Julia Steinberg

Bio: Julia Steinberg is an academic researcher from Harvard University. The author has contributed to research in topics: Butterfly effect & Diffusion (business). The author has an hindex of 7, co-authored 12 publications receiving 410 citations. Previous affiliations of Julia Steinberg include University of Pennsylvania.

Quantum quench of the Sachdev-Ye-Kitaev model

Abstract: We describe the nonequilibrium quench dynamics of the Sachdev-Ye-Kitaev models of fermions with random all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that, at long times, the fermion two-point function has a thermal form at a final temperature determined by energy conservation, and the numerical analysis is consistent with a thermalization rate proportional to this temperature. We also obtain an exact analytic solution of the quench dynamics in the large $q$ limit of a model with $q$ fermion interactions: in this limit, the thermalization of the two-point function is instantaneous.

Bulk Dirac points in distorted spinels.

Abstract: We report on a Dirac-like Fermi surface in three-dimensional bulk materials in a distorted spinel structure on the basis of density functional theory as well as tight-binding theory. The four examples we provide in this Letter are BiZnSiO4, BiCaSiO4, BiAlInO4, and BiMgSiO4. A necessary characteristic of these structures is that they contain a Bi lattice which forms a hierarchy of chainlike substructures, with consequences for both fundamental understanding and materials design.

Bulk Dirac Points in Distorted Spinels

Abstract: We report on a Dirac-like Fermi surface in three-dimensional bulk materials in a distorted spinel structure on the basis of density functional theory as well as tight-binding theory. The four examples we provide in this Letter are BiZnSiO4, BiCaSiO4, BiAlInO4, and BiMgSiO4. A necessary characteristic of these structures is that they contain a Bi lattice which forms a hierarchy of chainlike substructures, with consequences for both fundamental understanding and materials design.

Charge diffusion and the butterfly effect in striped holographic matter

Abstract: Recently, it has been proposed that the butterfly velocity — a speed at which quantum information propagates — may provide a fundamental bound on diffusion constants in dirty incoherent metals. We analytically compute the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength “hydrodynamic” disorder in a single spatial direction. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.

Thermalization and chaos in QED 3

Abstract: We study the real time dynamics of ${N}_{f}$ flavors of fermions coupled to a $U(1)$ gauge field in $2+1$ dimensions to leading order in a $1/{N}_{f}$ expansion. For large enough ${N}_{f}$, this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initially anticommuting fermion field operators. We compute such anticommutators in this gauge theory to leading order in $1/{N}_{f}$. We find that the anticommutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance.

Weyl and Dirac semimetals in three-dimensional solids

Abstract: Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals

Abstract: INTRODUCTION Condensed-matter systems have recently become a fertile ground for the discovery of fermionic particles and phenomena predicted in high-energy physics; examples include Majorana fermions, as well as Dirac and Weyl semimetals. However, fermions in condensed-matter systems are not constrained by Poincare symmetry. Instead, they must only respect the crystal symmetry of one of the 230 space groups. Hence, there is the potential to find and classify free fermionic excitations in solid-state systems that have no high-energy counterparts. RATIONALE The guiding principle of our classification is to find irreducible representations of the little group of lattice symmetries at high-symmetry points in the Brillouin zone (BZ) for each of the 230 space groups (SGs), the dimension of which corresponds to the number of bands that meet at the high-symmetry point. Because we are interested in systems with spin-orbit coupling, we considered only the double-valued representations, where a 2π rotation gives a minus sign. Furthermore, we considered systems with time-reversal symmetry that squares to –1. For each unconventional representation, we computed the low-energy k · p Hamiltonian near the band crossings by writing down all terms allowed by the crystal symmetry. This allows us to further differentiate the band crossings by the degeneracy along lines and planes that emanate from the high-symmetry point, and also to compute topological invariants. For point degeneracies, we computed the monopole charge of the band-crossing; for line nodes, we computed the Berry phase of loops encircling the nodes. RESULTS We found that three space groups exhibit symmetry-protected three-band crossings. In two cases, this results in a threefold degenerate point node, whereas the third case results in a line node away from the high-symmetry point. These crossings are required to have a nonzero Chern number and hence display surface Fermi arcs. However, upon applying a magnetic field, they have an unusual Landau level structure, which distinguishes them from single and double Weyl points. Under the action of spatial symmetries, these fermions transform as spin-1 particles, as a consequence of the interplay between nonsymmorphic space group symmetries and spin. Additionally, we found that six space groups can host sixfold degeneracies. Two of these consist of two threefold degeneracies with opposite chirality, forced to be degenerate by the combination of time reversal and inversion symmetry, and can be described as “sixfold Dirac points.” The other four are distinct. Furthermore, seven space groups can host eightfold degeneracies. In two cases, the eightfold degeneracies are required; all bands come in groups of eight that cross at a particular point in the BZ. These two cases also exhibit fourfold degenerate line nodes, from which other semimetals can be derived: By adding strain or a magnetic field, these line nodes split into Weyl, Dirac, or line node semimetals. For all the three-, six- and eight-band crossings, nonsymmorphic symmetries play a crucial role in protecting the band crossing. Last, we found that seven space groups may host fourfold degenerate “spin-3/2” fermions at high symmetry points. Like their spin-1 counterparts, these quasiparticles host Fermi surfaces with nonzero Chern number. Unlike the other cases we considered, however, these fermions can be stabilized by both symmorphic and nonsymmorphic symmetries. Three space groups that host these excitations also host unconventional fermions at other points in the BZ. We propose nearly 40 candidate materials that realize each type of fermion near the Fermi level, as verified with ab initio calculations. Seventeen of these have been previously synthesized in single-crystal form, whereas others have been reported in powder form. CONCLUSION We have analyzed all types of fermions that can occur in spin-orbit coupled crystals with time-reversal symmetry and explored their topological properties. We found that there are several distinct types of such unconventional excitations, which are differentiated by their degeneracies at and along high-symmetry points, lines, and surfaces. We found natural generalizations of Weyl points: three- and four-band crossings described by a simple k · S Hamiltonian, where S i is the set of spin generators in either the spin-1 or spin-3/2 representations. These points carry a Chern number and, consequently, can exhibit Fermi arc surface states. We also found excitations with six- and eightfold degeneracies. These higher-band crossings create a tunable platform to realize topological semimetals by applying an external magnetic field or strain to the fourfold degenerate line nodes. Last, we propose realizations for each species of fermion in known materials, many of which are known to exist in single-crystal form.

A quantum Newton's cradle

Abstract: It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

Classification of stable three-dimensional Dirac semimetals with nontrivial topology

Abstract: A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries We show that there are two distinct classes of 3D Dirac SMs In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant

Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography

Abstract: We compute the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number Q. We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low-temperature energy and Q fluctuations. We obtain higher-dimensional generalizations of the SYK models which display disordered metallic states without quasiparticle excitations, and we deduce their thermoelectric transport coefficients. We also examine the corresponding properties of Einstein-Maxwell-axion theories on black brane geometries which interpolate from either AdS4 or AdS5 to an AdS2×R2 or AdS2×R3 near-horizon geometry. These provide holographic descriptions of nonquasiparticle metallic states without momentum conservation. We find a precise match between low-temperature transport and thermodynamics of the SYK and holographic models. In both models, the Seebeck transport coefficient is exactly equal to the Q derivative of the entropy. For the SYK models, quantum chaos, as characterized by the butterfly velocity and the Lyapunov rate, universally determines the thermal diffusivity, but not the charge diffusivity.