Article
Physics, Condensed Matter
R. N. Lira, P. S. Riseborough, J. Silva-Valencia, M. S. Figueira
Summary: In this study, we employ the cumulant Green's functions method to analyze the single-band Hubbard model. By diagonalizing a cluster and using cumulants, we obtain the full Green's functions for the lattice. Our results are benchmarked against other methods and show that the cumulative Green's function method provides accurate results for various parameters in Hubbard models and other strongly correlated models.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2023)
Article
Physics, Multidisciplinary
R. N. Lira, P. S. Riseborough, J. Silva-Valencia, M. S. Figueira
Summary: We study the single-band one-dimensional Hubbard model in an arbitrary magnetic field and obtain the ground-state phase diagram in chemical potential vs. magnetic field coordinates. In addition, we demonstrate the application of the CGFM by constructing a single-electron transistor with spin-polarised conductance using a cluster as a correlated quantum dot connected to correlated leads.
Article
Multidisciplinary Sciences
Peizhi Mai, Seher Karakuzu, Giovanni Balduzzi, Steven Johnston, Thomas A. Maier
Summary: The observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method demonstrates that they survive in the doped Hubbard model in the thermodynamic limit.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Physics, Multidisciplinary
Hiroki Nishizawa
Summary: We investigate the excitation spectrum and momentum distribution of the ionic Bose-Hubbard model and derive Green's functions in different phases. The excitation spectrum has gapped and gapless modes in the superfluid and supersolid phases. The momentum distribution shows a peak at the zone corner in the supersolid phase and the charge density wave phase near the phase boundary, which can be explained by the excitation spectrum and spectral weights of hole modes.
Article
Computer Science, Interdisciplinary Applications
Nail A. Gumerov, Ramani Duraiswami
Summary: The paper introduces and studies the Green's functions for the Laplace equation on an infinite plane with a circular hole satisfying the Dirichlet and Neumann boundary conditions. These functions enable solutions to boundary value problems in domains with locally rough surfaces, considering arbitrary positive and negative ground elevations. Integral and series representations of the Green's functions are provided, and an efficient computational technique based on the boundary element method with fast multipole acceleration is developed, with numerical studies of benchmark problems presented.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Elena Tartaglia, Pasquale Calabrese, Bruno Bertini
Summary: We investigate the real-time evolution of the Hubbard model in the limit of infinite coupling, and determine the dynamics of occupation states in the occupation basis by considering the correlations in the tight-binding model. We find simplified expressions for the time evolution of the total density of particles and the two-point functions of spin-full fermions in terms of correlations of the tight binding model.
Article
Optics
A. Silant'ev
Summary: In this study, anticommutator Green's functions and energy spectra of C-80 fullerene and endohedral fullerene Y3N@C-80 with symmetry groups I-h were obtained in an analytical form within the Hubbard model in the mean-field approximation. Group-theory methods were used to classify the energy states and determine the allowed transitions in the energy spectra of C-80 and Y3N@C-80 molecules with symmetry groups I-h.
OPTICS AND SPECTROSCOPY
(2022)
Article
Chemistry, Physical
Kazuo Takatsuka, Yasuki Arasaki
Summary: In this paper, the intra- and inter-molecular electronic energy current is investigated by defining the probability current of electronic energy, referred to as energy flux. A numerical example of highly excited nonadiabatic electron wavepacket dynamics of a boron cluster B-12 is presented to demonstrate the potential applications in electronic energy transfer phenomena, including chemical reaction dynamics.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
R. S. Souza, Axel Pelster, F. E. A. dos Santos
Summary: This study analyzes the distinction between three different ground states of a system of spinless bosons with short-range interactions subjected to a random potential using the disordered Bose-Hubbard model. The criteria for identifying the superfluid, Mott-insulator, and Bose-glass phases at finite temperatures are discussed, and field theoretical considerations are used to construct a diagrammatic hopping expansion to the Green's function. By summing subsets of diagrams, the condition for long-range correlations leading to the phase boundary between superfluid and insulating phases is found. This analysis goes beyond mean-field theory results for the classification of these different ground states.
NEW JOURNAL OF PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Byungkyun Kang, Corey Melnick, Patrick Semon, Siheon Ryee, Myung Joon Han, Gabriel Kotliar, Sangkook Choi
Summary: The recent discovery of superconductivity in Nd1-δSrδNiO2 has attracted strong attention to correlated quantum materials. From a theoretical perspective, this provides an opportunity to uncover hidden physics in such unconventional superconducting materials. Through first principles calculations, we investigate the temperature and doping dependence of the local spectrum and various susceptibilities, revealing the presence of a Hund's metallic phase in the Ni-e(g) orbitals induced by the onsite Hund's coupling in Ni-d orbitals. Our findings suggest a new class of Hund's metals with potential implications for correlated two orbital systems away from half-filling.
NPJ QUANTUM MATERIALS
(2023)
Article
Physics, Multidisciplinary
A. B. Klyuchantsev, D. M. Dzebisashvili
Summary: The paper develops a theory of tunneling electron transport through atomic-scale systems with strong interaction, based on a diagram technique for nonequilibrium Green's functions. The use of Hubbard operators allows for a universal diagonal form of the quantum dot's Hamiltonian and its coupling with two leads. Modified rules of the diagram technique for Hubbard operators are required when all operators are defined for the same site. The theory is applied to calculate the current-voltage characteristics of the single-impurity Anderson model with infinite Coulomb repulsion, showing the emergence of a dip in the density of states and a peculiar feature in the bias voltage dependence of the differential conductivity.
Article
Engineering, Electrical & Electronic
Chunhui Zhu, Zhangqi Yang, Lijun Liu, Longfang Ye, Qing Huo Liu
Summary: This work focuses on the numerical computation of the pulse Green's function (PGF) that arises from electromagnetic radiation and scattering of bodies of revolutions (BoR). The aim is to improve computational efficiency for large-scale BoR problems. The study achieves spectral accuracy for PGF computation using high order Taylor expansions and overcomes the limitations of traditional methods, leading to significant savings in computational expenses as shown by numerical simulations.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2023)
Article
Geochemistry & Geophysics
He Tang, Wenke Sun
Summary: This study presents a set of analytical equations for an infinite series involving associated low-order Legendre functions, based on the generating function, with nearly sixty equations carefully verified and confirmed for accuracy and effectiveness. The open-source code written in Wolfram language, GNU Octave/MATLAB, and Fortran-90 is available on GitHub.
JOURNAL OF GEODESY
(2021)
Article
Computer Science, Interdisciplinary Applications
Bo Peng, Ajay Panyala, Karol Kowalski, Sriram Krishnamoorthy
Summary: GFCC calculations are limited by expensive higher dimensional tensor contractions, interprocess communication, and load imbalance on scientific computing clusters. This study presents a numerical library prototype designed for large-scale GFCC calculations with a focus on improving scalability and efficiency. The performance of the library is demonstrated through profiling analysis of running GFCC calculations on remote computing clusters.
COMPUTER PHYSICS COMMUNICATIONS
(2021)
Article
Nanoscience & Nanotechnology
Yu P. Chuburin, T. S. Tinyukova
Summary: This study analytically investigates the conditions and properties of zero-energy states in the Kitaev chain model. They find that in finite chains, zero-energy states exist only when the chemical potential is greater than the superconducting pairing potential and the number of sites is odd, while in semi-infinite chains, a single stable Majorana state exists as long as the superconducting pairing potential is greater than the chemical potential.
PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES
(2023)
Article
Multidisciplinary Sciences
Neel Malvania, Yicheng Zhang, Yuan Le, Jerome Dubail, Marcos Rigol, David S. Weiss
Summary: The theory of generalized hydrodynamics (GHD) shows promise in efficiently simulating nearly integrable systems, as demonstrated in experiments with ultracold 1D Bose gases. The results indicate that GHD can accurately describe the quantum dynamics of such systems, even with low particle numbers and rapid density changes.
Article
Physics, Multidisciplinary
Asmi Haldar, Krishnanand Mallayya, Markus Heyl, Frank Pollmann, Marcos Rigol, Arnab Das
Summary: Quantum phase transitions are important for understanding the distinct properties exhibited by matter at very low temperatures upon small changes in microscopic parameters. Locating these transitions accurately is challenging, but a new method involving sudden quenches to force systems out of equilibrium shows promise. The transitions leave distinctive features in intermediate-time dynamics and equilibrated local observables, with effective temperature showing minima near quantum critical points. Further research will focus on testing these results in experiments with Rydberg atoms and exploring nonequilibrium signatures of quantum critical points in models with topological transitions.
Article
Multidisciplinary Sciences
Xiqiao Wang, Ehsan Khatami, Fan Fei, Jonathan Wyrick, Pradeep Namboodiri, Ranjit Kashid, Albert F. Rigosi, Garnett Bryant, Richard Silver
Summary: In this study, Wang et al. demonstrate the control of electron ensembles and probing of many-body states in a 3 x 3 array of single/few-dopant quantum dots in silicon. By tuning lattice constants, they observe the finite-size analogue of a transition from metallic to Mott insulating behavior. These results open up new possibilities for simulating interacting fermionic models using engineered artificial lattices.
NATURE COMMUNICATIONS
(2022)
Article
Multidisciplinary Sciences
Yuan Le, Yicheng Zhang, Sarang Gopalakrishnan, Marcos Rigol, David S. Weiss
Summary: Hydrodynamics accurately describe relativistic heavy-ion collision experiments well before local thermal equilibrium is established. This unexpectedly rapid onset of hydrodynamics, called hydrodynamization, occurs when an interacting quantum system is quenched. During hydrodynamization, energy gets redistributed across different energy scales. Local prethermalization, which is local equilibration among momentum modes, can be observed after hydrodynamization. The timescale for local prethermalization has not been studied experimentally and existing theories cannot quantitatively model it.
Correction
Multidisciplinary Sciences
Yuan Le, Yicheng Zhang, Sarang Gopalakrishnan, Marcos Rigol, David S. Weiss
Article
Physics, Multidisciplinary
Patrycja Lydzba, Marcin Mierzejewski, Marcos Rigol, Lev Vidmar
Summary: Equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble are required for thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems. We provide evidence that observables exhibiting eigenstate thermalization in single-particle sectors equilibrate in many-body sectors of quantum-chaotic quadratic models. However, the same observables do not exhibit eigenstate thermalization in many-body sectors, indicating the need for the generalized Gibbs ensemble.
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Fluids & Plasmas
M. Kliczkowski, R. Swietek, L. Vidmar, M. Rigol
Summary: This article investigates the agreement between the average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians and that of random pure states. It is found that the leading terms are identical, but the differences in subleading terms remain unclear. State-of-the-art full exact diagonalization calculations are conducted on clean spin-1/2 XYZ and XXZ chains to determine the maximally chaotic regime. The study reveals that the negative O(1) correction for the average entanglement entropy is slightly larger than that predicted for random pure states, and a simple expression is derived to describe the ν dependence of the O(1) deviation.
Article
Optics
Kuan-Yu Li, Yicheng Zhang, Kangning Yang, Kuan-Yu Lin, Sarang Gopalakrishnan, Marcos Rigol, Benjamin L. Lev
Summary: We investigate the impact of tunable integrability-breaking dipole-dipole interactions on the equilibrium states of 1D Bose gases of dysprosium at low temperatures. Our experimental results show that in the strongly correlated Tonks-Girardeau regime, rapidity and momentum distributions are unaffected by the dipolar interactions. However, significant changes occur when the strength of the contact interactions is decreased. We propose a model that captures the main experimental observations by considering the system as an array of 1D gases with only contact interactions, dressed by the contribution of the short-range part of the dipolar interactions.
Article
Materials Science, Multidisciplinary
Xiaodong Jin, Yuhai Liu, Rubem Mondaini, Marcos Rigol
Summary: This study investigates the superconductor-insulator transition (SIT) in the attractive honeycomb Hubbard model with a staggered potential. The results show that the lowest-energy charge excitations in the SIT are bosonic, but transition to fermionic as the staggered potential strength increases. The study also reveals that the SIT belongs to the 3D-XY universality class, similar to its square lattice counterpart.
Article
Physics, Fluids & Plasmas
Yicheng Zhang, Lev Vidmar, Marcos Rigol
Summary: This study investigates the statistical properties of off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. It is found that these matrix elements are dense in the spin-1/2 XXZ chain, while being sparse in noninteracting systems. The distribution of off-diagonal matrix elements in the quasimomentum occupation of hard-core bosons in one dimension is well described by generalized Gamma distributions, irrespective of translational invariance but not in the presence of localization. Additionally, the off-diagonal matrix elements of observables in the spin-1/2 XXZ model can be well described by a generalized Gamma distribution.
Article
Quantum Science & Technology
Eugenio Bianchi, Lucas Hackl, Mario Kieburg, Marcos Rigol, Lev Vidmar
Summary: The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians can serve as a diagnostic of quantum chaos and integrability. This tutorial provides a pedagogical introduction to the entanglement entropy of typical pure states and typical pure Gaussian states, highlighting the differences between them. It also discusses the effect of particle-number conservation on the entanglement entropy.
Article
Materials Science, Multidisciplinary
Patrycja Lydzba, Yicheng Zhang, Marcos Rigol, Lev Vidmar
Summary: The matrix elements of local and nonlocal operators in the single-particle eigenstates of two quantum-chaotic quadratic Hamiltonians exhibit eigenstate thermalization for normalized observables. Specifically, the diagonal matrix elements show vanishing eigenstate-to-eigenstate fluctuations, with their variance proportional to the inverse Hilbert space dimension. The ratio between the variance of diagonal and off-diagonal matrix elements is 2, as predicted by random matrix theory.
Article
Materials Science, Multidisciplinary
Jacob Park, Ehsan Khatami
Summary: This research utilized numerical methods to study the thermodynamic properties of the disordered Fermi-Hubbard model on different geometries and explored the effects of disorder on the system properties.
Article
Materials Science, Multidisciplinary
Patrycja Lydzba, Marcos Rigol, Lev Vidmar
Summary: The study presents an analytic expression for the entanglement entropy of many-body eigenstates of random quadratic Hamiltonians, and explores its applicability to local Hamiltonians and those without particle-number conservation. The results provide new theoretical support and extensions for understanding entanglement entropy in quantum systems.
Article
Optics
Yang Ge, Marcos Rigol
Summary: In finite systems driven across topological phase transitions, the Chern number and Bott index exhibit different behaviors depending on boundary conditions and lattice commensurability. The scaling of the fields at which these indices change shows Landau-Zener and near-adiabatic regimes based on drive speed and system size. The dc Hall response can detect topological phase transitions independently of the behavior of the topological indices.
