Relevant Energy Scales Research Articles

Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions.

We show that numerical linked cluster expansions (NLCEs) based on sufficiently large building blocks allow one to obtain accurate low-temperature results for the thermodynamic properties of spin lattice models with continuous disorder distributions. Specifically, we show that such results can be obtained computing the disorder averages in the NLCE clusters before calculating their weights. We provide a proof of concept using three different NLCEs based on L, square, and rectangle building blocks. We consider both classical (Ising) and quantum (Heisenberg) spin-1/2 models and show that convergence can be achieved down to temperatures that are up to two orders of magnitude lower than the relevant energy scale in the model. Additionally, we provide evidence that in one dimension one can obtain accurate results for observables such as the energy down to their ground-state values.

Toward Direct Exploration of the Few-Femtosecond Dynamics of Electronic Coherence and Correlation in Quantum Materials Using Time- and Angle-Resolved Photoemission Spectroscopy

Over the last two decades, time- and angle-resolved photoemission spectroscopy (trARPES) has become a mature and established experimental technique for the study of ultrafast electronic and structural dynamics in materials. To date, most trARPES investigations have focused on the investigation of processes occurring on time scales of ≳30 fs, in particular, relaxation and thermalization, and have therefore been blind to the initial sub-10 fs dynamics related to electronic coherence and correlation effects. In this article, we illustrate how current trARPES setups reach their limits when it comes to addressing such extraordinarily short time scales and present an experimental configuration that provides the time, energy, and momentum resolutions required to monitor few-femtosecond dynamics on the relevant energy and momentum scales. We discuss the potential capabilities of such an experiment to study the electronic response of materials in the strong-field interaction regime at PHz frequencies and finally review a theoretical concept that may in the future even overcome the competing resolution limitations of trARPES experiments, as imposed by the time–bandwidth product of the probing laser pulse. Our roadmap for ultrafast trARPES indicates a path to break new experimental ground in quantum nonequilibrium electronic dynamics, from which new possibilities for ultrafast control of optical and electronic signals in quantum materials can be explored.

Heavy top quark mass in the minimal universal seesaw model

We study the hierarchy between MT , vL, and vR, the relevant energy scales of the Minimal Universal Seesaw Model (MUSM), where the two lightest quark families remain massless at tree level. We also predict the heavy top quark mass, mt′ . We do some numerical analysis using recent experimental data. Our numerical analysis demonstrates that MT is sensitive to the values of the Yukawa couplings. The heavy top quark mass (mt′ ) is predicted to be within the range from 1.4 TeV to 7.2 TeV for vR = 10 TeV.

Controlling crystal-electric field levels through symmetry-breaking uniaxial pressure in a cubic super heavy fermion

YbPtBi is one of the heavy-fermion systems with largest Sommerfeld coefficient γ and is thus classified as a ‘super’-heavy fermion material. In this work, we resolve the long-debated question about the hierarchy of relevant energy scales, such as crystal-electric field (CEF) levels, Kondo and magnetic ordering temperature, in YbPtBi. Through measurements of the a.c. elastocaloric effect and generic symmetry arguments, we identify an elastic level splitting that is unambiguously associated with the symmetry-allowed splitting of a quartet CEF level. This quartet, which we identify to be the first excited state at Δ/kB ≈ 1.6 K above the doublet ground state at ambient pressure, is well below the proposed Kondo temperature TK ≈ 10 K. Consequently, this analysis of the energy scheme can provide support models that predict that the heavy electron mass is a result of an enhanced degeneracy of the CEF ground state, i.e., a quasi-sextet in YbPtBi. At the same time, our study shows the potential of the a.c. elastocaloric effect to control and quantify strain-induced changes of the CEF schemes, opening a different route to disentangle the CEF energy scales from other relevant energy scales in correlated quantum materials.

Ab Initio Derivation of Lattice-Gauge-Theory Dynamics for Cold Gases in Optical Lattices

We introduce a method for quantum simulation of U$(1)$ lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices. The proposal enables the study of both gauge and fermionic-matter fields without integrating out one of them in one and two dimensions. We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species. Starting from an $ab\,initio$ modelling of the experimental setting, we systematically carry out a derivation of the target U$(1)$ gauge theory. This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that - while pivotal for a successful implementation - have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions, and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics. We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope $^{173}$Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one- and two-dimensional settings.

Inclusive production of J/ψ, ψ(2S), and Υ states in pNRQCD

Under some assumptions on the hierarchy of relevant energy scales, we compute the nonrelativistic QCD (NRQCD) long-distance matrix elements (LDMEs) for inclusive production of J/ψ, ψ(2S), and Υ states based on the potential NRQCD (pNRQCD) effective field theory. Based on the pNRQCD formalism, we obtain expressions for the LDMEs in terms of the quarkonium wavefunctions at the origin and universal gluonic correlators, which do not depend on the heavy quark flavor or the radial excitation. This greatly reduces the number of nonperturbative unknowns and substantially enhances the predictive power of the nonrelativistic effective field theory formalism. We obtain improved determinations of the LDMEs for J/ψ, ψ(2S), and Υ states thanks to the universality of the gluonic correlators, and obtain phenomenological results for cross sections and polarizations at large transverse momentum that agree well with measurements at the LHC.

Kondo quasiparticle dynamics observed by resonant inelastic x-ray scattering

Effective models focused on pertinent low-energy degrees of freedom have substantially contributed to our qualitative understanding of quantum materials. An iconic example, the Kondo model, was key to demonstrating that the rich phase diagrams of correlated metals originate from the interplay of localized and itinerant electrons. Modern electronic structure calculations suggest that to achieve quantitative material-specific models, accurate consideration of the crystal field and spin-orbit interactions is imperative. This poses the question of how local high-energy degrees of freedom become incorporated into a collective electronic state. Here, we use resonant inelastic x-ray scattering (RIXS) on CePd3 to clarify the fate of all relevant energy scales. We find that even spin-orbit excited states acquire pronounced momentum-dependence at low temperature—the telltale sign of hybridization with the underlying metallic state. Our results demonstrate how localized electronic degrees of freedom endow correlated metals with new properties, which is critical for a microscopic understanding of superconducting, electronic nematic, and topological states.

Free energy of twisting spins in Mn3Sn

The magnetic free energy is usually quadratic in magnetic field and depends on the mutual orientation of the magnetic field and the crystalline axes. Tiny in magnitude, this magnetocrystalline anisotropy energy (MAE) is nevertheless indispensable for the existence of permanent magnets. Here, we show that in Mn$_3$Sn, a non-collinear antiferromagnet attracting much attention following the discovery of its large anomalous Hall effect, the free energy of spins has superquadratic components, which drive the MAE. We experimentally demonstrate that the thermodynamic free energy includes terms odd in magnetic field ($\mathcal{O}(H^3)+\mathcal{O}(H^5)$) and generating sixfold and twelve-fold angular oscillations in the torque response. We show that they are quantitatively explained by theory, which can be used to quantify relevant energy scales (Heisenberg, Dzyaloshinskii-Moriya, Zeeman and single-ion anisotropy) of the system. Based on the theory, we conclude that, in contrast with common magnets, what drives the MAE in Mn$_3$Sn is the field-induced deformation of the spin texture.

Prototypical many-body signatures in transport properties of semiconductors

We devise a methodology for charge, heat, and entropy transport driven by carriers with finite lifetimes. Combining numerical simulations with analytical expressions for low temperatures, we establish a comprehensive and thermodynamically consistent phenomenology for transport properties in semiconductors. We demonstrate that the scattering rate (inverse lifetime) is a relevant energy scale: It causes the emergence of several characteristic features in each transport observable. The theory is capable to reproduce, with only a minimal input electronic structure, the full temperature profiles measured in correlated narrow-gap semiconductors. In particular, we account for the previously elusive low-$T$ saturation of the resistivity and the Hall coefficient, as well as the (linear) vanishing of the Seebeck and Nernst coefficients in systems such as ${\mathrm{FeSb}}_{2}, {\mathrm{FeAs}}_{2}, {\mathrm{RuSb}}_{2}$, and ${\mathrm{FeGa}}_{3}$.

Gauge-Symmetry Protection Using Single-Body Terms

Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of lattice gauge theories can have dramatic consequences, e.g., the generation of a photon mass in quantum electrodynamics. Here, we introduce an experimentally friendly method to protect gauge invariance in $\mathrm{U}(1)$ lattice gauge theories against coherent errors in a controllable way. Our method employs only single-body energy-penalty terms, thus enabling practical implementations. As we derive analytically, some sets of penalty coefficients render undesired gauge sectors inaccessible by unitary dynamics for exponentially long times, and, for few-body error terms, with resources independent of system size. These findings constitute an exponential improvement over previously known results from energy-gap protection or perturbative treatments. In our method, the gauge-invariant subspace is protected by an emergent global symmetry, meaning it can be immediately applied to other symmetries. In our numerical benchmarks for continuous-time and digital quantum simulations, gauge protection holds for all calculated evolution times (up to $t>10^{10}/J$ for continuous time, with $J$ the relevant energy scale). Crucially, our gauge-protection technique is simpler to realize than the associated ideal gauge theory, and can thus be readily implemented in current ultracold-atom analog simulators as well as digital noisy intermediate scale quantum (NISQ) devices.

Resistivity saturation in Kondo insulators

Resistivities of heavy-fermion insulators typically saturate below a characteristic temperature T*. For some, metallic surface states, potentially from a non-trivial bulk topology, are a likely source of residual conduction. Here, we establish an alternative mechanism: at low temperature, in addition to the charge gap, the scattering rate turns into a relevant energy scale, invalidating the semi-classical Boltzmann picture. Then, finite lifetimes of intrinsic carriers drive residual conduction, impose the existence of a crossover T*, and control—now on par with the gap—the quantum regime emerging below it. Assisted by realistic many-body simulations, we showcase the mechanism for the Kondo insulator Ce3Bi4Pt3, for which residual conduction is a bulk property, and elucidate how its saturation regime evolves under external pressure and varying disorder. Deriving a phenomenological formula for the quantum regime, we also unriddle the ill-understood bulk conductivity of SmB6—demonstrating a wide applicability of our mechanism in correlated narrow-gap semiconductors.

Database, Features, and Machine Learning Model to Identify Thermally Driven Metal–Insulator Transition Compounds

Metal-insulator transition (MIT) compounds are materials that may exhibit insulating or metallic behavior, depending on the physical conditions, and are of immense fundamental interest owing to their potential applications in emerging microelectronics. There is a dearth of thermally-driven MIT materials, however, which makes delineating these compounds from those that are exclusively insulating or metallic challenging. Here we report a material database comprising temperature-controlled MITs (and metals and insulators with similar chemical composition and stoichiometries to the MIT compounds) from high quality experimental literature, built through a combination of materials-domain knowledge and natural language processing. We featurize the dataset using compositional, structural, and energetic descriptors, including two MIT relevant energy scales, an estimated Hubbard interaction and the charge transfer energy, as well as the structure-bond-stress metric referred to as the global-instability index (GII). We then perform supervised classification, constructing three electronic-state classifiers: metal vs non-metal (M), insulator vs non-insulator (I), and MIT vs non-MIT (T). We identify two important descriptors that separate metals, insulators, and MIT materials in a 2D feature space: the average deviation of the covalent radius and the range of the Mendeleev number. We further elaborate on other important features (GII and Ewald energy), and examine how they affect classification of binary vanadium and titanium oxides. We discuss the relationship of these atomic features to the physical interactions underlying MITs in the rare-earth nickelate family. Last, we implement an online version of the classifiers, enabling quick probabilistic class predictions by uploading a crystallographic structure file.

Controlling exciton many-body states by the electric-field effect in monolayer MoS2

We report magneto-optical spectroscopy of gated monolayer MoS$_2$ in high magnetic fields up to 28T and obtain new insights on the many-body interaction of neutral and charged excitons with the resident charges of distinct spin and valley texture. For neutral excitons at low electron doping, we observe a nonlinear valley Zeeman shift due to dipolar spin-interactions that depends sensitively on the local carrier concentration. As the Fermi energy increases to dominate over the other relevant energy scales in the system, the magneto-optical response depends on the occupation of the fully spin-polarized Landau levels in both $K/K^{\prime}$ valleys. This manifests itself in a many-body state. Our experiments demonstrate that the exciton in monolayer semiconductors is only a single particle boson close to charge neutrality. We find that away from charge neutrality it smoothly transitions into polaronic states with a distinct spin-valley flavour that is defined by the Landau level quantized spin and valley texture.

Cascade of replica bands in flat-band systems: Predictions for twisted bilayer graphene

We investigate the effect of electron-phonon interactions (EPI) in systems exhibiting one or more flat electron bands close to the Fermi level and a comparatively large phonon energy scale. After solving the self-consistent full-bandwidth Eliashberg equations, we compute Angular Resolved Photo Emission Spectroscopy and Scanning Tunneling Spectroscopy/Microscopy spectra. We obtain a sequence of quasiparticle replica bands in both the normal and superconducting states that originate from frequency dependent features of the electron mass renormalization function. We show that these replica bands can be used to extract the relevant phonon energy scale from experiments. Focusing in particular on twisted bilayer graphene, we predict replica-band formation which, when observed, will shed light on the role of EPI in this archetypal flat-band system.

Are multi-quasiparticle interactions important in molecular ionization?

Photo-emission spectroscopy directly probes individual electronic states, ranging from single excitations to high-energy satellites, which simultaneously represent multiple quasiparticles (QPs) and encode information about electronic correlation. The first-principles description of the spectra requires an efficient and accurate treatment of all many-body effects. This is especially challenging for inner valence excitations where the single QP picture breaks down. Here, we provide the full valence spectra of small closed-shell molecules, exploring the independent and interacting quasiparticle regimes, computed with the fully correlated adaptive sampling configuration interaction method. We critically compare these results to calculations with the many-body perturbation theory, based on the GW and vertex corrected GWΓ approaches. The latter explicitly accounts for two-QP quantum interactions, which have often been neglected. We demonstrate that for molecular systems, the vertex correction universally improves the theoretical spectra, and it is crucial for the accurate prediction of QPs as well as capturing the rich satellite structures of high-energy excitations. GWΓ offers a unified description across all relevant energy scales. Our results suggest that the multi-QP regime corresponds to dynamical correlations, which can be described via perturbation theory.

Advanced First-Principle Modeling of Relativistic Ruddlesden—Popper Strontium Iridates

In this review, we provide a survey of the application of advanced first-principle methods on the theoretical modeling and understanding of novel electronic, optical, and magnetic properties of the spin-orbit coupled Ruddlesden–Popper series of iridates Srn+1IrnO3n+1 (n = 1, 2, and ∞). After a brief description of the basic aspects of the adopted methods (noncollinear local spin density approximation plus an on-site Coulomb interaction (LSDA+U), constrained random phase approximation (cRPA), GW, and Bethe–Salpeter equation (BSE)), we present and discuss select results. We show that a detailed phase diagrams of the metal–insulator transition and magnetic phase transition can be constructed by inspecting the evolution of electronic and magnetic properties as a function of Hubbard U, spin–orbit coupling (SOC) strength, and dimensionality n, which provide clear evidence for the crucial role played by SOC and U in establishing a relativistic (Dirac) Mott–Hubbard insulating state in Sr2IrO4 and Sr3Ir2O7. To characterize the ground-state phases, we quantify the most relevant energy scales fully ab initio—crystal field energy, Hubbard U, and SOC constant of three compounds—and discuss the quasiparticle band structures in detail by comparing GW and LSDA+U data. We examine the different magnetic ground states of structurally similar n = 1 and n = 2 compounds and clarify that the origin of the in-plane canted antiferromagnetic (AFM) state of Sr2IrO4 arises from competition between isotropic exchange and Dzyaloshinskii–Moriya (DM) interactions whereas the collinear AFM state of Sr3Ir2O7 is due to strong interlayer magnetic coupling. Finally, we report the dimensionality controlled metal–insulator transition across the series by computing their optical transitions and conductivity spectra at the GW+BSE level from the the quasi two-dimensional insulating n = 1 and 2 phases to the three-dimensional metallic n=∞ phase.

Heavy quarkonium at finite temperature and chemical potential

We generalize known results for heavy quarkonium in a thermal bath to the case of a finite baryonic density, and provide a number of formulas for the energy shift and decay width that hold at weak coupling for sufficiently large temperature and/or chemical potential. We find that a non-vanishing decay width requires a temperature larger than the typical binding energy, no matter how large the chemical potential is. This implies that at zero temperature the dissociation mechanism of heavy quarkonium is due entirely to screening, unlike in the finite temperature case. We use several effective theories in order to sort out the contributions of the relevant energy and momentum scales. In particular, we consider contributions of the so called quasi-static magnetic modes. The generalization to the case of a finite isospin/strangeness chemical potential is trivial. We discuss possible applications to the SIS and NICA conditions, and compare with available lattice results.

Testing an exotic magnet

Physics In quantum spin liquid (QSL), an exotic state of matter predicted to occur in certain materials, spins remain in a liquid-like state down to the lowest temperatures. A theoretical realization of a QSL is the Kitaev model, where spins reside on a two-dimensional hexagonal lattice. The layered material RuCl3 is thought to display the Kitaev model physics. Modic et al. studied magnetic anisotropy in RuCl3. They focused on the magnetotropic coefficient, which reflects the rigidity of a material to rotation in a magnetic field. In a certain temperature range, the coefficient scaled linearly with the magnetic field, indicating that the relevant energy scales were those set by temperature and magnetic field rather than by magnetic interactions intrinsic to the material. Nat. Phys. 10.1038/s41567-020-1028-0 (2020).

Efficient compression of the environment of an open quantum system

In order to simulate open quantum systems, many approaches (such as Hamiltonian-based solvers in dynamical mean-field theory) aim for a reproduction of a desired environment spectral density in terms of a discrete set of bath states, mimicking the open system as a larger closed problem. Existing strategies to find a compressed representation of the environment for this purpose can be numerically demanding, or lack the compactness and systematic improvability required for an accurate description of the system propagator. We propose a method in which bath orbitals are constructed explicitly by an algebraic construction based on the Schmidt-decomposition of response wave functions, efficiently and systematically compressing the description of the full environment. These resulting bath orbitals are designed to directly reproduce the system Green's function, not hybridization, which allows for consideration of the relevant system energy scales to optimally model. This results in an accurate and efficient truncation of the environment, with applications in a wide range of numerical simulations of open quantum systems.

Landau poles in condensed matter systems

The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $\phi^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $\phi^6$ potential, can significantly change the fate of the Landau pole in the $\phi^4$ theory. We obtain the coupled beta functions of a $\phi^4 + \phi^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $\phi^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $\phi^4$ theory, so graphene is free from Landau poles if the $\phi^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.