Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
TL;DR: In this paper, the short-range, one-band model for electron correlations in a narrow energy band is solved exactly in the one-dimensional case, and the ground-state energy, wave function, and chemical potentials are obtained, and it is found that the ground state exhibits no conductor-insulator transition as the correlation strength is increased.
Abstract: The short-range, one-band model for electron correlations in a narrow energy band is solved exactly in the one-dimensional case. The ground-state energy, wave function, and the chemical potentials are obtained, and it is found that the ground state exhibits no conductor-insulator transition as the correlation strength is increased.
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TL;DR: In this paper, the authors survey the local density functional formalism and some of its applications and discuss the reasons for the successes and failures of the local-density approximation and some modifications.
Abstract: A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.
3,285 citations
TL;DR: In this article, the properties of entanglement in many-body systems are reviewed and both bipartite and multipartite entanglements are considered, and the zero and finite temperature properties of entangled states in interacting spin, fermion and boson model systems are discussed.
Abstract: Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.
3,096 citations
TL;DR: A review of the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds is presented in this article, with the purpose of providing an updated summary of the extensive literature.
Abstract: The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.
3,077 citations
Cites background from "Absence of Mott Transition in an Ex..."
...…the quasiparticle dispersion in two dimensions is strongly renormalized by the magnetic interaction; second, in one dimension spin-charge separation occurs, and this frees the motion of the holon—an elementary excitation with spin 0 and charge e— from the magnetic interaction (Lieb and Wu, 1968)....
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TL;DR: This paper gives a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of D MRG algorithms in exclusively MPS terms transparent.
Abstract: The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.
2,977 citations
TL;DR: The density matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems as mentioned in this paper.
2,940 citations
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TL;DR: In this paper, the Hartree-Fock approximation of the correlation problem for the d-and f-bands was applied to a simple, approximate model for the interaction of electrons in narrow energy bands.
Abstract: It is pointed out that one of the main effects of correlation phenomena in d- and f-bands is to give rise to behaviour characteristic of the atomic or Heitler-London model. To investigate this situation a simple, approximate model for the interaction of electrons in narrow energy bands is introduced. The results of applying the Hartree-Fock approximation to this model are examined. Using a Green function technique an approximate solution of the correlation problem for this model is obtained. This solution has the property of reducing to the exact atomic solution in the appropriate limit and to the ordinary uncorrelated band picture in the opposite limit. The condition for ferromagnetism of this solution is discussed. To clarify the physical meaning of the solution a two-electron example is examined.
5,151 citations
IBM1
TL;DR: In this paper, the ground-state energy as a function of γ was derived for all γ, except γ = 0, and it was shown that Bogoliubov's perturbation theory is valid when γ is small.
Abstract: A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the solutions of a transcendental equation. The problem has one nontrivial coupling constant, γ. When γ is small, Bogoliubov’s perturbation theory is seen to be valid. In this paper, we explicitly calculate the ground-state energy as a function of γ and show that it is analytic for all γ, except γ=0. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrum—not one as is ordinarily supposed.
2,230 citations
TL;DR: In this paper, the ground-state problem of spin-textonehalf{} fermions is reduced to a generalized Fredholm equation, in a generalized form, by using Bethe's hypothesis.
Abstract: The repulsive $\ensuremath{\delta}$ interaction problem in one dimension for $N$ particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations $R$ of the permutation group ${S}_{N}$. For some $R'\mathrm{s}$ this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-\textonehalf{} fermions is reduced to a generalized Fredholm equation.
2,135 citations
TL;DR: In this paper, the ground-state energy for the electrons in a narrow $s$ band is investigated for arbitrary density of electrons and arbitrary strength of interaction. And the expectation values of the one-particle and twoparticle density matrix are computed for the ferromagnetic and for the nonferromagnetic case.
Abstract: The ground-state wave function for the electrons in a narrow $s$ band is investigated for arbitrary density of electrons and arbitrary strength of interaction. An approximation is proposed which limits all the calculations to counting certain types of configurations and attaching the proper weights. The expectation values of the one-particle and two-particle density matrix are computed for the ferromagnetic and for the non-ferromagnetic case. The ground-state energy is obtained under the assumption that only the intra-atomic Coulomb interaction is of importance. Ferromagnetism is found to occur if the density of states is large at the band edges rather than in the center, and if the intra-atomic Coulomb repulsion is sufficiently strong. The relation of this approximation to certain exact results for one-dimensional models is discussed.
650 citations
TL;DR: In this article, the ground-state energy of an infinite system is studied as a function of the magnetization of the system and the ground state energy of the lattice site.
Abstract: The ground-state energy $2f$ per lattice site for an infinite system is studied as a function of $\ensuremath{\Delta}$ and of the magnetization $y$. Analyticity properties of $f(\ensuremath{\Delta}, y)$ are proved. The behavior of $f(\ensuremath{\Delta}, y)$ at and near $y=0$ and $y=1$ are investigated.
536 citations