 Award ID(s):
 2116679
 NSFPAR ID:
 10429848
 Date Published:
 Journal Name:
 Quantum
 Volume:
 7
 ISSN:
 2521327X
 Page Range / eLocation ID:
 1004
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Quantum manybody systems involving bosonic modes or gauge fields have infinitedimensional local Hilbert spaces which must be truncated to perform simulations of realtime dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and nonabelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ − 1 , an exponential improvement over previous bounds based on energy conservation. For the HubbardHolstein model, we numerically compute a bound on Λ that achieves accuracy ϵ , obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ = polylog ( ϵ − 1 ) .more » « less

BACKGROUND Landau’s Fermi liquid theory provides the bedrock on which our understanding of metals has developed over the past 65 years. Its basic premise is that the electrons transporting a current can be treated as “quasiparticles”—electronlike particles whose effective mass has been modified, typically through interactions with the atomic lattice and/or other electrons. For a long time, it seemed as though Landau’s theory could account for all the manybody interactions that exist inside a metal, even in the socalled heavy fermion systems whose quasiparticle mass can be up to three orders of magnitude heavier than the electron’s mass. Fermi liquid theory also lay the foundation for the first successful microscopic theory of superconductivity. In the past few decades, a number of new metallic systems have been discovered that violate this paradigm. The violation is most evident in the way that the electrical resistivity changes with temperature or magnetic field. In normal metals in which electrons are the charge carriers, the resistivity increases with increasing temperature but saturates, both at low temperatures (because the quantized lattice vibrations are frozen out) and at high temperatures (because the electron mean free path dips below the smallest scattering pathway defined by the lattice spacing). In “strange metals,” by contrast, no saturation occurs, implying that the quasiparticle description breaks down and electrons are no longer the primary charge carriers. When the particle picture breaks down, no local entity carries the current. ADVANCES A new classification of metallicity is not a purely academic exercise, however, as strange metals tend to be the hightemperature phase of some of the best superconductors available. Understanding hightemperature superconductivity stands as a grand challenge because its resolution is fundamentally rooted in the physics of strong interactions, a regime where electrons no longer move independently. Precisely what new emergent phenomena one obtains from the interactions that drive the electron dynamics above the temperature where they superconduct is one of the most urgent problems in physics, attracting the attention of condensed matter physicists as well as string theorists. One thing is clear in this regime: The particle picture breaks down. As particles and locality are typically related, the strange metal raises the distinct possibility that its resolution must abandon the basic building blocks of quantum theory. We review the experimental and theoretical studies that have shaped our current understanding of the emergent strongly interacting physics realized in a host of strange metals, with a special focus on their posterchild: the copper oxide hightemperature superconductors. Experiments are highlighted that attempt to link the phenomenon of nonsaturating resistivity to parameterfree universal physics. A key experimental observation in such materials is that removing a single electron affects the spectrum at all energy scales, not just the lowenergy sector as in a Fermi liquid. It is observations of this sort that reinforce the breakdown of the singleparticle concept. On the theoretical side, the modern accounts that borrow from the conjecture that strongly interacting physics is really about gravity are discussed extensively, as they have been the most successful thus far in describing the range of physics displayed by strange metals. The foray into gravity models is not just a pipe dream because in such constructions, no particle interpretation is given to the charge density. As the breakdown of the independentparticle picture is central to the strange metal, the gravity constructions are a natural tool to make progress on this problem. Possible experimental tests of this conjecture are also outlined. OUTLOOK As more strange metals emerge and their physical properties come under the scrutiny of the vast array of experimental probes now at our disposal, their mysteries will be revealed and their commonalities and differences cataloged. In so doing, we should be able to understand the universality of strange metal physics. At the same time, the anomalous nature of their superconducting state will become apparent, offering us hope that a new paradigm of pairing of nonquasiparticles will also be formalized. The correlation between the strength of the linearintemperature resistivity in cuprate strange metals and their corresponding superfluid density, as revealed here, certainly hints at a fundamental link between the nature of strange metallicity and superconductivity in the cuprates. And as the gravityinspired theories mature and overcome the challenge of projecting their powerful mathematical machinery onto the appropriate crystallographic lattice, so too will we hope to build with confidence a complete theory of strange metals as they emerge from the horizon of a black hole. Curved spacetime with a black hole in its interior and the strange metal arising on the boundary. This picture is based on the string theory gaugegravity duality conjecture by J. Maldacena, which states that some strongly interacting quantum mechanical systems can be studied by replacing them with classical gravity in a spacetime in one higher dimension. The conjecture was made possible by thinking about some of the fundamental components of string theory, namely Dbranes (the horseshoeshaped object terminating on a flat surface in the interior of the spacetime). A key surprise of this conjecture is that aspects of condensed matter systems in which the electrons interact strongly—such as strange metals—can be studied using gravity.more » « less

Abstract Mesoscopic quantum systems exhibit complex manybody quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, noninteracting theories display a rich landscape of energy states—distinct manyparticle configurations connected by spin and energydependent transition rates. The ways in which these energy states interact is difficult to characterize or predict, especially in regimes of frustration where manybody effects create a multiply degenerate landscape. Here, we use network science to characterize the complex interconnection patterns of these energystate transitions. Using an experimentally verified computational model of electronic transport through quantum antidots, we construct networks where nodes represent accessible energy states and edges represent allowed transitions. We find that these networks exhibit Rentian scaling, which is characteristic of efficient transportation systems in computer circuitry, neural circuitry, and human mobility, and can be used to measure the interconnection complexity of a network. We find that the topological complexity of the state transition networks—as measured by Rent’s exponent— correlates with the amount of current flowing through the antidot system. Furthermore, networks corresponding to points of frustration (due, for example, to spinblockade effects) exhibit an enhanced topological complexity relative to nonfrustrated networks. Our results demonstrate that network characterizations of the abstract topological structure of energy landscapes capture salient properties of quantum transport. More broadly, our approach motivates future efforts to use network science to understand the dynamics and control of complex quantum systems.

The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement1. Although these phases were discovered in a solidstate setting2,3, recent innovations in systems of ultracold neutral atoms—uncharged atoms that do not naturally experience a Lorentz force—allow the synthesis of artificial magnetic, or gauge, fields4,5,6,7,8,9,10. This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in coldatom systems11,12. However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated manybody states4,13,14,15,16,17. Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a twobody system with a chiral band structure. We observe and explain the way in which interparticle interactions induce chirality in the propagation dynamics of particles in a ladderlike, realspace lattice governed by the interacting Harper–Hofstadter model, which describes latticeconfined, coherently mobile particles in the presence of a magnetic field18. We use a bottomup strategy to prepare interacting chiral quantum states, thus circumventing the challenges of a topdown approach that begins with a manybody system, the size of which can hinder the preparation of controlled states. Our experimental platform combines all of the necessary components for investigating highly entangled topological states, and our observations provide a benchmark for future experiments in the fractional quantum Hall regime.more » « less

Abstract Osteological correlates preserve more readily than their soft tissue counterparts in the fossil record; therefore, they can more often provide insight into the soft tissue anatomy of the organism. These insights can in turn elucidate the biology of these extinct organisms. In this study, we reconstruct the pelvic girdle and hind limb musculature of the giant titanosaurian sauropod
Dreadnoughtus schrani based on observations of osteological correlates and Extant Phylogenetic Bracket comparisons. Recovered fossils ofDreadnoughtus exhibit remarkably well‐preserved, well‐developed, and extensive muscle scars. Furthermore, this taxon is significantly larger bodied than any titanosaurian for which a myological reconstruction has previously been performed, rendering this contribution highly informative for the group. All 20 of the muscles investigated in this study are sufficiently well supported to enable reconstruction of at least one division, including reconstruction of the M. ischiocaudalis for the first time in a sauropod dinosaur. In total, 34 osteological correlates were identified on the pelvic girdle and hind limb remains ofDreadnoughtus , allowing the reconstruction of 14 muscles on the basis of Level I or Level II inferences (i.e., not Level I' or Level II' inferences). Comparisons among titanosaurians suggest widespread myological variation, yet potential phylogenetic and other paleobiologic patterns are often obscured by fragmentary preservation, infrequent myological studies, and lack of consensus on the phylogenetic placement of many taxa. However, a ventrolateral accessory process is present on the preacetabular lobe of the ilium in all of the largest titanosauriforms that preserve this skeletal element, suggesting that the presence of this process (representing the origin of the M. puboischiofemoralis internus part II) may be associated with extreme body size. By identifying such myological patterns among titanosauriforms, we can begin to address specific evolutionary and biomechanical questions related to their skeletal anatomy, how they were capable of leaving wide‐gauge trackways, and resulting locomotor attributes unique to this clade.