Mean-field Theory Research Articles

Low-temperature magnetic refrigeration in Gd20Tb20Er20Al20M20 (M = Fe, Co) high-entropy metallic glasses

This paper focuses on the magnetocaloric effect (MCE) of Gd20Tb20Er20Al20M20 (M = Fe, Co) high-entropy metallic glasses (HE-MGs). XRD and TEM results indicate that both HE-MGs are amorphous. Magnetic studies show that both HE-MGs display spin-glass behavior, undergo a second-order phase transition from ferromagnetic to paramagnetic, and exhibit soft magnetic properties at the Curie temperature (TC). Notable large and broad table-like magnetic entropy change characteristics of Gd20Tb20Er20Al20Fe20 (Gd20Tb20Er20Al20Co20) appear near a TC of 92 (51) K. Hence, under 7 T magnetic field, |-∆SMmax|, ∆ TFWHM, and RCP are 7.83 (10.10) J·kg-1·K-1, 120.07 (71.88) K, and 1008.26 (805.70) J·kg-1, respectively. Furthermore, the modulation of the magnetic and magnetocaloric properties of the samples after substitution of Fe for Co was revealed by the intricate 3d-3d and 3d-4f exchange interactions within the system. The magnetic phase transition critical behaviors in both HE-MGs were analyzed using the scaling law to clarify the deviation of amorphous materials from the mean-field theory. Thus, this study not only highlights the potential of this material for low-temperature magnetic refrigeration applications, but also expands our understanding of its physical properties.

Interplay between disorder and electronic correlations in compositionally complex alloys

Owing to their exceptional mechanical, electronic, and phononic transport properties, compositionally complex alloys, including high-entropy alloys, represent an important class of materials. However, the interplay between chemical disorder and electronic correlations, and its influence on electronic structure-derived properties, remains largely unexplored. This is addressed for the archetypal CrMnFeCoNi alloy using resonant and valence band photoemission spectroscopy, electrical resistivity, and optical conductivity measurements, complemented by linear response calculations based on density functional theory. Utilizing dynamical mean-field theory, correlation signatures and damping in the spectra are identified, highlighting the significance of many-body effects, particularly in states distant from the Fermi edge. Electronic transport remains dominated by disorder and potentially short-range order, especially at low temperatures, while visible-spectrum optical conductivity and high-temperature transport are influenced by short quasiparticle lifetimes. These findings improve our understanding of element-specific electronic correlations in compositionally complex alloys and facilitate the development of advanced materials with tailored electronic properties.

Dynamical Correlations and Order in Magic-Angle Twisted Bilayer Graphene

The interplay of dynamical correlations and electronic ordering is pivotal in shaping phase diagrams of correlated quantum materials. In magic-angle twisted bilayer graphene, transport, thermodynamic, and spectroscopic experiments pinpoint a competition between distinct low-energy states with and without electronic order, as well as between localized and delocalized charge carriers. In this study, we utilize dynamical mean-field theory on the topological heavy fermion model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We contrast moment formation, Kondo screening, and ordering on a temperature basis and explain the nature of emergent correlated states based on three central phenomena: (i) the formation of local spin and valley isospin moments around 100 K, (ii) the ordering of the local isospin moments around 10 K preempting Kondo screening, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low-energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a “bad metal” above the ordering temperature, where scattering off the disordered local moments suppresses electronic coherence, and a “good metal” in the ordered states with coherence of quasiparticles facilitated by isospin order. This finding reveals coherence from order as the microscopic mechanism behind the Pomeranchuk effect observed experimentally by Rozen [] and by Saito []. Upon doping, there is a periodic charge reshuffling between localized and delocalized electronic orbitals leading to cascades of doping-induced Lifshitz transitions, local spectral weight redistributions, and periodic variations of the electronic compressibility ranging from nearly incompressible to negative. Our findings highlight the essential role of charge transfer, hybridization, and ordering in shaping the electronic excitations and thermodynamic properties in twisted bilayer graphene and provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments. Published by the American Physical Society 2024

A model for zwitterionic polymers and their capacitance applications.

Zwitterions have been shown experimentally to enhance the dielectric constant of ionic media, owing to their large molecular dipole. Many studies since explored the enhancement of ionic conductivity with zwitterion additives as well as bulk behavior of zwitterions. Here, we examine the capacitance behavior of zwitterions between charged parallel plates using a mean-field theory. Employing only chain connectivity of a cation and anion with neutral monomers in between with mean-field electrostatics, we show that our model captures the high-dielectric behavior of zwitterions. We also predict an optimum in the capacitance of zwitterionic media as a function of chain length. To address the issue of zwitterion screening near charged surfaces, we demonstrate that zwitterions simultaneously partially screen charged walls and act as a pure dielectric that propagates the electric field far from the surface. Moreover, we show that salt solutions with zwitterionic additives outperform the energy density of both salt-only and zwitterion-only capacitors. We find that salt-only capacitors perform better at low applied potential, whereas salt capacitors with zwitterionic additives perform better at high applied potential.

Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

In previous work [] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. While this earlier work focused on spatial dimensions d=1–4, here we extend the analysis to higher dimensions in order to make connections to high-dimensional sphere packings and the mean-field theory of glasses. We exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice in contrast to real-space hard spheres, whose densest configuration is conjectured to be disordered. In passing, we give a concise form for the position of the first Bragg peak. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as a function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d=2–8, which have only recently been made possible due to a highly parallelized algorithm. Published by the American Physical Society 2024

Kinetic ferromagnetism and topological magnons of the hole-doped Kitaev spin liquid

We study the effect of hole doping on the Kitaev spin liquid (KSL) and find that for ferromagnetic (FM) Kitaev exchange K the system is very susceptible to the formation of a FM spin polarization. Through density matrix renormalization group simulations on finite systems, we uncover that the introduction of a single hole, corresponding to ≈1% hole doping for the system size we consider, with a hopping strength of just t ~ 0.28K is enough to disrupt fractionalization and polarize the spins in the [001] direction due to an order-by-disorder mechanism. Taking into account a material relevant FM anisotropic exchange Γ drives the polarization towards the [111] direction via a transition into a topological FM state with chiral magnon excitations. We develop a parton mean-field theory incorporating fermionic holons and bosonic magnons, which accounts for the doping induced FM phases and topological magnon excitations. We discuss experimental implications for Kitaev candidate materials.

Nonequilibrium relaxation of soft responsive colloids.

Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching between states. Such a multi-stability is useful for the development of soft functional materials. Here, we introduce a mean-field dynamical density functional theory for a model of responsive colloids to study the nonequilibrium dynamics of a colloidal dispersion in time-dependent external fields, with a focus on the coupling of translational and conformational dynamics during their relaxation. Specifically, we consider soft Gaussian particles with a bimodal size distribution between two confining walls with time-dependent (switching-on and off) external gravitational and osmotic fields. We find a rich relaxation behavior of the systems in excellent agreement with particle-based Brownian dynamics computer simulations. In particular, we find time-asymmetric relaxations of integrated observables (wall pressures, mean size, and liquid center-of-mass) for activation/deactivation of external potentials, respectively, which are tunable by the ratio of translational and conformational diffusion time scales. Our work thus paves the way for studying the nonequilibrium relaxation dynamics of complex soft matter with multiple degrees of freedom and hierarchical relaxations.

Emergence of economic and social disparities through competitive gift-giving

Several tiers of social organization with varying economic and social disparities have been observed. However, a quantitative characterization of the types and the causal mechanisms for the transitions have hardly been explained. While anthropologists have emphasized that gift exchange, rather than market exchange, prevails in traditional societies and shapes social relations, few mathematical studies have explored its consequences for social organizations. In this study, we present a simple model of competitive gift-giving that describes how gifts bring goods to the recipient and honor to the donor, and simulate social change. Numerical simulations and an analysis of the corresponding mean-field theory demonstrate the transitions between the following four phases with different distribution shapes of wealth and social reputation: the band, without economic or social disparities; the tribe, with economic but without social disparities; the chiefdom, with both; and the kingdom, with economic disparity and weak social disparity except for an outlier, namely, the “monarch”. The emergence of strong disparities is characterized by power law distributions and is attributed to the “rich get richer” process. In contrast, the absence of such a process leads to exponential distributions due to random fluctuations. The phases depend on the parameters characterizing the frequency and scale of gift interactions. Our findings provide quantitative criteria for classifying social organizations based on economic and social disparities, consistent with both anthropological theory and empirical observations. Thus, we propose empirically measurable explanatory variables and characteristic indices for the evolution of social organizations. The constructive model, guided by social scientific theory, can provide the basic mechanistic explanation of social evolution and integrate theories of the social sciences.

Fermi Surface Nesting with Heavy Quasiparticles in the Locally Noncentrosymmetric Superconductor CeRh2As2

Abstract The locally noncentrosymmetric heavy fermion superconductor CeRh2As2 has attracted considerable interests due to its rich superconducting phases, accompanied by possible quadrupole density wave and pronounced antiferromagnetic excitations. To understand the underlying physics, here we report measurements from high-resolution angle-resolved photoemission. Our results reveal fine splittings of the conduction bands related to the locally noncentrosymmetric structure, as well as a quasi-two-dimensional Fermi surface (FS) with strong 4f contributions. The FS shows signs of nesting with an in-plane vector q 1 = (π/a, π/a), which is facilitated by the heavy bands near X ¯ arising from the characteristic conduction-f hybridization. The FS nesting provides a natural explanation for the observed antiferromagnetic spin fluctuations at (π/a, π/a), which might be the driving force for its unconventional superconductivity. Our experimental results can be reasonably explained by density functional theory plus dynamical mean field theory calculations, which can capture the strong correlation effects. Our study not only provides spectroscopic signature of the key factors underlying the field-induced superconducting transition, but also uncovers the critical role of FS nesting and lattice Kondo effect in the underlying magnetic fluctuations.

Quenched Pair Breaking by Interlayer Correlations as a Key to Superconductivity in La_{3}Ni_{2}O_{7}.

The recent discovery of superconductivity in La_{3}Ni_{2}O_{7} with T_{c}≃80 K under high pressure opens up a new route to high-T_{c} superconductivity. This material realizes a bilayer square lattice model featuring a strong interlayer hybridization unlike many unconventional superconductors. A key question in this regard concerns how electronic correlations driven by the interlayer hybridization affect the low-energy electronic structure and the concomitant superconductivity. Here, we demonstrate using a cluster dynamical mean-field theory that the interlayer electronic correlations (IECs) induce a Lifshitz transition resulting in a change of Fermi surface topology. By solving an appropriate gap equation, we further show that the leading pairing instability, s± wave, is enhanced by the IECs. The underlying mechanism is the quenching of a strong ferromagnetic channel, resulting from the Lifshitz transition driven by the IECs. Based on this picture, we provide a possible reason of why superconductivity emerges only under high pressure.

Anisotropy-driven magnetic phase transitions in SU(4)-symmetric Fermi gas in three-dimensional optical lattices

Abstract We study SU(4)-symmetric ultracold fermionic mixture in the cubic optical lattice with the variable tunneling amplitude along one particular crystallographic axis in the crossover region from the two- to three-dimensional spatial geometry. To theoretically analyze emerging magnetic phases and physical observables, we describe the system in the framework of the Fermi-Hubbard model and apply dynamical mean-field theory. We show that in two limiting cases of anisotropy there are two phases with different antiferromagnetic orderings in the zero temperature limit and determine a region of their coexistence. We also study the stability regions of different magnetically-ordered states and density profiles of the gas in the harmonic optical trap.

Weyl nodes in Ce3Bi4Pd3 revealed by dynamical mean-field theory

Experimental studies have found unusual transport properties in Ce3Bi4Pd3 which are potentially a consequence of the interplay between band-structure topology and electronic correlations. Based on these measurements, the existence of Weyl points in strongly renormalized, flat quasiparticle bands has been postulated. However, so far there has been neither a direct spectroscopic observation of these nor a calculation from first principles that would confirm their existence close to the Fermi energy. Here we present density functional theory and dynamical mean-field theory calculations and study the low-energy excitations and their topological properties. We find that the Kondo effect promotes two out of the six angular momentum J=5/2 states, with the other four pushed to higher energies. Further, we find Weyl nodes close to the Fermi energy as previously suggested for explaining the observed giant spontaneous Hall effect in Ce3Bi4Pd3 as well as nodal lines. Published by the American Physical Society 2024

Antiferromagnetic and spin spiral correlations in the doped two-dimensional Hubbard model: Gauge symmetry, Ward identities, and dynamical mean-field theory analysis

Antiferromagnetic and spin spiral correlations in the doped two-dimensional Hubbard model: Gauge symmetry, Ward identities, and dynamical mean-field theory analysis

Multiscale fatigue life prediction model for CFRP laminates considering the mechanical degradation of its constituents and the local stress concentration of the matrix

In the present research, a novel approach for predicting the fatigue life of composites is proposed using a multiscale fatigue model. This model considers two critical physical phenomena that occur in CFRP laminates under tension-tension cyclic loading – the degradation of the physical properties of CFRP constituents and the localized stress concentrations within the matrix. To achieve this, Mori-Tanaka’s mean field theory, a well-known micromechanics model, is employed to consider the deterioration of material properties in various phases, which is dependent on the applied stress level. Localized stress concentration phenomena within the matrix of a composite material are common when CFRP laminate is subjected to cyclic loading. The localized stress concentration on a matrix with different numbers of fibers and orientations using representative volume elements (RVE) is investigated. Two other scales of failure criteria are defined to evaluate its constituent at the material level and ply level at the macroscale. A comparison with fatigue experiment data of AS4/3501-6 composite shows good reliability of the proposed multiscale fatigue model.

Decomposing Imaginary-Time Feynman Diagrams Using Separable Basis Functions: Anderson Impurity Model Strong-Coupling Expansion

We present a deterministic algorithm for the efficient evaluation of imaginary-time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary-time Green’s functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary-time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong-coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an Mth-order diagram at inverse temperature β and spectral width ωmax from O((βωmax)2M−1) for a direct quadrature to O(M(log(βωmax))M+1), with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multiband impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca2RuO4, demonstrating the promise of the method for modeling realistic strongly correlated multiband materials. For both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust blackbox evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams. Published by the American Physical Society 2024

Density-matrix mean-field theory

Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean-field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.

Mean-field theory of first-order quantum superconductor-insulator transition

Mean-field theory of first-order quantum superconductor-insulator transition

Fluctuation-dominated quantum oscillations in excitonic insulators

The realization of excitonic insulators in transition metal dichalcogenide systems has opened the door to explorations of the exotic properties that such a state exhibits. We study theoretically the potential for excitonic insulators to show an anomalous form of quantum oscillations: the de Haas–van Alphen effect in an insulating system. We focus on the role of the interactions that generate the energy gap and show that it is crucial to consider quantum fluctuations that go beyond the mean-field treatment. Remarkably, quantum fluctuations can be dominant and lead to quantum oscillations that are significantly larger than those predicted using mean-field theory. Indeed, in experimentally accessible parameter regimes these fluctuation-generated quantum oscillations can even be larger than what would be found for the corresponding gapless system. Published by the American Physical Society 2024

Self-organized time crystal in driven-dissipative quantum system

Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time-translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in various driven-dissipative quantum platforms. The current understanding of CTCs is mainly based on mean-field theories, which fail to address the problem of whether the continuous time-translation symmetry can be broken in noisy, spatially extended systems absent in all-to-all couplings. Here, we propose a CTC realized in a quantum contact model through self-organized bistability. The CTCs stem from the interplay between collective dissipation induced by the first-order absorbing phase transitions and slow constant driving provided by an incoherent pump. The stability of such oscillatory phases in finite dimensions under the action of intrinsic quantum fluctuations is scrutinized by the functional renormalization group method and numerical simulations. Occurring at the edge of many-body synchronization, the CTC phase exhibits an inherent period and amplitude with a coherence time linearly diverging with system size, thus also constituting a boundary time crystal. Our results serve as a solid route towards self-protected CTCs in strongly interacting open systems. Published by the American Physical Society 2024

Spurious self-feedback of mean-field predictions inflates infection curves.

The susceptible-infected-recovered (SIR) model and its variants form the foundation of our understanding of the spread of diseases. Here, each agent can be in one of three states (susceptible, infected, or recovered), and transitions between these states follow a stochastic process. The probability of an agent becoming infected depends on the number of its infected neighbors, hence all agents are correlated. The simplest mean-field theory of the same stochastic process, however, assumes that the agents are statistically independent. This leads to a self-feedback effect in the approximation: when an agent infects its neighbors, this infection may subsequently travel back to the original agent at a later time, leading to a self-infection of the agent which is not present in the underlying stochastic process. We here compute the first-order correction to the mean-field assumption from a systematic expansion, called dynamical TAP theory. This correction, which takes fluctuations up to second order in the interaction strength into account, cancels the self-feedback effect, leading to smaller infection rates. The correction significantly improves predictions compared to mean-field theory. In particular, it captures how sparsity dampens the spread of the disease: this indicates that reducing the number of contacts is more effective than predicted by mean-field models. We further apply the expansion to variants of the SIR model, such as the SIRS model, in which the immunity of an individual to the disease wanes over time. We find that up to the second order, the correction terms in the SIR and SIRS model are equivalent, meaning that fluctuations partially cancel the self-feedback effect even when self-feedback is in principle allowed.