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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO 4

We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO 4 , an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4 f orbitals of the thulium (Tm 3 + ) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4 f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO 4 as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Some exactly solvable and tunable frustrated spin models

In this report we discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubedát decorations. We then consider a 1-parameter family generalization of the Villain’s fully frustrated model, which interpolates between Onsager’s 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions a lá Bethe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/$\textit{t}$ algorithm, in particular the short iteration performance. Further, a proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li 0.5 La 0.5 TiO 3 . This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li 0.5 La 0.5 TiO 3 are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li 0.5 La 0.5 TiO 3 system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Improving Schrödinger Equation Implementations with Gray Code for Adiabatic Quantum Computers

We reformulate the continuous-space Schrödinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. A binary encoding of position produces a spin-1/2 Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code (BRGC), and a Hamming-distance-2 Gray code (H2GC) reduces the model complexity down to the 𝑋⁢𝑍 and transverse Ising model, respectively. For 𝐴 qubits BRGC yields 2 𝐴 positions and is reduced to its 2-local form with O⁡(𝐴) ancillary qubits. H2GC yields 2 𝐴/2+1 positions with O⁡(𝐴 2 ) three-local penalty terms. We also identify the bijective mapping between diagonal unitaries and the Walsh series, producing the mapping of any real potential to a series of 𝑘 -local Ising models through the fast Walsh transform. Finally, in a finite volume, we provide some numerical evidence to support the claim that the total time needed for adiabatic evolution is protected by the infrared cutoff of the system. As a result, initial state preparation from a free-field wave function to an interacting system is expected to exhibit polynomial time complexity with volume and constant scaling with respect to lattice discretization for all encodings. For H2GC, if the evolution starts with the transverse Hamiltonian due to hardware restrictions, then penalties are dynamically introduced such that the low-lying spectrum reproduces the energy levels of the Laplacian. The adiabatic evolution of the penalty Hamiltonian is therefore sensitive to the ultraviolet scale. It is expected to exhibit polynomial time complexity with lattice discretization, or exponential time complexity with respect to the number of qubits given a fixed volume.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the origin of cooperativity effects in the formation of self-assembled molecular networks at the liquid/solid interface

In this work we investigate the behaviour of molecules at the nanoscale using scanning tunnelling microscopy in order to explore the origin of the cooperativity in the formation of self-assembled molecular networks (SAMNs) at the liquid/solid interface. By studying concentration dependence of alkoxylated dimethylbenzene, a molecular analogue to 5-alkoxylated isophthalic derivatives, but without hydrogen bonding moieties, we show that the cooperativity effect can be experimentally evaluated even for low-interacting systems and that the cooperativity in SAMN formation is its fundamental trait. We conclude that cooperativity must be a local effect and use the nearest-neighbor Ising model to reproduce the coverage vs. concentration curves. The Ising model offers a direct link between statistical thermodynamics and experimental parameters, making it a valuable tool for assessing the thermodynamics of SAMN formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Magnetic properties of the Ising-like rare earth pyrosilicate: D-Er 2 Si 2 O 7

Ising-like spin-1/2 magnetic materials are of interest for their ready connection to theory, particularly in the context of quantum critical behavior. In this work we report detailed studies of the magnetic properties of a member of the rare earth pyrosilicate family, D-Er 2 Si 2 O 7 , which is known to display a highly anisotropic Ising-like g-tensor and effective spin-1/2 magnetic moments. We used powder neutron diffraction, powder inelastic neutron spectroscopy (INS), and single crystal AC susceptibility to characterize its magnetic properties. Neutron diffraction enabled us to determine the magnetic structure below the known transition temperature (T N = 1.9 K) in zero field, confirming that the magnetic state is a four-sublattice antiferromagnetic structure with two non-collinear Ising axes, as was previously hypothesized. Our powder INS data revealed a gapped excitation at zero field, consistent with anisotropic (possibly Ising) exchange. An applied field of 1 T produces a mode softening, which is consistent with a field-induced second order phase transition. To assess the relevance of D-Er 2 Si 2 O 7 to the transverse field Ising model, we performed AC susceptibility measurements on a single crystal with the magnetic field oriented in the direction transverse to the Ising axes. This revealed a transition at 2.65 T at 0.1 K, a field significantly higher than the mode-softening field observed by powder INS, showing that the field-induced phase transitions are highly field-direction dependent as expected. Furthermore, these measurements suggest that D-Er 2 Si 2 O 7 may be a candidate for further exploration related to the transverse field Ising model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Slowly decaying zero mode in a weakly nonintegrable boundary impurity model

The transverse field Ising model (TFIM) on the half-infinite chain possesses an edge zero mode. This work considers an impurity model: TFIM perturbed by a boundary integrability-breaking interaction. For sufficiently large transverse field, but in the ordered phase of the TFIM, the zero mode is observed to decay. The decay is qualitatively different from zero modes where the integrability-breaking interactions are nonzero all along the chain. It is shown that for the impurity model, the zero mode decays by relaxing to a nonlocal quasiconserved operator, the latter being exactly conserved when the opposite edge of the chain has no noncommuting perturbations so as to ensure perfect degeneracy of the spectrum. In the thermodynamic limit, the quasiconserved operator vanishes, and a regime is identified where the decay of the zero mode obeys Fermi's golden rule. Furthermore, a toy model for the decay is constructed in Krylov space and it is highlighted how Fermi's golden rule may be recovered from this toy model.

1-dimensional systems↗
NASA NTRS2003

Kinetic Monte Carlo Simulations of Rod Eutectics and the Surface Roughening Transition in Binary Alloys

In this paper we report on two related topics: Kinetic Monte Carlo simulations of the steady state growth of rod eutectics from the melt, and a study of the surface roughness of binary alloys. We have implemented a three dimensional kinetic Monte Carlo (kMC) simulation with diffusion by pair exchange only in the liquid phase. Entropies of fusion are first chosen to fit the surface roughness of the pure materials, and the bond energies are derived from the equilibrium phase diagram, by treating the solid and liquid as regular and ideal solutions respectively. A simple cubic lattice oriented in the {100} direction is used. Growth of the rods is initiated from columns of pure B material embedded in an A matrix, arranged in a close packed array with semi-periodic boundary conditions. The simulation cells typically have dimensions of 50 by 87 by 200 unit cells. Steady state growth is compliant with the Jackson-Hunt model. In the kMC simulations, using the spin-one Ising model, growth of each phase is faceted or nonfaceted phases depending on the entropy of fusion. There have been many studies of the surface roughening transition in single component systems, but none for binary alloy systems. The location of the surface roughening transition for the phases of a eutectic alloy determines whether the eutectic morphology will be regular or irregular. We have conducted a study of surface roughness on the spin-one Ising Model with diffusion using kMC. The surface roughness was found to scale with the melting temperature of the alloy as given by the liquidus line on the equilibrium phase diagram. The density of missing lateral bonds at the surface was used as a measure of surface roughness.

Bentz, Daniel N.↗
NASA NTRS1976

The Pioneer 11 1976 solar conjunction: A unique opportunity to explore the heliographic latitudinal variations of the solar corona

The 1976 Pioneer II Solar Conjunction provided the opportunity to accumulate a substantial quantity of doppler noise data over a dynamic range of signal closest approach point heliographic latitudes. The observed doppler noise data were fit to the doppler noise model ISED, and the deviations of the observed doppler noise data from the model were used to construct a (multiplicative) function to describe the effect of heliographic latitude. This expression was then incorporated into the ISED model to produce a new doppler noise model-ISEDB.

Berman, A. L.↗
DOE OSTI2021

Z 2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z 2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first order, in contrast to the conventional Z 2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic X X interaction while keeping the local gauge symmetry intact. We find that the Z 2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.

2-dimensional systems↗
DOE OSTI2023

Effective and asymptotic criticality of structurally disordered magnets

Changes in magnetic critical behaviour of quenched structurally-disordered magnets are usually exemplified in experiments and in MC simulations by diluted systems consisting of magnetic and non-magnetic components. In our study we aim to show that similar effects can be observed not only for diluted magnets with non-magnetic impurities but may be implemented, e.g., by the presence of two (and more) chemically different magnetic components as well. Therefore we consider a model of the structurally-disordered quenched magnet where all lattice sites are occupied by Ising-like spins of different lengths L. In such a random spin length Ising model, the length L of each spin is a random variable governed by the distribution function p (L). We demonstrate that this model belongs to the universality class of the site-diluted Ising model. This proves that both models are described by the same values of asymptotic critical exponents. However, their effective critical behaviour differs. As a case study, we consider a quenched mixture of two different magnets with values of elementary magnetic moments L 1 = 1 and L 2 = s, and of concentration c and 1 - c, correspondingly. We apply field-theoretical renormalization group approach to analyse the renormalization group flow for different initial conditions, triggered by s and c, and to calculate effective critical exponents further away from the fixed points of the renormalization group transformation. We show how the effective exponents are governed by difference in properties of the magnetic components.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Floquet operator dynamics and orthogonal polynomials on the unit circle

Operator spreading under stroboscopic time evolution under a unitary is studied. An operator Krylov space is constructed and mapped to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parametrizing the ITFIM. The relations between the OPUC and spectral functions are summarized and several applications are presented. These include derivation of analytic expressions for the OPUC under persistent m-periodic dynamics, and the numerical construction of the OPUC for autocorrelations of the homogeneous Floquet-Ising model as well as the Z 3 clock model. The numerically obtained Krylov angles of the Z 3 clock model with long-lived period tripled autocorrelations show a spatial periodicity of six, and this observation is used to develop an analytically solvable model for the ITFIM that mimics this behavior.

Floquet systems↗
DOE OSTI2024

CFT and lattice correlators near an RG domain wall between minimal models

Conformal interfaces separating two conformal field theories (CFTs) provide maps between different CFTs, and naturally exist in nature as domain walls between different phases. One particularly interesting construction of a conformal interface is the renormalization group (RG) domain wall between CFTs. For a given Virasoro minimal model \mathcal{M}_{k+3,k+2} ℳ k + 3 , k + 2 , an RG domain wall can be generated by a specific deformation which triggers an RG flow towards its adjacent Virasoro minimal model \mathcal{M}_{k+2,k+1} ℳ k + 2 , k + 1 with the deformation turned on over part of the space. An algebraic construction of this domain wall was proposed by Gaiotto in [J. High Energy Phys. 12, 103 (2012)]. In this paper, we will provide a study of this RG domain wall for the minimal case k=2 k = 2 , which can be thought of as a nonperturbative check of the construction. In this case the wall is separating the Tricritical Ising Model (TIM) CFT and the Ising Model (IM) CFT. We will check the analytical results of correlation functions from the RG brane construction with the numerical density matrix renormalization group (DMRG) calculation using a lattice model proposed in [arXiv.1206.1332, Science 344, 280 (2014)], and find a perfect agreement. We comment on possible experimental realizations of this RG domain wall.

Cogburn, Cameron V.↗
DOE OSTI2022

Misanthropic entropy and renormalization as a communication channel

A central physical question is the extent to which infrared (IR) observations are sufficient to reconstruct a candidate ultraviolet (UV) completion. We recast this question as a problem of communication, with messages encoded in field configurations of the UV being transmitted to the IR degrees of freedom via a noisy channel specified by renormalization group (RG) flow, with noise generated by coarse graining/decimation. We present an explicit formulation of these considerations in terms of lattice field theory, where we show that the “misanthropic entropy” — the mutual information obtained from decimating neighbors — encodes the extent to which information is lost in marginalizing over/tracing out UV degrees of freedom. Our considerations apply both to statistical field theories as well as density matrix renormalization of quantum systems, where in the quantum case, the statistical field theory analysis amounts to a leading-order approximation. As a concrete example, we focus on the case of the 2D Ising model, where we show that the misanthropic entropy detects the onset of the phase transition at the Ising model critical point.

Physics↗
DOE OSTI2021

Diagnosis of information scrambling from Hamiltonian evolution under decoherence

We apply a quantum teleportation protocol based on the Hayden-Preskill thought experiment to quantify how scrambling a given quantum evolution is. It has an advantage over the direct measurement of out-of time ordered correlators when used to diagnose the information scrambling in the presence of decoherence effects stemming from a noisy quantum device. We demonstrate the protocol by applying it to two physical systems: Ising spin chain and SU(2) lattice Yang-Mills theory. To this end, we numerically simulate the time evolution of the two theories in the Hamiltonian formalism. The lattice Yang-Mills theory is implemented with a suitable truncation of Hilbert space on the basis of the Kogut-Susskind formalism. On a two-leg ladder geometry and with the lowest nontrivial spin representations, it can be mapped to a spin chain, which we call Yang-Mills-Ising model and is also directly applicable to future digital quantum simulations. Here, we find that the Yang-Mills-Ising model shows the signal of information scrambling at late times.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Permutation matrix representation quantum Monte Carlo

We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its off-diagonal terms and is both parameter-free and Trotter error-free. In our approach, the quantum dimension consists of products of elements of a permutation group. As such, it allows for the study of a very wide variety of models on an equal footing. To demonstrate the utility of our technique, we use it to clarify the emergence of the sign problem in the simulations of non-stoquastic physical models. We showcase the flexibility of our algorithm and the advantages it offers over existing state-of-the-art by simulating transverse- field Ising model Hamiltonians and comparing the performance of our technique against that of the stochastic series expansion algorithm. Furthermore, we also study a transverse-field Ising model augmented with randomly chosen two-body transverse-field interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1976

Doppler noise considered as a function of the signal path integration of electron density

The hypothesis is advanced that observed Doppler noise during solar conjunctions is proportional to total columnar electron content along the signal path. This assumption leads directly to a geometrical model (ISED) for observed Doppler noise which is shown to be in very good agreement with Doppler noise data accumulated during the 1975 Pioneer 10, Pioneer 11 and Helios 1 solar conjunctions. An augmented model is constructed which quantitatively indicates correlation between earth observed sunspot activity and systematic, cyclical deviations from the ISED model.

Berman, A. L.↗
DOE OSTI2021

On the degeneracy of spin ice graphs, and its estimate via the Bethe permanent

The concept of spin ice can be extended to a general graph. We study the degeneracy of spin ice graph on arbitrary interaction structures via graph theory. We map spin ice graphs to the Ising model on a graph and clarify whether the inverse mapping is possible via a modified Krausz construction. From the gauge freedom of frustrated Ising systems, we derive exact, general results about frustration and degeneracy. We demonstrate for the first time that every spin ice graph, with the exception of the one-dimensional Ising model, is degenerate. We then study how degeneracy scales in size, using the mapping between Eulerian trails and spin ice manifolds, and a permanental identity for the number of Eulerian orientations. Furthermore, we show that the Bethe permanent technique provides both an estimate and a lower bound to the frustration of spin ices on arbitrary graphs of even degree. While such a technique can also be used to obtain an upper bound, we find that in all finite degree examples we studied, another upper bound based on Schrijver inequality is tighter.

97 MATHEMATICS AND COMPUTING↗