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The Mott-Hubbard Transition on the D = ∞ Bethe Lattice
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gros, Claudius Wenzel, Wolfgang Valent́ı, Roser Hülsenbeck, Georg Stolze, Joachim |
| Copyright Year | 2006 |
| Abstract | – In view of a recent controversy we investigated the Mott-Hubbard transition in D = ∞ with a novel cluster approach. i) We show that any truncated Bethe lattice of order n can be mapped exactly to a finite Hubbard-like cluster. ii) We evaluate the self-energy numerically for n = 0, 1, 2 and compare with a series of self-consistent equation-of-motion solutions. iii) We find the gap to open continously at the critical Uc ∼ 2.5t * (t ≡ t * / √ 4d). iv) A low-energy theory for the Mott-Hubbard transition is developed and relations between critical exponents are presented. Introduction. – The Mott-Hubbard (MH) transition, as the metal-insulator transition in translationally invariant systems of interacting electrons is called, is little understood at present. The nature of the order parameter remains unresolved and a number of phenomeno-logical scenarios have been proposed to describe the underlying physics. In the Brinkmann-Rice [1] scenario the number of charge carriers drives the MH transition, another view [2] suggests a binding/unbinding transition of doubly-occupied and empty sites as the appropriate model. In this second picture the MH transition coincides with the convergence radius of a large-interaction expansion [3]. The study of interacting electrons in the limit of high dimensions [4, 5] has proven very useful, as both analytical and numerical methods simplify in the limit of infinite dimensions. For instance, Monte Carlo studies [6, 7] are not limited by finite-cluster effects, only by the imaginary-time resolution in infinite dimensions. Here we focus on the zero-temperature half-filled Hubbard model on the infinite-dimensional Bethe lattice in the paramagnetic state(1). A Mott-Hubbard transition is known [7, 8] to occur as a function of interaction strength and has been examined by Quantum Monte Carlo [7], by the iterative perturbation theory [7–10], by self-consistent diagonalization studies [11], by a non-crossing approximation [12] and a modified-equation-of-motion approach [13]. In a recently predicted [10, 11] scenario for the Mott-Hubbard transition the Fermi-liquid effective mass would diverge on the metallic side of the transition, while no precursor of the transition would be seen on the insulating side for any observable, e.g. that the gap would close discontinuously from a finite value to zero at the transition point. Here we want to examine this unusual scenario with a novel approach. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/cond-mat/9312031v2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Approximation Arabic numeral 0 Bethe lattice Bose–Hubbard model Dimensions Electrons Femtometer Fill Hubbard model Imaginary time Interaction Intrinsic drive Iterative method Kosterlitz–Thouless transition Leucaena pulverulenta Modified Huffman coding Monte Carlo method Numerical method Observable Perturbation theory Population Parameter Quantum Monte Carlo Solutions Topological insulator UC Browser |
| Content Type | Text |
| Resource Type | Article |
