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DOE OSTI2024

Precision Computations in Strongly Coupled Conformal Field Theories (Final Technical Report)

Conformal Field Theories (CFTs) are quantum field theories that are invariant under the conformal symmetry group (which includes translations and rotations, but also local rescalings of spacetime). They are building blocks of general quantum field theories, and appear in many areas of physics, including statistical physics, condensed matter physics, particle physics, and quantum gravity. Because of their extra symmetries, the mathematical structure of CFTs is tightly constrained, and this leads to the idea of the ``conformal bootstrap," which is to use these mathematical structures to constrain, and in some cases determine, CFT observables. A new numerical implementation of the conformal bootstrap idea appeared in 2008 with the work of Rattazzi, Rychkov, Tonni, and Vichi. Their observation was that certain bootstrap constraints (conformal symmetry and unitarity) could be combined to yield a convex optimization problem that constraints CFT data. By solving this convex optimization problem on a computer, one could obtain bounds on observables like critical exponents and operator product expansion (OPE) coefficients. Over the course of this award, the PI has improved numerical bootstrap techniques by optimizing known algorithms and finding new ones for performing the required convex optimization computations. The PI has applied these techniques to compute high-precision observables in several important strongly-coupled systems. The PI has also explored both analytical and numerical bootstrap methods for constraining the space of low energy effective field theories of quantum gravity, and developed new analytical techniques for CFT and QFT more broadly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Quantum simulation: From spin models to gauge-gravity correspondence

Quantum many-body systems with coherent and controllable interactions enable the realization of novel quantum materials, the quantum simulation of problems that cannot be simulated on classical computers, computational systems that are exponentially faster than existing classical algorithms, and the direct investigation of the conjectured duality between gravitational theories and quantum field theories. This project focusses on quantum phase transitions in strongly interacting many-body spin systems, and in particular on the dynamical evolution near the critical point and across the phase transition. The dynamics of a large quantum system containing more than 50 qubits is investigated in various critical regimes. In particular, the Kibble-Zurek transition has been characterized and critical exponents have been measured. Furthermore, quantum many-body scars have been observed and characterized for the first time. We are investigating the Kibble-Zurek mechanism in the quantum phase transition in one dimension from a disordered system to a system with ordering induced by Rydberg interactions between neighboring atoms. The Kibble-Zurek mechanism describes the formation of topological defects as a system evolves across a phase transitions, and is expected to apply to a large number of problems, including cosmology, where it should describe the structure of domain formation in the early universe.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Dynamics of the O ( 4 ) critical point in QCD: Critical pions and diffusion in model G

We present a detailed study of the finite momentum dynamics of the O ( 4 ) critical point of QCD, which lies in the dynamic universality class of “model G.” The critical scaling of the model is analyzed in multiple dynamical channels. For instance, the finite momentum analysis allows us to precisely extract the pion dispersion curve below the critical point. The pion velocity is in striking agreement with the predictions relation and static universality. The pion damping rate and velocity are both consistent with the dynamical critical exponent ζ = 3 / 2 of model G. Similarly, although the critical amplitude for the diffusion coefficient of the conserved O ( 4 ) charges is small, it is clearly visible both in the restored phase and with finite explicit symmetry breaking, and its dynamical scaling is again consistent with ζ = 3 / 2 . We determine a new set of universal dynamical critical amplitude ratios relating the diffusion coefficient to a suitably defined order parameter relaxation time. We also show that in a finite volume simulation, the chiral condensate diffuses on the coset manifold in a manner consistent with dynamical scaling, and with a diffusion coefficient that is determined by the transport coefficients of hydrodynamic pions. Finally, the amplitude ratios (together with other nonuniversal amplitudes also reported here) compile all relevant information for further studies of model G both in and out of equilibrium. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

The color of magnetic monopole noise

We relate the anomaly in the noise color of spin ice to the emergent nature of its magnetic monopoles and their random walk. Monopoles are quasi-particles, and the spin vacuum in which they wander is not structureless. Rather, the underlying spin ensemble filters the thermal white noise, leading to non-trivial coevolution. Thus, monopoles can be considered as "dressed" random walkers, activated by a non-trivial stochastic noise that subsumes mutual interactions and the coevolution of their spin vacuum. From this, we suggest that recent experimental results are interpretable in terms of monopole subdiffusion. Furthermore, we then conjecture relations between the color of the noise and other observables, such as relaxation time, monopole density, the dynamic exponent, and the order of the annihilation reaction, which suggests to us the introduction of spin-ice-specific critical exponents in a neighborhood of the ice manifold criticality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dynamical criticality of spin-shear coupling in van der Waals antiferromagnets

Abstract The interplay between a multitude of electronic, spin, and lattice degrees of freedom underlies the complex phase diagrams of quantum materials. Layer stacking in van der Waals (vdW) heterostructures is responsible for exotic electronic and magnetic properties, which inspires stacking control of two-dimensional magnetism. Beyond the interplay between stacking order and interlayer magnetism, we discover a spin-shear coupling mechanism in which a subtle shear of the atomic layers can have a profound effect on the intralayer magnetic order in a family of vdW antiferromagnets. Using time-resolved X-ray diffraction and optical linear dichroism measurements, interlayer shear is identified as the primary structural degree of freedom that couples with magnetic order. The recovery times of both shear and magnetic order upon optical excitation diverge at the magnetic ordering temperature with the same critical exponent. The time-dependent Ginzburg-Landau theory shows that this concurrent critical slowing down arises from a linear coupling of the interlayer shear to the magnetic order, which is dictated by the broken mirror symmetry intrinsic to the monoclinic stacking. Our results highlight the importance of interlayer shear in ultrafast control of magnetic order via spin-mechanical coupling.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Extending a scaling equation of state to QCD

Whether quantum chromodynamics (QCD) exhibits a phase transition at finite temperature and density is an open question. It is important for hydrodynamic modeling of heavy ion collisions and neutron-star mergers. Lattice QCD simulations have definitively shown that the transition from hadrons to quarks and gluons is a crossover when the baryon chemical potential is zero or small. Here, we combine the parametric scaling equation of state, usually associated with the three-dimensional Ising model, with a background equation of state based on a smooth crossover from hadrons to quarks and gluons. Comparison to experimental data from the Beam Energy Scan II at the Relativistic Heavy Ion Collider or in heavy ion experiments at other accelerators may allow the critical exponents and amplitudes in the scaling equation of state to be determined for QCD if a critical point exists.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical 𝑂⁡(2) nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature 𝑇 𝑐 = 2.2017⁢(2) with the critical exponent 𝜈 = 0.663⁢(33) for the 3D 𝑂⁡(2) model. In addition, we also study the Berezinskii–Kosterlitz–Thouless (BKT) criticality of the 2D classical 𝑂⁡(2) model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, 𝑇 BKT = 0.8928⁢(2).

lattice field theory↗
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 OSTI2020

Transport characterization and pinning analysis of BaFe 1.9 Ni 0.1 As 2.05 thin films

In this paper, we report on the vortex-glass transition and superconducting performance of BaFe 1.9 Ni 0.1 As 2.05 thin films with T c = 17.8 K on CaF 2 (00 l ) single crystals by pulsed laser deposition. Atomic force microscopy characterization indicates the volumes of droplets appearing on the film surface increase with thickness and Magneto-optical imaging proves slight inhomogeneities in the current flow within the ab -plane of thin film. The thin films show a transport current density J c of ~1.14 MA cm –2 in self-field, and 0.34 and 0.28 MA cm –2 for H // c and H // ab up to 9 T at 4.2 K. Pinning mechanism associated with the fluctuations in the mean free path of the charge carries is found to be dominant in the thin films. The vortex-glass (VG) to vortex-liquid phase transition is identified in terms of the plots of the logarithmic derivative of the resistivity curves under different fields, allowing us to deduce the values of the VG transition temperature T g , and the critical exponent s . The ρ – T curves are well scaled by VG theory. A phase diagram combining the VG transition temperature, irreversibility field and upper critical field is constructed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2021

Delocalization Transition of a Disordered Axion Insulator

The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that, under quenched disorder respecting inversion symmetry on average, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be ν = 1.42 ± 0.12. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. Finally, we also quantitatively map our quantum network model to an effective Hamiltonian and we find its low-energy k ∙ p expansion.

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↗
DOE OSTI2020

Universal finite-time thermodynamics of many-body quantum machines from Kibble-Zurek scaling

We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary strokes. Specifically, we consider a quantum engine powered by dissipative energizing and relaxing baths. We show that under very generic conditions, the output work is governed by the Kibble-Zurek mechanism; i.e., it exhibits a universal power-law scaling with the driving speed through the critical points. We also optimize the finite-time thermodynamics as a function of the driving speed. The maximum power and the corresponding efficiency take a universal form, and are reached for an optimal speed that is governed by the critical exponents. We exemplify our results by considering a transverse-field Ising spin chain as the working medium. For this model, we also show how the efficiency and power vary as the engine becomes critical.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2021

Ferroelectric phase-transition frustration near a tricritical composition point

Phase transition describes a mutational behavior of matter states at a critical transition temperature or external field. Despite the phase-transition orders are well sorted by classic thermodynamic theory, ambiguous situations interposed between the first- and second-order transitions were exposed one after another. Here, we report discovery of phase-transition frustration near a tricritical composition point in ferroelectric Pb(Zr 1-x Ti x )O 3 . Our multi-scale transmission electron microscopy characterization reveals a number of geometrically frustrated microstructure features such as self-assembled hierarchical domain structure, degeneracy of mesoscale domain tetragonality and decoupled polarization-strain relationship. Associated with deviation from the classic mean-field theory, dielectric critical exponent anomalies and temperature dependent birefringence data unveil that the frustrated transition order stems from intricate competition of short-range polar orders and their decoupling to long-range lattice deformation. With supports from effective Hamiltonian Monte Carlo simulations, our findings point out a potentially universal mechanism to comprehend the abnormal critical phenomena occurring in phase-transition materials.

42 ENGINEERING↗
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↗