Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions
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The phenomenon of T-linear resistivity commonly observed in a number of strange metals has been widely seen as evidence for the breakdown of the quasiparticle picture of metals. This study shows that a recently discovered H/T scaling relationship in the magnetoresistance of the strange metal BaFe 2 (As 1- x P x ) 2 is independent of the relative orientations of current and magnetic field. Rather, its magnitude and form depend only on the orientation of the magnetic field with respect to a single crystallographic axis: the direction perpendicular to the magnetic iron layers. In this work, this finding suggests that the magnetotransport scaling does not originate from the conventional averaging or orbital velocity of quasiparticles as they traverse a Fermi surface, but rather from dissipation arising from two-dimensional correlations.
A powerful perspective in understanding nonequilibrium quantum dynamics is through the time evolution of its entanglement content. Yet apart from a few guiding principles for the entanglement entropy,to date, much less is known about the refined characteristics of entanglement propagation. In this paper we unveil signatures of the entanglement evolving and information propagating out of equilibrium, from the view of the entanglement Hamiltonian. We investigate quantum quench dynamics of prototypical Bose-Hubbard model using state-of-the-art numerical technique combined with conformal field theory. Before reaching equilibrium, it is found that a current operator emerges in the entanglement Hamiltonian, implying that entanglement spreading is carried by particle flow. In the long-time limit the subsystem enters a steady phase, evidenced by the dynamic convergence of the entanglement Hamiltonian to the expectation of a thermal ensemble. Importantly, the entanglement temperature in steady state is spatially independent,which provides an intuitive trait of equilibrium. These findings not only provide crucial information on how equilibrium statistical mechanics emerges in many-body dynamics, but also add a tool to exploring quantum dynamics from the perspective of the entanglement Hamiltonian.
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Studies on quantum algorithms for ground-state energy estimation often assume perfect ground-state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here, we address that problem in two ways: by faster preparation of matrix-product-state (MPS) approximations and by more efficient filtering of the prepared state to find the ground-state energy. We show how to achieve unitary synthesis with a Toffoli complexity about 7 × lower than that in prior work and use that to derive a more efficient MPS-preparation method. For filtering, we present two different approaches: sampling and binary search. For both, we use the theory of window functions to avoid large phase errors and minimize the complexity. We find that the binary-search approach provides better scaling with the overlap at the cost of a larger constant factor, such that it will be preferred for overlaps less than about 0.003 . Finally, we estimate the total resources to perform ground-state energy estimation of Fe - S cluster systems, including the Fe Mo cofactor by estimating the overlap of different MPS initial states with potential ground states of the Fe Mo cofactor using an extrapolation procedure. With a modest MPS bond dimension of 4000 , our procedure produces an estimate of approximately 0.9 overlap squared with a candidate ground state of the Fe Mo cofactor, producing a total resource estimate of 7.3 × 10 10 Toffoli gates; neglecting the search over candidates and assuming the accuracy of the extrapolation, this validates prior estimates that have used perfect ground-state overlap. This presents an example of a practical path to prepare states of high overlap in a challenging-to-compute chemical system. Published by the American Physical Society 2025
The thermal evolution of the conductivity of a VO{sub 2} film and database-obtained band gap E{sub g} of film nanocrystallites is traced in the temperature range of –196°C < T < 100°C (77 K < T < 273 K); the level position of donor impurity centers is determined to be E{sub d} = 0.04 eV. It is shown that energy E{sub g} decreases from 0.8 to ∼0 eV with an increase in temperature in the range of 273 K < T < 300 K, which is caused by the narrowing of the energy gap due to correlation effects and considered as the temperature-extended Mott “insulator–metal” electron phase transition with the monoclinic lattice symmetry retained. The subsequent jump in the symmetry from monoclinic to tetragonal with a further increase in temperature is considered as the Peierls structural phase transition, the temperature of which is in the vicinity of 340 K and determined by the size effects, nonstoichiometry of VO{sub 2} film nanocrystallites, and degree of their adhesion to the substrate.
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The goal of this project was to develop a new formalism for the correlated electron problem, which we call, the Multi Scale Many Body formalism. This report will focus on the work done at the Louisiana State University (LSU) since the mid term report. The LSU group moved from the University of Cincinnati (UC) to LSU in the summer of 2008. In the last full year at UC, only half of the funds were received and it took nearly two years for the funds to be transferred from UC to LSU . This effectively shut down the research at LSU until the transfer was completed in 2011, there were also two no-cost extensions of the grant until August of this year. The grant ended for the other SciDAC partners at Davis and ORNL in 2011. Since the mid term report, the LSU group has published 19 papers [P1-P19] acknowledging this SciDAC, which are listed below. In addition, numerous invited talked acknowledged the SciDAC. Below, we will summarize the work at LSU since the mid-term report and mainly since funding resumed. The projects include the further development of multi-scale methods for correlated systems (1), the study of quantum criticality at finite doping in the Hubbard model (2), the description of a promising new method to study Anderson localization with a million-fold reduction of computational complexity!, the description of other projects (4), and (5) a workshop to close out the project that brought together exascale program developers (Stellar, MPI, OpenMP,...) with applications developers.
Basic-Energy Sciences of the Department of Energy (BES/DOE) has made large investments in x-ray sources in the U.S. (NSLS-II, LCLS, NGLS, ALS, APS) as powerful enabling tools for opening up unprecedented new opportunities for exploring properties of matter at various length and time scales. The coming online of the pulsed photon source literally allows us to see and follow the dynamics of processes in materials at their natural timescales. There is an urgent need therefore to develop theoretical methodologies and computational models for understanding how x-rays interact with matter and the related spectroscopies of materials. The present project addressed aspects of this grand challenge of X-ray science. In particular, our Collaborative Research Team (CRT) focused on understanding and modeling of elastic and inelastic resonant X-ray scattering processes. We worked to unify the three different computational approaches currently used for modeling X-ray scattering—density functional theory, dynamical mean-field theory, and small-cluster exact diagonalization—to achieve a more realistic material-specific picture of the interaction between X-rays and complex matter. To achieve a convergence in the interpretation and to maximize complementary aspects of different theoretical methods, we concentrated on the cuprates, where most experiments have been performed. Our team included both US and international researchers, and it fostered new collaborations between researchers currently working with different approaches. In addition, we developed close relationships with experimental groups working in the area at various synchrotron facilities in the US. Our CRT thus helped toward enabling the US to assume a leadership role in the theoretical development of the field, and to create a global network and community of scholars dedicated to X-ray scattering research.
We propose a method of implementing projected wave functions for second-quantized auxiliary-field quantum Monte Carlo (AFQMC) techniques. The method is based on expressing the two-body projector as one-body terms coupled to binary Ising fields. To benchmark the method, we choose to study the two-dimensional (2D) one-band Hubbard model with repulsive interactions using the constrained-path MC (CPMC). The CPMC uses a trial wave function to guide the random walks so that the so-called fermion sign problem can be eliminated. The trial wave function also serves as the importance function in Monte Carlo sampling. As such, the quality of the trial wave function has a direct impact to the efficiency and accuracy of the simulations.
The research supported by this grant focused on the quantum mechanical theory of the electrons in materials and molecules. Progress was made in dealing with electronic correlation effects in the ground state energy of molecular systems, and with topological concepts to classify the electronic state of molecules and materials, including excitation and transport properties. The physical and chemical properties of molecules and materials derive from their electronic structure, but the latter cannot be calculated exactly even with the most powerful computers because the computational cost of solving the exact equations of quantum mechanics increases exponentially with the number of electrons. The exponential cost originates from the correlations among the electrons that repel each other via Coulombic forces. In this project we have developed a new functional approximation for the ground state electronic energy that includes explicitly, and in a controllable way, the effects of the interelectronic correlations. In addition we have further developed topological concepts for classifying the electronic states of periodic ring molecules and solids. Topological concepts are very powerful because they allow us to predict subtle properties of materials and molecules using very general geometrical properties of the electron wavefunctions that do not depend on the quantitative details of the electronic interactions, which are very difficult to calculate with high accuracy. The development of a new class of controlled functional approximations for the ground state energy of molecules and materials was the main goal of the project. It has been fulfilled with the formulation of the occupation-probabilities natural orbital functional theory (OP-NOFT). This approach introduces new theoretical concepts but practical application has proved to be harder than anticipated. So far it has been utilized only at its lowest level of approximation in the context of relatively small molecules (with up to 16 atoms). The study of topological properties of the electron wavefunctions in materials was not proposed in the original proposal but was prompted during the funding period by our interaction with leading experimental groups in materials chemistry and physics at Princeton University.
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