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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Critical fluctuations in liquid–liquid extraction organic phases controlled by extractant and diluent molecular structure

Extractant aggregation in liquid–liquid extraction organic phases impacts extraction energetics and is related to the deleterious efficiency-limiting liquid–liquid phase transition known as third phase formation. Using small angle X-ray scattering, we find that structural heterogeneities across a wide range of compositions in binary mixtures of malonamide extractants and alkane diluents are well described by Ornstein–Zernike scattering. This suggests that structure in these simplified organic phases originates from the critical point associated with the liquid–liquid phase transition. To confirm this, we measure the temperature dependence of the organic phase structure, finding critical exponents consistent with the 3D Ising model. Molecular dynamics simulations were also consistent with this mechanism for extractant aggregation. Due to the absence of water or any other polar solutes required to form reverse-micellar-like nanostructures, these fluctuations are inherent to the binary extractant/diluent mixture. Further, we also show how the molecular structure of the extractant and diluent modulate these critical concentration fluctuations by shifting the critical temperature: critical fluctuations are suppressed by increasing extractant alkyl tail lengths or decreasing diluent alkyl chain lengths. This is consistent with how extractant and diluent molecular structure are known to impact metal and acid loading capacity in many-component LLE organic phases, suggesting phase behavior of practical systems may be effectively studied in simplified organic phases. Overall, the explicit connection between molecular structure, aggregation and phase behavior demonstrated here will enable the design of more efficient separations processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Scaling behavior of the quantum phase transition from a quantum-anomalous-Hall insulator to an axion insulator

The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker–Coddington network model. We extract a critical exponent κ ~ 0.38 ± 0.02 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker–Coddington model at ν ~ 2.6, rather than the generally-accepted value of 2.33.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Fixed points in three dimensions described by conformal field theories with \ensuremath{M N}_{m,n} = O(m)^n\rtimes S_n M N m , n = O ( m ) n ⋊ S n global symmetry have extensive applications in critical phenomena. Associated experimental data for m=n=2 m = n = 2 suggest the existence of two non-trivial fixed points, while the \varepsilon ε expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters m m and n n , with critical exponents in good agreement with experimental determinations in the m=n=2 m = n = 2 case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters m m and n n . We find that one family of kinks approaches a perturbative limit as m m increases, and using large spin perturbation theory we construct a large m m expansion that fits well with the numerical data. This new expansion, akin to the large N N expansion of critical O(N) O ( N ) models, is compatible with the fixed point found in the \varepsilon ε expansion. For the other family of kinks, we find that it persists only for n=2 n = 2 , where for large m m it approaches a non-perturbative limit with \Delta_\phi\approx 0.75 Δ ϕ ≈ 0.75 . We investigate the spectrum in the case \ensuremath{M N}_{100,2} M N 100 , 2 and find consistency with expectations from the lightcone bootstrap.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Quantum Noise Spectroscopy of Dynamical Critical Phenomena

The transition between distinct phases of matter is characterized by the nature of fluctuations near the critical point. We demonstrate that noise spectroscopy can not only diagnose the presence of a phase transition, but can also determine fundamental properties of its criticality. In particular, by analyzing a scaling collapse of the decoherence profile, one can directly extract the critical exponents of the transition and identify its universality class. Our approach naturally captures the presence of conservation laws and distinguishes between classical and quantum phase transitions. In the context of quantum magnetism, our proposal complements existing techniques and provides a novel toolset optimized for interrogating two-dimensional magnetic materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Pressure-tuned quantum criticality in the large-D antiferromagnet DTN

Strongly correlated spin systems can be driven to quantum critical points via various routes. In particular, gapped quantum antiferromagnets can undergo phase transitions into a magnetically ordered state with applied pressure or magnetic field, acting as tuning parameters. These transitions are characterized by z = 1 or z = 2 dynamical critical exponents, determined by the linear and quadratic low-energy dispersion of spin excitations, respectively. Employing high-frequency susceptibility and ultrasound techniques, we demonstrate that the tetragonal easy-plane quantum antiferromagnet NiCl 2 · 4SC(NH 2 ) 2 (aka DTN) undergoes a spin-gap closure transition at about 4.2 kbar, resulting in a pressure-induced magnetic ordering. The studies are complemented by high-pressure-electron spin-resonance measurements confirming the proposed scenario. Powder neutron diffraction measurements revealed that no lattice distortion occurs at this pressure and the high spin symmetry is preserved, establishing DTN as a perfect platform to investigate z = 1 quantum critical phenomena. The experimental observations are supported by DMRG calculations, allowing us to quantitatively describe the pressure-driven evolution of critical fields and spin-Hamiltonian parameters in DTN.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantum criticality using a superconducting quantum processor

Quantum criticality emerges from the collective behavior of many interacting quantum particles, often at the transition between different phases of matter. It is one of the cornerstones of condensed matter physics, which we access on noisy intermediate-scale (NISQ) quantum devices by leveraging a dynamically driven phenomenon. Here we probe the critical properties of the one-dimensional quantum Ising model on a programmable superconducting quantum chip via a Kibble-Zurek process, obtain scaling laws, and estimate critical exponents despite inherent sources of errors on the hardware. In addition, we investigate how the improvement of NISQ computers (more qubits, less noise) will consolidate the computation of those universal physical properties. A one-parameter noise model captures the effect of imperfections and reproduces the experimental data. Its systematic study reveals that the noise, analogously to temperature, induces a new length scale in the system. We introduce and successfully verify modified scaling laws, directly accounting for the noise without any prior knowledge. It makes data analyses for extracting physical properties transparent to noise. By understanding how imperfect quantum hardware modifies the genuine properties of quantum states of matter, we enhance the power of NISQ processors considerably for addressing quantum criticality and potentially other phenomena and algorithms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Nonequilibrium universality of the nonreciprocally coupled 𝑂⁡(𝑛 1 ) × 𝑂⁡(𝑛 2 ) model

Nonequilibrium dynamics play an important role in all contexts of physics, both classical and quantum as well as living and nonliving, so it is crucial to develop a foundational understanding of nonequilibrium phase transitions. In this work we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular we study how nonreciprocal coupling between two 𝑂⁡(𝑛𝑖) order parameters (with 𝑖 = 1,2) affects the universality at a multicritical point, extending the analysis of J. T. Young et al. [Phys. Rev. X 10, 011039 (2020)], which considered the case 𝑛 1 = 𝑛 2 = 1, i.e., a ℤ 2 × ℤ 2 model. We show that nonequilibrium fixed points (NEFPs) emerge for a broad range of 𝑛 1 ,𝑛 2 and exhibit intrinsically nonequilibrium critical phenomena, namely a violation of fluctuation-dissipation relations at all scales and underdamped oscillations near criticality in contrast to the overdamped relaxational dynamics of the corresponding equilibrium models. Furthermore, the NEFPs exhibit an emergent discrete scale invariance in certain physically relevant regimes of 𝑛 1 ,𝑛 2 , but not others, depending on whether the critical exponent 𝜈 is real or complex. The boundary between these two regions is described by an exceptional point in the renormalization group (RG) flow, leading to distinctive features in correlation functions and the phase diagram. Another contrast with the previous work is the number and stability of the NEFPs as well as the underlying topology of the RG flow. Lastly, we investigate an extreme form of nonreciprocity where one order parameter is independent of the other order parameter but not vice versa. Unlike the ℤ 2 × ℤ 2 model, which becomes nonperturbative in this case, we identify a distinct nonequilibrium universality class whose dependent field similarly violates fluctuation-dissipation relations but does not exhibit discrete scale invariance or underdamped oscillations near criticality.

Critical phenomena↗
DOE OSTI2022

Finite-Size Scaling on a Digital Quantum Simulator Using Quantum Restricted Boltzmann Machine

The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occurring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g., in the Quantum Rabi Model (QRM). Since these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space. This approach has previously been used to calculate the critical parameters for stability and symmetry breaking of electronic structure configurations of atomic and molecular systems. We calculate the critical point for the quantum phase transition of the QRM using this approach. We also provide a protocol to implement this method on a digital quantum simulator using the Quantum Restricted Boltzmann Machine algorithm. Our work opens up a new direction in the study of quantum phase transitions on quantum devices.

Khalid, Bilal↗
DOE OSTI2022

Three-state majority-vote model on small-world networks

Abstract In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1- q , and a different opinion with chance q , where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p , we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise $$q_c$$ q c , as well as the standard critical exponents $$\beta /\nu$$ β / ν , $$\gamma /\nu$$ γ / ν , and $$1/\nu$$ 1 / ν for several values of the rewiring probability p . We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

Superuniversality from disorder at two-dimensional topological phase transitions

We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (“anyons”) identified with “electric charge” excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Furthermore, using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is “superuniversal” across a wide range of such condensation transitions and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Hidden sector monopole dark matter with matter domination

The thermal freeze-out mechanism for relic dark matter heavier than O (10 – 100 TeV) requires cross-sections that violate perturbative unitarity. Yet the existence of dark matter heavier than these scales is certainly plausible from a particle physics perspective, pointing to the need for a non-thermal cosmological history for such theories. Topological dark matter is a well-motivated scenario of this kind. Here the hidden-sector dark matter can be produced in abundance through the Kibble-Zurek mechanism describing the non-equilibrium dynamics of defects produced in a second order phase transition. We revisit the original topological dark matter scenario, focusing on hidden-sector magnetic monopoles, and consider more general cosmological histories. We find that a monopole mass of order (1–10 5 ) PeV is generic for the thermal histories considered here, if monopoles are to entirely reproduce the current abundance of dark matter. In particular, in a scenario involving an early era of matter domination, the monopole number density is always less than or equal to that in a pure radiation dominated equivalent provided a certain condition on critical exponents is satisfied. This results in a larger monopole mass needed to account for a fixed relic abundance in such cosmologies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Hidden first-order phase transitions and large magnetocaloric effects in GdNi 1-x Co x

We report a large magnetocaloric effect tunable between 70 and 115 K in a series of rare earth intermetallic compounds GdNi 1-x Co x with x varying from 0 to 0.15 that manifest rather unconventional second-order phase transitions with concurrent changes in both magnetic and crystallographic sublattices. While the Curie temperature, TC, linearly increases with x(Co), the maximum isothermal entropy change induced by magnetic field varying between 0 and 50 kOe slightly decreases from 14 J/kg K at 71 K when x(Co) = 0 to10 J/kg K at 115 K when x(Co) = 0.15. Additionally, the temperature-averaged entropy change figures of merit calculated at temperature spans of 10 K for all examined compositions are comparable to those of the best known magnetocaloric materials that exhibit second-order phase transitions, including elemental Gd and La(Fe,Co,Si) 13 alloys. Through a detailed analysis of the magnetic field-induced entropy changes along with assessment of critical exponents we explore the role magneto-elastic coupling plays in controlling magnetocaloric properties of GdNi 1-x Co x compounds. We also formulate a model based on the mean field theory approximation to describe both magnetic and magnetocaloric properties of the title materials in qualitative agreement with experimental results.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Metamagnetism and kinetic arrest in a long-range ferromagnetically ordered multicaloric double perovskite Y 2 CoMnO 6

A systematic magnetic study of the double perovskite oxide Y 2 CoMnO 6 (YCMO) has been performed. A monoclinic P21/n phase of YCMO was synthesized using a sol-gel method. Neutron diffraction (ND) measurements evidence the onset of long-range ferromagnetic (FM) ordering at TC ~ 76 K, which persists down to 5 K. The presence of 25% antisite disorder, estimated from the ND data, leads to the appearance of short-range antiferromagnetic (AFM) interactions. The existence of thermal hysteresis due to competing interactions between FM and AFM phases is observed in the M vs. T measurements. The pinning of magnetic domain walls at the Co/Mn antiphase boundaries results in a metamagnetic-like behavior. The field dependence of thermomagnetic irreversibility and the nature of virgin curves indicate the occurrence of a kinetic arrest phenomenon, which is further verified via cooling and heating of the system in an unequal fields (CHUF) protocol. In full agreement with the ND data, a detailed analysis of critical exponents near the paramagnetic (PM)-FM phase transition also establishes YCMO as a long-range interacting mean-field system. A close examination of the temperature- and field-dependent magnetic entropy change yields an in-depth understanding of coexisting magnetically ordered and disordered phases in YCMO, leading to a comprehensive magnetic phase diagram of this multifunctional double perovskite system.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Extracted Water Induces Concentration Fluctuations in Model Ternary Liquid–Liquid Extraction System

Organic phase aggregation and phase splitting are two important (and connected) phenomena in liquid–liquid extraction of metal ions. Previously, we demonstrated how structure in binary mixtures of extractant and diluent originates from concentration fluctuations associated with the so-called “third-phase formation” liquid–liquid phase instability. For more complex systems, we sought to understand how extracted aqueous components affect these concentration fluctuations. Here, in this study, we use small-angle X-ray scattering and molecular dynamics simulations to investigate organic phase structural changes upon contact with water in a model ternary system of water/alkane/extractant. Critical exponents were determined from scattering with temperature variation and were consistent with mean field values. Then, by controlling the water content in the organic phase through direct dissolution of fixed quantities at constant temperature, we relate the observed increase in the fluctuation length scale to changes to the spinodal temperature of the third-phase formation phase boundary. We find a roughly linear relationship between water concentration and the spinodal temperature and a similar slope in that relationship for different linear alkane diluents. This suggests that the mechanism by which water extraction impacts the organic phase structure is to enhance concentration fluctuations through the introduction of additional polar extractant-water complexes, which increases the spinodal temperature and thereby decreases the reduced temperature, i.e., the distance to the instability. This explanation for how solutes induce aggregation in liquid–liquid extraction organic phases may extend to more complex systems, explaining the large increases in correlation lengths reported under high acid and metal loading.

Bonnett, Brittany L. [Argonne National Laboratory ↗
DOE OSTI2022

Evidence for pressure induced unconventional quantum criticality in the coupled spin ladder antiferromagnet C 9 H 18 N 2 CuBr 4

Quantum phase transitions in quantum matter occur at zero temperature between distinct ground states by tuning a nonthermal control parameter. Often, they can be accurately described within the Landau theory of phase transitions, similarly to conventional thermal phase transitions. However, this picture can break down under certain circumstances. Here, we present a comprehensive study of the effect of hydrostatic pressure on the magnetic structure and spin dynamics of the spin-1/2 ladder compound C 9 H 18 N 2 CuBr 4 . Single-crystal heat capacity and neutron diffraction measurements reveal that the Néel-ordered phase breaks down beyond a critical pressure of Pc~1.0 GPa through a continuous quantum phase transition. Estimates of the critical exponents suggest that this transition may fall outside the traditional Landau paradigm. The inelastic neutron scattering spectra at 1.3 GPa are characterized by two well-separated gapped modes, including one continuum-like and another resolution-limited excitation in distinct scattering channels, which further indicates an exotic quantum-disordered phase above Pc.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

3D Heisenberg universality in the van der Waals antiferromagnet NiPS 3

Van der Waals (vdW) magnetic materials are comprised of layers of atomically thin sheets, making them ideal platforms for studying magnetism at the two-dimensional (2D) limit. These materials are at the center of a host of novel types of experiments, however, there are notably few pathways to directly probe their magnetic structure. We confirm the magnetic order within a single crystal of NiPS 3 and show it can be accessed with resonant elastic X-ray diffraction along the edge of the vdW planes in a carefully grown crystal by detecting structurally forbidden resonant magnetic X-ray scattering. We find the magnetic order parameter has a critical exponent of β ~ 0.36, indicating that the magnetism of these vdW crystals is more adequately characterized by the three-dimensional (3D) Heisenberg universality class. We verify these findings with first-principles density functional theory, Monte-Carlo simulations, and density matrix renormalization group calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Percolative phase transition in few-layered MoSe 2 field-effect transistors using Co and Cr contacts

The metal-to-insulator phase transition (MIT) in two-dimensional (2D) materials under the influence of a gating electric field has revealed interesting electronic behavior and the need for a deeper fundamental understanding of electron transport processes, while attracting much interest in the development of next-generation electronic and optoelectronic devices. Although the mechanism of the MIT in 2D semiconductors is a topic under debate in condensed matter physics, our work demonstrates the tunable percolative phase transition in few-layered MoSe 2 field-effect transistors (FETs) using different metallic contact materials. Here, we attempted to understand the MIT through temperature-dependent electronic transport measurements by tuning the carrier density in a MoSe 2 channel under the influence of an applied gate voltage. In particular, we have examined this phenomenon using the conventional chromium (Cr) and ferromagnetic cobalt (Co) as two metal contacts. For both Cr and Co, our devices demonstrated n-type behavior with a room-temperature field-effect mobility of 16 cm 2 V −1 s −1 for the device with Cr-contacts and 92 cm 2 V −1 s −1 for the device with Co-contacts, respectively. Further, with low temperature measurements at 50 K, the mobilities increased significantly to 65 cm 2 V −1 s −1 for the device with Cr and 394 cm 2 V −1 s −1 for the device with Co-contacts. By fitting our experimental data to the percolative phase transition theory, the temperature-dependent conductivity data show a transition from an insulating-to-metallic behavior at a bias of ∼28 V for Cr-contacts and ∼20 V for Co-contacts. This cross-over of the conductivity can be attributed to an increase in carrier density as a function of the gate bias in temperature-dependent transfer characteristics. By extracting the critical exponents, we find that the transport behavior in the device with Co-contacts aligns closely with the 2D percolation theory. In contrast, the devices with Cr-contacts deviate significantly from the 2D limit at low temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Neutron diffraction study of magnetism in van der Waals layered MnBi 2n Te 3n+1

Two-dimensional van der Waals MnBi 2 n Te 3 n +1 ( n = 1, 2, 3, 4) compounds have been recently found to be intrinsic magnetic topological insulators rendering quantum anomalous Hall effect and diverse topological states. Here, we summarize and compare the crystal and magnetic structures of this family, and discuss the effects of chemical composition on their magnetism. We found that a considerable fraction of Bi occupies at the Mn sites in MnBi 2 n Te 3 n +1 ( n = 1, 2, 3, 4) while there is no detectable Mn at the non-magnetic atomic sites within the resolution of neutron diffraction experiments. The occupancy of Mn monotonically decreases with the increase of n . The polarized neutron diffraction on the representative MnBi 4 Te 7 reveals that its magnetization density is exclusively accumulated at the Mn site, in good agreement with the results from the unpolarized neutron diffraction. The defects of Bi at the Mn site naturally explain the continuously reduced saturated magnetic moments from n = 1 to n = 4. The experimentally estimated critical exponents of all the compounds generally suggest a three-dimensional character of magnetism. Our work provides material-specified structural parameters that may be useful for band structure calculations to understand the observed topological surface states and for designing quantum magnetic materials through chemical doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗