Scaling Collapse Research Articles

Fidelity susceptibility probes of dynamical quantum criticality

Fidelity susceptibility is a quantum information-based approach that has been an effective tool for detecting and characterizing quantum phase transitions in an equilibrium setting. Motivated by the usefulness of the static counterpart, we propose that it can serve as a versatile tool to identify dynamical quantum phase transitions. Further, we develop linear-scale simulation methods for dynamical fidelity susceptibility calculations, which are based on the Chebyshev polynomial-expansion approach. We study the Aubry–André model as a benchmark for the validation of the computational technique. Numerical simulations show nonanalytic behaviors of the fidelity susceptibility in the time domain, signaling the existence of dynamical quantum phase transitions triggered by the incommensurate potential modulation of quantum quench systems. In addition, we find an excellent scaling collapse of the data onto a single curve in the limiting quench processes, which leads to a single-parameter scaling in the fidelity susceptibility. The feasibility of experimental measurement of the fidelity susceptibility opens up a new avenue toward an understanding of the nonequilibrium transport of quantum systems.

Vortex-glass transition and vortex pinning behavior in three-dimensional NbTiN epitaxial films

In the present paper, the vortex dynamics in two NbTiN epitaxial films have been explored via analyzing the current–voltage (I–V) curves measured at different temperatures and fields. The thicknesses of the two films are ∼50 and ∼100 nm, respectively, and they are three-dimensional (3D) with respect to superconductivity. The films transform from normal state to superconducting state with decreasing temperature at zero field, and the values of superconducting transition temperature Tc are 8.73 and 12.03 K for the ∼50- and ∼100-nm-thick films, respectively. When a magnetic field with magnitude 0.5T≲μ0H≲7 T and perpendicular to the film plane is applied, the isothermal I–V data show a 3D vortex-glass (VG) scaling collapse at each field, suggesting that a 3D vortex-liquid phase to VG phase transition occurs in the NbTiN films. By analyzing the critical current density, we found that core pinning is the main pinning mechanism in the films. In addition, it is found that the normal point-like pinning dominates the pinning behavior at low field regime. While in the high field regime, besides the normal point-like pinning, other pinning mechanisms, such as Δκ pinning, also exist in the films. Our results not only provide strong experimental support for the occurrence of VG phase transition in conventional superconductors, but also provide fundamental information for the application of NbTiN films.

Link between T-Linear Resistivity and Quantum Criticality in Ambipolar Black Phosphorus.

The interplay between strong Coulomb interactions and kinetic energy leads to intricate many-body competing ground states owing to quantum fluctuations in 2D electron and hole gases. However, the simultaneous observation of quantum critical phenomena in both electron and hole regimes remains elusive. Here, we utilize anisotropic black phosphorus (BP) to show density-driven metal-insulator transition with a critical conductance ∼e2/h which highlights the significant role of quantum fluctuations in both hole and electron regimes. We observe a T-linear resistivity from the deep metallic phase to the metal-insulator boundary at moderate temperatures, while it turns to Fermi liquid behavior in the deep metallic phase at low temperatures in both regimes. An analysis of the resistivity suggests that disorder-dominated transport leads to T-linear behavior in the hole regime, while in the electron regime, the T-linear resistivity results from strong Coulomb interactions, suggestive of strange-metal behavior. Successful scaling collapse of the resistivity in the T-linear region demonstrates the link between quantum criticality and the T-linear resistivity in both regimes. Our study provides compelling evidence that ambipolar BP could serve as an exciting testbed for investigating exotic states and quantum critical phenomena in hole and electron regimes of 2D semiconductors.

Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity.

We investigate the impact of nonreciprocity on universality and critical phenomena in open quantum interacting many-body systems. Nonreciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse, irrespective of the reciprocity. We find that the LSE only becomes relevant when a healing length scale ξ_{heal} at the system's edge (which is different from the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of nonreciprocal models in the vicinity of a critical point. The driven-dissipative quantum criticality we observe has no classical analog and stems from the existence of multiple dark states.

Evidence of second-order transition and critical scaling for the dynamical ordering transition in current-driven vortices

Dynamical ordering from a disordered plastic flow to an anisotropically ordered smectic flow induced by a dc force has been studied in various many-particle systems, including vortices in type-II superconductors. However, it remains unclear whether the dynamical ordering is a true phase transition because of lack of suitable experimental methods. Here, we study the response of vortex flow to the transverse force using a cross-shaped amorphous Mox\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{x}$$\\end{document}Ge1-x\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{1-x}$$\\end{document} film. From transverse current-voltage (force-velocity) characteristics under various longitudinal currents, we find a change of the transverse response in low voltage (velocity) regions from a nonlinear to linear behavior at a well-defined longitudinal current that marks the dynamical ordering transition. We also find the scaling collapse of the transverse current-voltage curves to a universal scaling function, providing evidence of the second-order transition for the dynamical ordering transition.

Honeycomb oxide heterostructure as a candidate host for a Kitaev quantum spin liquid

Kitaev quantum spin liquid, massively quantum entangled states, is so scarce in nature that searching for new candidate systems remains a great challenge. Honeycomb heterostructure could be a promising route to realize and utilize such an exotic quantum phase by providing additional controllability of Hamiltonian and device compatibility, respectively. Here, we provide epitaxial honeycomb oxide thin film Na3Co2SbO6, a candidate of Kitaev quantum spin liquid proposed recently. We found a spin glass and antiferromagnetic ground states depending on Na stoichiometry, signifying not only the importance of Na vacancy control but also strong frustration in Na3Co2SbO6. Despite its classical ground state, the field-dependent magnetic susceptibility shows remarkable scaling collapse with a single critical exponent, which can be interpreted as evidence of quantum criticality. Its electronic ground state and derived spin Hamiltonian from spectroscopies are consistent with the predicted Kitaev model. Our work provides a unique route to the realization and utilization of Kitaev quantum spin liquid.

Dynamical Scaling as a Signature of Multiple Phase Competition in Yb_{2}Ti_{2}O_{7}.

Yb_{2}Ti_{2}O_{7} is a celebrated example of a pyrochlore magnet with highly frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of Yb_{2}Ti_{2}O_{7}. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple-phase competition, and confirm that a scaling collapse is also seen in semiclassical simulations of a microscopic model of Yb_{2}Ti_{2}O_{7}. These results suggest that dynamical scaling may be general to systems with competing ground states.

Universal scaling of specific heat in the S=12 quantum kagome antiferromagnet herbertsmithite

Despite tremendous investigations, a quantum spin liquid (QSL) state realized in a spin-1/2 kagome Heisenberg antiferromagnet remains largely elusive. In herbertsmithite $\mathrm{Zn}{\mathrm{Cu}}_{3}{(\mathrm{O}\mathrm{H})}_{6}{\mathrm{Cl}}_{2}$, a quantum spin liquid candidate on the perfect kagome lattice, precisely characterizing the intrinsic physics of the kagome layers is extremely challenging due to the presence of interlayer Cu/Zn antisite disorder within its crystal structure. Here we measured the specific heat and thermal conductivity of single-crystal herbertsmithite in magnetic fields with high resolution. Strikingly, intrinsic magnetic specific heat contribution arising from the kagome layers exhibits excellent scaling collapse as a function of $T/H$ (temperature/magnetic field). In addition, no residual linear term in the thermal conductivity $\ensuremath{\kappa}/T(T\ensuremath{\rightarrow}0)$ is observed in zero and applied magnetic fields, indicating the absence of itinerant gapless excitations. These results capture a new essential feature of the QSL state of the kagome layers; localized orphan spins are induced by exchange bond randomness, surrounded by a nonitinerant QSL.

Snap-through of graphene nanowrinkles under out-of-plane compression

Nanowrinkles (i.e. the buckled nanoribbons) are widely observed in nano-devices assembled by two-dimensional (2D) materials. The existence of nanowrinkles significantly affects the physical (such as mechanical, electrical and thermal) properties of 2D materials, and thus further, impedes the applications of those devices. In this paper, we take the nanowrinkle formed in a monolayer graphene as a model system to study its deformation behaviours, especially the configuration evolution and the snap-through buckling instabilities, when subjected to the out-of-plane compression. By performing molecular dynamics simulation, the graphene nanowrinkles with or without self-adhesion (which are notated as ‘clipped’ state or ‘bump’ state, respectively) are obtained depending on the geometric size and the applied axial compressive pre-strain. The elastica theory is employed to quantify the shape of ‘bump’ nanowrinkles, as well as the critical condition of the transition between ‘clipped’ and ‘bump’ states. By applying out-of-plane compression to the generated graphene nanowrinkle, it flips to an opposite configuration via snap-through buckling. We identify four different buckling modes according to the configuration evolution. An unified phase diagram is constructed to describe those buckling modes. For the cases with negligible van der Waals interaction getting involved in the snap-buckling process, i.e. without self-adhesion, the force–displacement curves for nanowrinkles with same axial pre-strain but different sizes can be scaled to collapse. Moreover, the critical buckling loads can also be scaled and predicted by the extended elastica theory. Otherwise, for the cases with self-adhesion, which corresponds to the greater axial pre-strain, the van der Waals interaction makes the scaling collapse break down. It is expected that the analysis about the snap-through buckling of graphene nanowrinkles reported in this work will advance the understanding of the mechanical behaviours of wrinkled 2D materials and promote the design of functional nanodevices, such as nanomechanical resonators and capacitors.

Scaling Collapse of Longitudinal Conductance near the Integer Quantum Hall Transition.

Within the mature field of Anderson transitions, the critical properties of the integer quantum Hall transition still pose a significant challenge. Numerical studies of the transition suffer from strong corrections to scaling for most observables. In this Letter, we suggest to overcome this problem by using the longitudinal conductance g of the network model as the scaling observable, which we compute for system sizes nearly 2 orders of magnitude larger than in previous studies. We show numerically that the sizable corrections to scaling of g can be accounted for in a remarkably simple form, which leads to an excellent scaling collapse. Surprisingly, the scaling function turns out to be indistinguishable from a Gaussian. We propose a cost-function-based approach and estimate ν=2.609(7) for the localization length exponent, consistent with previous results, but considerably more precise than in most works on this problem. Extending previous approaches for Hamiltonian models, we also confirm our finding using integrated conductance as a scaling variable.

Universal scaling of mean skin friction in turbulent boundary layers and fully developed pipe and channel flows

A dynamically consistent scaling of mean skin friction in zero-pressure-gradient turbulent boundary layers and fully developed pipe and channel flows, is derived. Theoretical arguments are based on transfer of kinetic energy from mean flow to large eddies of turbulence. A single new velocity scale $M/\nu$ is shown to be dynamically relevant for scaling skin friction in all flows; $M$ is the planar kinematic momentum rate of the shear flow and $\nu$ is fluid kinematic viscosity. An asymptotic $-1/2$ power scaling law (in $M$ – $\nu$ scaling) is shown to be universally applicable. It is observed that the semi-empirical finite- $Re$ skin friction model, resulting from the asymptotic scaling law, applies well to individual flows, but fails to describe all flows in a universal fashion. This non-universality could be due to the differences in flow boundary conditions at finite Reynolds numbers and flow geometry, that affect the outer-layer structures in these flows. It is argued that these differences may be simply absorbed by considering differences in the shapes of mean velocity profiles amongst these flows. An empirical correction to $M$ – $\nu$ scaling is proposed based on Clauser's shape factor $G$ . It is demonstrated that data from all flows in this new, semi-empirical $M$ – $\nu$ – $G$ scaling collapse remarkably well onto a single universal curve. The corresponding universal finite- $Re$ model in $M$ – $\nu$ – $G$ scaling is shown to describe this curve to an excellent accuracy. These results underscore the importance of a dynamically consistent approach towards revealing universality of skin friction scaling in wall turbulence.

Quantum computing critical exponents

We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the transition due to a slowdown of the quantum algorithm when crossing the phase transition. In order to assess performance of the quantum algorithm and compute correlations in a system of up to 752 qubits, we use techniques from integrability to derive closed-form analytical expressions for expectation values with respect to the output of the quantum circuit. We also reduce a conjecture made by Ho and Hsieh about the exact preparation of the transverse field Ising ground state to a system of equations.

Stark many-body localization transitions in superconducting circuits

Recent numerical and experimental works have revealed a disorder-free many-body localization (MBL) in an interacting system subjecting to a linear potential, known as the Stark MBL. The conventional MBL, induced by disorder, has been widely studied by using quantum simulations based on superconducting circuits. Here, we consider the Stark MBL in two types of superconducting circuits, i.e., the 1D array of superconducting qubits, and the circuit where non-local interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highly-excited eigenstates, and obtain the lower bound of the critical linear potential $\gamma_{c}$, using the finite-size scaling collapse. Moreover, we study the non-equilibrium properties of the Stark MBL. In particular, we observe an anomalous relaxation of the imbalance, dominated by the power-law decay $t^{-\xi}$. The exponent $\xi$ satisfies $\xi\propto|\gamma-\gamma_{c}|^{\nu}$ when $\gamma<\gamma_{c}$, and vanishes for $\gamma\geq \gamma_{c}$, which can be employed to estimate the $\gamma_{c}$. Our work indicates that superconducting circuits are a promising platform for investigating the critical properties of the Stark MBL transition.

Investigation on Distribution Characteristics of Deterioration in Helan Pass Rock Arts

The Helan Pass rock arts in Ningxia Province, China, have undergone severe decay and showed some typical forms of deterioration, including scaling off, crack, and collapse. These three forms of deterioration in the Tiger Town region to water-off were quantitatively counted to analyze their distribution characteristics. The statistical windows were used for crack studies to investigate distribution regularities of ten aspects such as attitude, class number, and spacing. The findings reveal that 17 of the 25 rock arts in the Helan Pass study area developed scaling off in the rock masses’ surfaces. A total of 130 cracks in the 19 statistical windows were located predominantly in the lower part of the mountain. In addition, 15 collapses occurred and were mostly in the upper part of the mountain. The crack locations with different filling types were concentrated. Further, the crack apertures were related to their filling types, and the apertures of siliceous filling cracks were generally larger, whereas the argillaceous filling cracks were mostly medium apertures. In addition, the apertures of grouting cracks were varied, and the apertures of nonfilling cracks were small.

Continuous Mott transition in semiconductor moiré superlattices.

The evolution of a Landau Fermi liquid into a non-magnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics1-6. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids4-7, exciton condensates8 and unconventional superconductivity1. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice9-22, providing a unique opportunity to drive a metal-insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electrically tuning the effective interaction strength in MoTe2/WSe2 moiré superlattices, we observe a continuous MIT at a fixed filling of one electron per unit cell. The existence of quantum criticality is supported by the scaling collapse of the resistance, a continuously vanishing charge gap as the critical point is approached from the insulating side, and a diverging quasiparticle effective mass from the metallic side. We also observe a smooth evolution of the magnetic susceptibility across the MIT and no evidence of long-range magnetic order down to ~5% of the Curie-Weiss temperature. This signals an abundance of low-energy spinful excitations on the insulating side that is further corroborated by the Pomeranchuk effect observed on the metallic side. Our results are consistent with the universal critical theory of a continuous Mott transition in two dimensions4,23.

Improvement of the free-interaction theory for shock wave/turbulent boundary layer interactions

Free-interaction theory is widely used for the analysis and modeling of the flow structure for shock wave/turbulent boundary layer interactions (SWTBLIs). However, many studies have demonstrated that the value of the nondimensional pressure rise function at the plateau should not be treated as a universal constant, which is an assumption taken in the traditional free-interaction theory. Such an assumption brings huge uncertainty to the theoretical prediction of shock wave/boundary layer interaction flows. To improve the accuracy of free-interaction theory, numerical simulations on the incident shock wave/turbulent boundary layer interactions are carried out in this study over an extensive flow range (Ma0 = 2.0–5.0, Reδ = 7.4 × 104–7.29 × 105). Utilizing the simulated flow field structures and literature data, this paper analyzes the essential influencing factors for determining the plateau pressure. Two nondimensional parameters—the incompressible shape factor of the incoming boundary layer and the nondimensional separation-bubble height—are identified as the essential influencing factors for the nondimensional pressure rise function at the plateau. A new scaling rule is proposed by taking these two nondimensional parameters into consideration, and the experimental data of the SWTBLIs after scaling collapse well onto a single curve with an R2 value of 0.918. The experimental data used to validate the scaling rule include incident and ramp SWTBLIs and the leading SWTBLIs in shock trains. The proposed scaling rule can be used to establish more accurate theoretical predicting models for SWTBLIs.

Quartic multifractality and finite-size corrections at the spin quantum Hall transition

The spin quantum Hall (or class C) transition represents one of the few localization-delocalization transitions for which some of the critical exponents are known exactly. Not known, however, is the multifractal spectrum, $\tau_q$, which describes the system-size scaling of inverse participation ratios $P_q$, i.e., the $q$-moments of critical wavefunction amplitudes. We here report simulations based on the class C Chalker-Coddington network and demonstrate that $\tau_q$ is (essentially) a quartic polynomial in $q$. Analytical results fix all prefactors except the quartic curvature that we obtain as $\gamma=(2.22\pm{0.15})\cdot10^{-3}$. In order to achieve the necessary accuracy in the presence of sizable corrections to scaling, we have analyzed the evolution with system size of the entire $P_q$-distribution function. As it turns out, in a sizable window of $q$-values this distribution function exhibits a (single-parameter) scaling collapse already in the pre-asymptotic regime, where finite-size corrections are not negligible. This observation motivates us to propose a novel approach for extracting $\tau_q$ based on concepts borrowed from the Kolmogorov-Smirnov test of mathematical statistics. We believe that our work provides the conceptual means for high-precision investigations of multifractal spectra also near other localization-delocalization transitions of current interest, especially the integer (class A) quantum Hall effect.

CMB birefringence from ultralight-axion string networks

The polarization of Cosmic Microwave Background (CMB) photons is rotated as they pass through (ultralight-) axion string loops. Studying this birefringence can reveal valuable information about the axion-photon coupling and the structure of the string network. We develop an approximate analytic formalism and identify a kernel function that can be used to calculate the two-point correlation function for CMB birefringence induced by an arbitrary axion string network. Using this formalism, we evaluate the birefringence signal for some simple loop distributions (including scaling and network collapse). We find that the angular correlation function has a characteristic angular scale set by θmin, which corresponds to the angular extent of the loops at the time of recombination. This results in a peak in the birefringence power spectrum around ℓp ∼ 1/θmin. An additional scale, controlled by the axion's mass, is introduced if the network collapses before today.

Localization dynamics in a centrally coupled system

In systems where interactions couple a central degree of freedom and a bath, one would expect signatures of the bath's phase to be reflected in the dynamics of the central degree of freedom. This has been recently explored in connection with many-body localized baths coupled with a central qubit or a single cavity mode -- systems with growing experimental relevance in various platforms. Such models also have an interesting connection with Floquet many-body localization via quantizing the external drive, although this has been relatively unexplored. Here we adapt the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method, a well-known tree tensor network algorithm, to numerically simulate the dynamics of a central degree of freedom, represented by a $d$-level system (qudit), coupled to a disordered interacting 1D spin bath. ML-MCTDH allows us to reach $\approx 10^2$ lattice sites, a far larger system size than what is feasible with exact diagonalization or kernel polynomial methods. From the intermediate time dynamics, we find a well-defined thermodynamic limit for the qudit dynamics upon appropriate rescaling of the system-bath coupling. The spin system shows similar scaling collapse in the Edward-Anderson spin glass order parameter or entanglement entropy at relatively short times. At longer time scales, we see slow growth of the entanglement, which may arise from dephasing mechanisms in the localized system or long-range interactions mediated by the central degree of freedom. Similar signs of localization are shown to appear as well with unscaled system-bath coupling.

Maneuvering in the Interval: Reflections on Immanent Entanglements

Both perspective and leverage are needed in order to arrive at a place where it is possible to do the philosophical work required in order to adequately account for our present sociotechnical landscape. One of the key characteristics of this landscape is the collapse of scale, as things become more like fluid assemblages and the economic incentives of surveillance capitalism turn ordinary things into surveillance devices tuned for others’ profit. In this context we need a language not only of imagination and humility in the face of countless gaps between things, but also one of entanglement, care, and response-ability.