increases the correlation length, in support of our recent hypothesis [Phys. Rev. B 108, 144434 (2023)2469-995010.1103/PhysRevB.108.144434] that coupling to a metal enhances the charge fluctuations in the insulator. We confirm our conclusions using density matrix renormalization group (DMRG) calculations. The proposed method can be applied to experimentally measured observables, such as differential reflectivity or the high harmonic generation (HHG) spectrum to extract doublon-hole correlation length.

CFT and lattice correlators near an RG domain wall between minimal models

Conformal interfaces separating two conformal field theories (CFTs) provide maps between different CFTs, and naturally exist in nature as domain walls between different phases. One particularly interesting construction of a conformal interface is the renormalization group (RG) domain wall between CFTs. For a given Virasoro minimal model \mathcal{M}_{k+3,k+2}ℳk+3,k+2, an RG domain wall can be generated by a specific deformation which triggers an RG flow towards its adjacent Virasoro minimal model \mathcal{M}_{k+2,k+1}ℳk+2,k+1 with the deformation turned on over part of the space. An algebraic construction of this domain wall was proposed by Gaiotto in [J. High Energy Phys. 12, 103 (2012)]. In this paper, we will provide a study of this RG domain wall for the minimal case k=2k=2, which can be thought of as a nonperturbative check of the construction. In this case the wall is separating the Tricritical Ising Model (TIM) CFT and the Ising Model (IM) CFT. We will check the analytical results of correlation functions from the RG brane construction with the numerical density matrix renormalization group (DMRG) calculation using a lattice model proposed in [arXiv.1206.1332, Science 344, 280 (2014)], and find a perfect agreement. We comment on possible experimental realizations of this RG domain wall.

Nematic phase of the n-component cubic-spin spin glass in d = 3: Liquid-crystal phase in a dirty magnet

A nematic phase, previously seen in the d=3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the-high temperature disordered phase, for number of components n≥3, in spatial dimension d=3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. This result is obtained from renormalization-group calculations that are exact on the hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. The nematic phase completely intervenes between the spin-glass phase and the disordered phase. The Lyapunov exponents of the spin-glass chaos are calculated from n=1 up to n=12 and show odd-even oscillations with respect to n.

DivERGe implements various Exact Renormalization Group examples

We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU(2) models in all of the three included FRG variants: TU^22FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.

Codebase release 0.5 for divERGe

We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU(2) models in all of the three included FRG variants: TU^22FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.

Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice t-J Model.

The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t_{2}>0) but a dominant charge density wave (CDW) order on the hole-doped side (t_{2}<0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ=1/16-1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1/8 doping, demonstrating the winning of SC over CDW by increasing the system width. Our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.

The energy spectrum and magnetization profile of the decorated spin ladder systems

The peculiarities of the energy spectrum of the decorated mixed spin two-leg ladder system having three spin unit cells have been studied by the perturbation theory in the limit of dominant spin coupling in ladder rungs. It is shown, that despite the singlet ground state, this spin ladder may have an intermediate plateau in a low-temperature magnetization profile. The existence of a similar plateau was shown also in the case of some intermediate values of coupling parameters by means of exact diagonalization study of small ladder clusters and by the density-matrix renormalization group calculations. We also found that the Ising type of interactions in ladder rungs may lead to the disappearance of the above intermediate magnetization plateau for the corresponding isotropic spin ladder.

Singlet quantum phases of the frustrated spin-1/2 ladder with ferromagnetic (F) exchange in legs and alternating F-AF exchange in rungs

Ladders with 2N spins-1/2 and singlet (S = 0) ground states are studied numerically using exact diagonalization and density matrix renormalization group (DMRG) calculations. The curvatures E ″(s) of states with the lowest energy E(s) at spin s = S/N ≤ 1 are obtained in the thermodynamic limit. All states have E ″(s) > 0 in two phases, one with strong F exchange J F in rungs, the other with strong F exchange J L in legs. The Dimer phase with frustrated F exchanges has one or more states with E ″(s) < 0. All three phases have finite gaps to the lowest triplet state. The ladder at J F → ∞ is adiabatically connected to the spin-1 Heisenberg AF chain, and at J L → ∞ to the J 1 − J 2 model.

Ground-state phase diagram and universality of sequential topological valence-bond-solid quantum transitions in a mixed tetramer chain

The ground-state ordering of a quantum mixed-spin Heisenberg tetramer chain composed of an alternate sequence of s = 1 and S=3/2 dimers is studied in detail as a function of two considered exchange interactions ascribed to similar and dissimilar spin pairs. At zero magnetic field, the ferrimagnetic mixed spin-(1, 1, 3/2, 3/2) Heisenberg tetramer chain displays, depending on a mutual interplay between two considered exchange interactions, three distinct gapped valence-bond-solid phases separated by gap-closing quantum critical points. Using density-matrix renormalization group calculations we construct the full ground-state phase diagram as a function of the interaction ratio and magnetic field, which exhibits besides three gapped valence-bond-solid phases special Kosterlitz–Thouless and topological quantum critical points. A tangential finite-size scaling analysis is employed to obtain precise estimates of the zero-field valence-bond-solid transitions and unveil their common logarithmic correction to a power-law scaling of the correlation length.

Ground-state mass of 22Al and test of state-of-the-art ab initio calculations* *Supported in part by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000), the CAS Project for Young Scientists in Basic Research (YSBR-002), the National Nature Science Foundation of China (12135017, 12121005, 11975280, 12105333, 12205340, 12322507, 12305126, 12305151), the Gansu Natural Science Foundation (22JR5RA123, 23JRRA614) and the

The ground-state mass excess of the drip-line nucleus Al is measured for the first time as keV using the newly-developed B ρ-defined isochronous mass spectrometry method at the cooler storage ring in Lanzhou. The new mass excess value allowed us to determine the excitation energies of the two low-lying states in Al with significantly reduced uncertainties of 51 keV. When compared to the analogue states in its mirror nucleus F, the mirror energy differences of the two states in the Al- F mirror pair are determined to be keV and keV. The excitation energies and mirror energy differences are used to test the state-of-the-art ab initio valence-space in-medium similarity renormalization group calculations with four sets of interactions derived from the chiral effective field theory. The mechanism leading to the large mirror energy differences is investigated and attributed to the occupation of the orbital.

Predicting the FCI Energy of Large Systems to Chemical Accuracy from Restricted Active Space Density Matrix Renormalization Group Calculations.

We theoretically derive and validate with large scale simulations a remarkably accurate power law scaling of errors for the restricted active space density matrix renormalization group (DMRG-RAS) method [J. Phys. Chem. A 126, 9709] in electronic structure calculations. This yields a new extrapolation method, DMRG-RAS-X, which reaches chemical accuracy for strongly correlated systems such as the chromium dimer, dicarbon up to a large cc-pVQZ basis and even a large chemical complex such as the FeMoco with significantly lower computational demands than those of previous methods. The method is free of empirical parameters, performed robustly and reliably in all examples we tested, and has the potential to become a vital alternative method for electronic structure calculations in quantum chemistry and more generally for the computation of strong correlations in nuclear and condensed matter physics.

Trimer quantum spin liquid in a honeycomb array of Rydberg atoms

Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.

Auger spectroscopy beyond the ultra-short core-hole relaxation time approximation

We present a time-dependent computational approach to study Auger electron spectroscopy (AES) beyond the ultra-short core-hole relaxation time approximation and, as a test case, we apply it to the paradigmatic example of a one-dimensional Mott insulator represented by a half-filled Hubbard chain. The Auger spectrum is usually calculated by assuming that, after the creation of a core-hole, the system thermalizes almost instantaneously. This leads to a relatively simple analytical expression that uses the ground-state with a core-hole as a reference state and ignores all the transient dynamics related to the screening of the core-hole. In this picture, the response of the system can be associated to the pair spectral function. On the other hand, in our numerical calculations, the core hole is created by a light pulse, allowing one to study the transient dynamics of the system in terms of the pulse duration and in the non-perturbative regime. Time-dependent density matrix renormalization group calculations reveal that the relaxation process involves the creation of a polarization cloud of doublon excitations that have an effect similar to photo-doping. As a consequence, there is a leak of spectral weight to higher energies into what otherwise would be the Mott gap. For longer pulses, these excited states, mostly comprised of doublons, can dominate the spectrum. By changing the duration of the light-pulse, the entire screening process can be resolved in time.

The PointGroupNRG code for numerical renormalization group calculations with discrete point-group symmetries

The numerical renormalization group (NRG) has been widely used as a magnetic impurity solver since the pioneering works by Wilson. Over the past decades, a significant attention has been focused on the application of symmetries in order to reduce the computational cost of the calculations and to improve their accuracy. In particular, a notable progress has been made in implementing continuous symmetries such as SO(3), useful for studying impurities in an isotropic medium, or SU(N), which is applicable to a wide range of systems. In this work, we focus on the application of discrete point group symmetries, which are particularly relevant for impurity systems in metals where crystal field effects are important. With this aim, we have developed an original NRG code written in the Julia language, PointGroupNRG, where we have implemented crystal point-group symmetries for the Anderson impurity model, as well as the continuous spin and charge symmetries. Among other results, we demonstrate the advantage of our procedure by applying the code to a two-impurity model with RKKY interaction and an impurity system with two orbitals of Eg symmetry and two channels. We also provide benchmarks to show the performance improvements obtained by exploiting the orbital symmetries.

Ab initio calculations for well deformed nuclei: 40Mg and 42Si

We performed ab initio valence-space in-medium similarity renormalization group calculations based on chiral nucleon-nucleon and three-nucleon interactions to study the neutron-rich nuclei around N=28, where the experimental and theoretical evidence point to a rapid transition from spherical to rotational regimes. First, the rotational spectra of 40Mg, 42Si, and 44S are established theoretically, anchored by the calculated E2 transition strength. The results suggest that 40Mg and 42Si exhibit large deformations. After that, the erosion of the N=28 shell closure, especially the evolutions of shape deformation and the emergence of shape coexistence, are discussed in N=28 even-even isotones ranging from 40Mg to 48Ca. Finally, the shell evolution of N=28 in Mg and Si chains is discussed based on the experimental and predicted excitation energies of low-lying states. The results from our ab initio calculations align well with available experimental data, furnishing essential insights into the structure of neutron-rich nuclei, particularly deformations in the vicinity of 40Mg and 42Si.