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DOE OSTI2025

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗
DOE OSTI2025

Strong Kitaev Interaction in BaCo 2⁢ (AsO 4 ) 2

The inelastic neutron scattering results and their analysis unequivocally point to a dominant Kitaev interaction in the honeycomb-lattice cobaltate BaCo 2 ⁢(AsO 4 ) 2 . Our anisotropic-exchange model closely describes all available neutron scattering data in the material’s field-polarized phase. Furthermore, the density-matrix renormalization group results for our model are in close accord with the unusual double-zigzag magnetic order and the low in-plane saturation field of BaCo 2 ⁢(AsO 4 ) 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Lieb-Robinson Bounds with Exponential-in-Volume Tails

Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Intuitively, Lieb-Robinson bounds state that, with local or exponentially decaying interactions, the correlation that can be built up between two sites separated by distance 𝑟 after a time 𝑡 decays as exp (𝑣⁢𝑡 −𝑟), where 𝑣 is the emergent Lieb-Robinson velocity. In many problems, it is important to also capture how much of an operator grows to act on 𝑟 𝑑 sites in 𝑑 spatial dimensions. Perturbation theory and cluster expansion methods suggest that, at short times, these volume-filling operators are suppressed as exp (−𝑟 𝑑 ). We confirm this intuition, showing that, for 𝑟 >𝑣⁢𝑡, the volume-filling operator is suppressed by exp (−(𝑟−𝑣⁢𝑡) 𝑑 /(𝑣⁢𝑡) 𝑑−1 ). This closes a conceptual and practical gap between the cluster expansion and the Lieb-Robinson bound. We then present two very different applications of this new bound. Firstly, we obtain improved bounds on the classical computational resources necessary to simulate many-body dynamics with error tolerance 𝜀 for any finite time 𝑡: as 𝜀 becomes sufficiently small, only 𝜀 −O⁡(𝑡 𝑑−1 ) resources are needed. A protocol that likely saturates this bound is given. Secondly, we prove that disorder operators have volume-law suppression near the “solvable (Ising) point” in quantum phases with spontaneous symmetry breaking, which implies a new diagnostic for distinguishing many-body phases of quantum matter.

computational complexity↗
DOE OSTI2024

Thermodynamic stability of a spin microemulsion in Rashba spin-orbit-coupled bosons

Recent finite-temperature numerical simulations have unveiled a quantum “spin” microemulsion analog, found by raising the temperature of a stripe supersolid phase in a Rashba spin-orbit coupled Bose gas. This microemulsion state is a highly correlated, isotropic normal fluid where atoms self-arrange based on their internal pseudospin into patterns that resemble bicontinuous microemulsions. This finding leaves several open questions regarding the broader accessibility of this phase in experiments. Here, we use equilibrium finite-temperature numerical simulations based on a coherent-state path integral representation to perform a computational investigation into the thermodynamic stability of the spin microemulsion state. Numerical simulations emphasize the requirement of a nearly, but not perfectly, isotropic spin-orbit coupling in order to achieve the microemulsion phase in cold-atom experiments. Moreover, the microemulsion state exists independent of miscibility of the pseudospin components and for a wide range of pseudospin population imbalance, suggesting a high degree of flexibility in choosing the atom and hyperfine states in an experimental realization. Lastly, we demonstrate this feasibility by mimicking a Rashba spin-orbit-coupled 87 Rb experiment in an isotropic harmonic trap, where we confirm the microemulsion's existence via its density profile and equilibrium quasimomentum distribution.

Complex Langevin dynamics↗
DOE OSTI2020

High field magnetization of FePS 3

High field magnetization measurements in pulsed fields up to 65 T have been performed on FePS 3 , which is nominally a good example of a two-dimensional Ising-like antiferromagnet on a honeycomb lattice. Measurements with the field parallel to the moment direction confirm the presence of two first-order transitions above 35 T, to M/M sat = 1/2 and M/M sat = 1, respectively, at 4 K. The measurements are in contradiction with published estimates for the magnetic exchange parameters, but the contradiction can be resolved by allowing for anisotropic exchange parameters in the Hamiltonian. Furthermore, the magnetization with the field perpendicular to the moment direction is anisotropic, with no transitions observed for fields along the a axis while a cascade of first-order transitions is observed for fields above 50 T along the b axis, the latter case also showing a strong degradation of the sample after repeated pulses. The results indicate a strong magnetolattice coupling in FePS 3 . Temperature-dependent measurements hint at a possible tricritical point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Pressure-induced suppression of ferromagnetism in the itinerant ferromagnet LaCrSb 3

We have performed an extensive pressure-dependent structural, spectroscopic, and electrical transport study of LaCrSb 3 . The ferromagnetic phase (TC=120 K at p = 0 GPa) is fully suppressed by p = 26.5 GPa and the Cr moment decreases steadily with increasing pressure. The unit-cell volume decreases smoothly up to p = 55 GPa. We find that the bulk modulus and suppression of the magnetism are in good agreement with theoretical predictions, but the Cr moment decreases smoothly with pressure, in contrast to steplike drops predicted by theory. The ferromagnetic ordering temperature appears to be driven by the Cr moment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Ferromagnetic cluster-glass phase in Ca(Co 1-x Ir x ) 2-y As 2 crystals

In this study, single crystals of Ca(Co 1-x Ir x ) 2-y As 2 with 0≤x≤0.35 and 0.10≤y≤0.14 have been grown using the self-flux technique and characterized by single-crystal x-ray diffraction (XRD), energy-dispersive x-ray spectroscopy, magnetization M, and magnetic susceptibility χ measurements versus temperature T, magnetic field H, and time t, and heat-capacity C p (H,T) measurements. The XRD refinements reveal that all the Ir-substituted crystals crystallize in a collapsed-tetragonal structure as does the parent CaCo 2-y As 2 compound. A small 3.3% Ir substitution for Co in CaCo 1.86 As 2 drastically lowers the A-type antiferromagnetic (AFM) transition temperature T N from 52 to 23 K with a significant enhancement of the Sommerfeld electronic heat-capacity coefficient. The A-type AFM structure consists of ab-plane layers of spins ferromagnetically aligned along the c axis with AFM alignment of the spins in adjacent layers along this axis. The positive Weiss temperatures obtained from Curie-Weiss fits to the χ(T>T N ) data indicate that the dominant magnetic interactions are ferromagnetic (FM) for all x. A magnetic phase boundary is inferred to be present between x=0.14 and x=0.17 from a discontinuity in the x dependencies of the effective moment and Weiss temperature in the Curie-Weiss fits. FM fluctuations that strongly increase with increasing x are also revealed from the χ(T) data. Furthermore, the magnetic ground state for x≥0.17 is a spin glass as indicated by hysteresis in χ(T) between field-cooled and zero-field-cooled measurements and from the relaxation of M in a small field that exhibits a stretched-exponential time dependence. The spin glass has a small FM component to the ordering and is hence inferred to be comprised of small FM clusters. The competing AFM and FM interactions along with crystallographic disorder associated with Ir substitution are inferred to be responsible for the development of a FM cluster-glass phase. A logarithmic T dependence of Cp at low T for x=0.14 is consistent with the presence of significant FM quantum fluctuations. This composition is near the T=0 boundary at x≈0.16 between the A-type AFM phase containing ferromagnetically-aligned layers of spins and the FM cluster-glass phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Thermal effects on the electronic properties of sodium electride under high pressures

Sodium is a simple metal at ambient conditions, while it transits to an electride phase at pressures above ~160 GPa along the room temperature isotherm. Here we explore the thermal effects on the electronic properties of the $hP4$ phase of sodium along the $ρ$ = 5.872 g/cm 3 isochore. We quantitatively classify this phase as an insulator based on the criterion of nearsightedness of the one-particle density matrix. Ab initio calculations suggest that the band gap of this insulator decreases with increasing temperature along the isochore, primarily because of ionic distortions; culminating in an insulator-to-metal transition upon melting at $T_m \approx 2100$ $\hbox{K}$. This transition is accompanied by residual electronic localization (in d orbitals) in the form of dynamic electron bubbles and a change in hybridization form $p–d$ to $s–p$ upon melting. This transition is explored by tracking the electronic and electro-optical properties along the isochore under consideration.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene

We analyze density wave and Pomeranchuk orders in twisted bilayer graphene. This complements our earlier analysis of the pairing instabilities. We assume that near half filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading intervalley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong-coupling approaches, indicating that this order is robust. Here, the other is a mixed state with 120° complex spin order and orthogonal complex charge order. In addition, we find a weaker but still attractive interaction in nematic channels, and discuss the type of a nematic order.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Shock compression of vanadium at extremes: Theory and experiment

Here, the equation of state (EOS) and shock compression of bulk vanadium were investigated using canonical ab initio molecular dynamic simulations, with experimental validation to 865 GPa from shock data collected at Sandia's Z Pulsed Power Facility. In simulations the phase space was sampled along isotherms ranging from 3000 K to 50 000 K, for densities between ρ = 3 and 15 g / cm 3 , with a focus on the liquid regime and the body-centered-cubic phase in the vicinity of the melting limit. The principal Hugoniot predicted from first principles is overall consistent with shock data, while it showed that current multiphase SESAME-type EOS for vanadium needed revision in the liquid regime. A more accurate SESAME EOS was developed using constraints from experiments and simulations. This work emphasizes the need to use a combined theoretical and experimental approach to develop high-fidelity EOS models for extreme conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Competing antiferromagnetic-ferromagnetic states in a d 7 Kitaev honeycomb magnet

The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet Li 3 Co 2 SbO 6 , built of high-spin d 7 (Co 2+ ) ions, in contrast to the more typical low-spin d 5 electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of C C 2/m, below T N = 11K at μ 0 H = 0T. The magnetic entropy recovered between T = 2 and 50 K is estimated to be 0.6Rln2, in good agreement with the value expected for systems close to a Kitaev quantum spin liquid state. The temperature-dependent magnetic order parameter demonstrates a β value of 0.19(3), consistent with XY anisotropy and in-plane ordering, with Ising-like interactions between layers. Further, we observe a spin-flop-driven crossover to ferromagnetic order with space group of C2/m under an applied magnetic field of μ 0 H ≈ 0.7T at T = 2K. Magnetic structure analysis demonstrates these magnetic states are competing at finite applied magnetic fields even below the spin-flop transition. Both the d 7 compass model, a quantitative comparison of the specific heat of Li 3 Co 2 SbO 6 , and related honeycomb cobaltates to the anisotropic Kitaev model further support proximity to a Kitaev spin liquid state. Furthermore, this material demonstrates the rich playground of high-spin d 7 systems for spin liquid candidates and complements known d 5 Ir- and Ru-based materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Influence of hydrostatic pressure on hidden order, the Kondo lattice, and magnetism in URu 2 Si 2-x P x

Within the chemical substitution series URu 2 Si 2-x P x , there is an evolution in the ground-state behavior from hidden ordered (HO) for x ≲ 0.03, to Kondo lattice behavior with no ordering (NO) for 0.03 ≲ x ≲ 0.26, to antiferromagnetism (AFM-2) for 0.26 ≲ x ≲ 0.5 [A. Gallagher et al., Nat. Commun. 7, 10712 (2016); A. Gallagher et al., J. Phys.: Condens. Matter 29, 024004 (2016)]. To better understand what factors control this behavior, temperature-dependent electrical resistivity measurements are performed for this series under applied pressures P up to 20.5 kbar. Specimens in the HO x region show similarities to the parent compound, where HO transforms into antiferromagnetism (AFM-1) at a critical pressure (P c ). P c decreases with increasing x and collapses towards P = 0 near x ≈ 0.03, suggesting that AFM-1 occurs at ambient pressure for this concentration. No pressure-induced phase transitions are observed in the NO x region and the AFM-2 state is only weakly suppressed by P. Measurements further reveal that AFM-1 and AFM-2 are distinct from each other. Calculations of the wave functions using the tight-binding Hartree-Fock approximation are performed and show (i) that the radial probability distributions for the phosphorus ions are more tightly bound than those for the silicon and (ii) that the energy difference between the orbitals decreases with increasing x. The cumulative effect of these two factors is that Si → P substitution decreases the hybridization strength, which correlates with the weakening of HO. At large x, additional effects such as electrical charge tuning also play an important role in determining the ground-state

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Emergent moments in a Hund's impurity

Here, motivated by the relevance of Hund's coupling in the context of multiorbital superconductors, we revisit the problem of a multiorbital Kondo impurity with Hund's interaction. Using dynamical large-N techniques, we propose an efficient approach that retains the essential physics at play, while providing a pathway to scalable quantum impurity solvers. We are able to follow the ground state, dynamic, and thermodynamic properties of this system over many decades of temperature. Our approach captures the emergence of large moments and follows the stretched evolution of the physics down to their exponentially suppressed Kondo temperature. We focus our analysis on the intermediate finite temperature phase which presents an alternate paramagnetic state due to the emergent moment and discuss the relevance of this regime to Hund's metals.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Flexosensitive polarization vortices in thin ferroelectric films

In this work, we present a theoretical study on the influence of the flexoelectric coupling on the spatial distribution and temperature behavior of the spontaneous polarization for several types of stable domain structure in thin ferroelectric films, such as stripe domains and vortices. Finite-element modeling (FEM) for BaTiO 3 films and analytical calculations within the Landau-Ginzburg-Devonshire approach reveals that an out-of-plane polarization component can be very sensitive to the flexoelectric coupling for periodic quasi-2D stripe domains and 3D vortex-antivortex structures. However, the influence is rather different for these structures. The flexoelectric coupling increases significantly the amplitude of a small out-of-plane polarization component in the stripe domains, and the “up” or “down” direction of the component is defined by the sign of the flexoelectric coefficients. Concerning the vortex-antivortex pairs, their antivortices with in-plane antiсirculation have smooth wide dipolar cores through the entire film, whose shape and other features are almost insensitive to the coupling. The vortices with in-plane vorticity have spikelike cores with an out-of-plane quadrupolar moment induced by the flexoelectric coupling. The cores are located near the film–dead-layer interfaces. FEM results corroborated by analytical calculations prove that a change of the flexoelectric coefficient sign leads to a reorientation of the core axial polarization, making the flexosensitive 3D vortices similar to the recently introduced “flexons” in cylindrical nanoparticles. The relatively wide temperature range (from 200 to 400 K) of the flexosensitive vortices' existence gives us confidence that they can be observed experimentally in thin ferroelectric films by scanning-probe and nonlinear optical microscopy methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Experimental thermal equation of state of B 2–KCl

The alkali halides are often used as optically-transparent pressure-transmitting media and thermal insulators in laser-heated diamond anvil cell experiments. High P-T equations of state for these materials would allow them to be used simultaneously as sensitive in situ pressure markers, making sample preparation and data analysis simpler. KCl is especially useful for this application because its high melting point, crystallographic simplicity, and low electron density are ideal for use in high-temperature X-ray diffraction experiments. However, the high-temperature static equation of state data for this material is limited in pressure to 8 GPa. As experiments routinely exceed 100 GPa in pressure and thousands of Kelvin, it is necessary for the equation of state of KCl to be determined experimentally at these conditions if it is to be used as an equation of state calibrant in the future. This work combines new high-pressure, high-temperature data of the B2 phase of KCl (up to 167 GPa and 2400 K) with the previously published room-temperature data of Dewaele et al. (2012) to produce a Mie-Gruneisen-Debye thermal equation of state for this material. The room temperature equation of state parameters are similar to those reported previously: V 0 = 32.0(3) cm 3 /mole, K 0 = 24(1) GPa and $K$$^{'}_{0}$ = 4.56(5). The thermal parameters, 0 and q, are 2.9(4) and 1.0(1), respectively. While a q of 1 is expected, the 0 is higher than expected from previous calculations, lower pressure experimental data, and the available shockwave data. Here, previously-reported equations of state underestimate the pressure of KCl at high temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗