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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Universality of Shallow Global Quenches in Critical Spin Chains

Measuring universal data in the strongly correlated regime of quantum critical points remains a fundamental objective for quantum simulators. In foundational work, Calabrese and Cardy demonstrated how these data govern the dynamics of certain global quenches to 1+1-dimensional conformal field theories. While the quasiparticle picture they introduce has been widely successful in both theory and experiment, their seminal prediction that the critical exponents are simply encoded in the relaxation rates of local observables is challenging to investigate experimentally. In this Letter, we examine the critical quench dynamics of local observables from two types of readily accessible initial conditions: ground states and finite-temperature ensembles. Here, we identify universal scaling collapses and scaling functions, utilizing a combination of conformal perturbation theory and tensor network numerics. For the finite-temperature quenches, we determine a regime in which the conformal field theory results are recovered, thereby allowing universal quantum critical data to be extracted from realistic quenches.

Quantum many-body systems↗
DOE OSTI2022

Physical properties of the layered $\mathcal{f}$-electron van der Waals magnet Ce 2 Te 5

Here. we report a detailed study of the magnetic, transport, and thermodynamic properties of Ce 2 Te 5 single crystals, a layered $\mathcal{f}$-electron van der Waals magnet. Four consecutive transitions at ~5.2, 2.1, 0.9, and 0.4 K were observed in the ac-plane electrical resistivity $\rho(T)$, which were further confirmed in specific heat $C_\text{p}(T)$ measurements. Analysis of the magnetic susceptibility $\chi(T)$, the magnetic-field variation of $\rho(T)$, and the increase of the first transition temperature ($T_c$ ~ 5.2 K) with applied magnetic field indicates ferromagnetic order, while the decrease of the other transitions with field suggests different states with dominant antiferromagnetic interactions below $T_2$ ~ 2.1 K, $T_3$ ~ 0.9 K, and $T_4$ = 0.4 K. Critical behavior analysis around Tc that gives critical exponents $\beta$ = 0.31(2), $\gamma$ = 0.99(2), $\delta$ = 4.46(1), and $T_c$ = 5.32(1) K indicates that Ce 2 Te 5 shows a three-dimensional magnetic critical behavior. Moreover, the Hall resistivity ρxy indicates that Ce2Te5 is a multiband system with a relatively high electron mobility ~2900 cm 2 V –1 s –1 near $T_c$, providing further opportunities for future device applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Critical nematic correlations throughout the superconducting doping range in Bi 2–z Pb z Sr 2–y La y CuO 6+x

Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-T c superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi 2–z Pb z Sr 2–y La y CuO 6+x . The ratio of the phase correlation length ξ CDW to the orientation correlation length ξ orient points to unidirectional charge modulations. By computing new critical exponents at free surfaces including that of the pair connectivity correlation function, we show that these locally 1D charge modulations are actually a bulk effect resulting from classical 3D criticality of the random field Ising model throughout the entire superconducting doping range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Emergence of the isotropic Kitaev honeycomb lattice $α$–RuCl 3 and its magnetic properties

Here, we present a comprehensive investigation of the crystal and magnetic structures of the van der Waals antiferromagnet $α$–RuCl 3 using single crystal x-ray and neutron diffraction. The crystal structure at room temperature is a monoclinic (C2/m). However, with decreasing temperature, a remarkable first-order structural phase transition is observed, leading to the emergence of a rhombohedral ($R\bar3$) structure characterized by three-fold rotational symmetry forming an isotropic honeycomb lattice. On further cooling, a zigzag-type antiferromagnetic order develops below $T_{\textrm{N}} = 6\sim6.6$ K. The critical exponent of the magnetic order parameter was determined to be $\beta = 0.11(1)$, which is close to the two-dimensional Ising model. Additionally, the angular dependence of the magnetic critical field of the zigzag antiferromagnetic order for the polarized ferromagnetic phase reveals a six-fold rotational symmetry within the ab–plane. These findings reflect the symmetry associated with the Ising-like bond-dependent Kitaev spin interactions and underscore the universality of the Kitaev interaction-dominated antiferromagnetic system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates

Here, using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.

36 MATERIALS SCIENCE↗
NASA NTRS2008

Shear Thinning Near the Critical Point of Xenon

We measured shear thinning, a viscosity decrease ordinarily associated with complex liquids, near the critical point of xenon. The data span a wide range of reduced shear rate: 10(exp -3) < gamma-dot tau < 700, where gamma-dot tau is the shear rate scaled by the relaxation time tau of critical fluctuations. The measurements had a temperature resolution of 0.01 mK and were conducted in microgravity aboard the Space Shuttle Columbia to avoid the density stratification caused by Earth's gravity. The viscometer measured the drag on a delicate nickel screen as it oscillated in the xenon at amplitudes 3 mu,m < chi (sub 0) >430 mu, and frequencies 1 Hz < omega/2 pi < 5 Hz. To separate shear thinning from other nonlinearities, we computed the ratio of the viscous force on the screen at gamma-dot tau to the force at gamma-dot tau approximates 0: C(sub gamma) is identical with F(chi(sub 0), omega tau, gamma-dot tau )/F)(chi(sub 0, omega tau, 0). At low frequencies, (omega tau)(exp 2) < gamma-dot tau, C(sub gamma) depends only on gamma-dot tau, as predicted by dynamic critical scaling. At high frequencies, (omega tau)(exp 2) > gamma-dot tau, C(sub gamma) depends also on both x(sub 0) and omega. The data were compared with numerical calculations based on the Carreau-Yasuda relation for complex fluids: eta(gamma-dot)/eta(0)=[1+A(sub gamma)|gamma-dot tau|](exp - chi(sub eta)/3+chi(sub eta)), where chi(sub eta) =0.069 is the critical exponent for viscosity and mode-coupling theory predicts A(sub gamma) =0.121. For xenon we find A(sub gamma) =0.137 +/- 0.029, in agreement with the mode coupling value. Remarkably, the xenon data close to the critical temperature T(sub c) were independent of the cooling rate (both above and below T(sub c) and these data were symmetric about T(sub c) to within a temperature scale factor. The scale factors for the magnitude of the oscillator s response differed from those for the oscillator's phase; this suggests that the surface tension of the two-phase domains affected the drag on the screen below T(sub c).

Zimmerli, Gregory A.↗
DOE OSTI2023

Kibble–Zurek mechanism of Ising domains

The formation of topological defects after a symmetry-breaking phase transition is an overarching phenomenon that encodes the underlying dynamics. The Kibble-Zurek mechanism (KZM) describes these non-equilibrium dynamics of second-order phase transitions and predicts a power-law relationship between the cooling rates and the density of topological defects. It has been verified as a successful model in a wide variety of physical systems, including structure formation in the early Universe and condensed-matter materials. However, it is uncertain if the KZM mechanism is also valid for topologically trivial Ising domains, one of the most common and fundamental types of domain in condensed-matter systems. Here we show that the cooling rate dependence of Ising domain density follows the KZM power law in two different three-dimensional structural Ising domains: ferro-rotation domains in NiTiO 3 and polar domains in BiTeI. However, although the KZM slope of NiTiO 3 agrees with the prediction of the 3D Ising model, the KZM slope of BiTeI exceeds the theoretical limit, providing an example of steepening KZM slope with long-range dipolar interactions. Finally, our results demonstrate the validity of KZM for Ising domains and reveal an enhancement of the power-law exponent for transitions of non-topological quantities with long-range interactions. The Kibble-Zurek mechanism is shown to apply to structural Ising domains in three-dimensional materials. Long-range interactions modify the critical exponents away from theoretical predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Strain-tuning of transport gaps and semiconductor-to-conductor phase transition in twinned graphene

We show, through the use of the Landauer-Büttiker (LB) formalism and a tight-binding (TB) model, that the transport gap of twinned graphene can be tuned through the application of a uniaxial strain in the direction normal to the twin band. Remarkably, we find that the transport gap E gap bears a square-root dependence on the control parameter ϵ x – ϵ c , where ϵ x is the applied uniaxial strain and ϵ c ~ 19% is a critical strain. We interpret this dependence as evidence of criticality underlying a continuous phase transition, with ϵ x – ϵ c playing the role of control parameter and the transport gap E gap playing the role of order parameter. For ϵ x < ϵ c , the transport gap is non-zero and the material is semiconductor, whereas for ϵ x < ϵ c the transport gap closes to zero and the material becomes conductor, which evinces a semiconductor-to-conductor phase transition. The computed critical exponent of 1/2 places the transition in the meanfield universality class, which enables far-reaching analogies with other systems in the same class.

36 MATERIALS SCIENCE↗
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 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↗
NASA NTRS1990

On the formation and expansion of H II regions

The evolution of H II regions in spherical clouds with small, constant-density cores and power-law density distributions r exp -w outside the core is described analytically. It is found that there is a critical exponent above which the cloud becomes completely ionized. Its value in the formation phase depends on the initial conditions, but it has a well-defined value w(crit) = 3/2 during the expansion phase. For w less than w(crit), the radius of the H II region grows at a given rate, while neutral mass accumulates in the interphase between the ionization and shock fronts. For w = w(crit), the fronts move together without mass accumulation. Cases with w greater than w(crit) lead to the champagne phase: once the cloud is fully ionized, the expansion becomes supersonic. For self-gravitating disks without magnetic fields, the main features include a new 'variable-size' stage. The initial shape of the H II region has a critical point beyond which the disk becomes completely ionized.

Franco, Jose↗
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 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↗