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arXiv:2001.10526 · Physical review. B./Physical review. B

The Mott transition as a topological phase transition

Sudeshna Sen, Patrick J. Wong, Andrew K. Mitchell

Published Aug 14, 2020• 18 citations
arXivHTMLPDF

Abstract

The Mott transition is a classic paradigm in quantum many-body physics, in which electronic interactions can produce an insulating state. By contrast, a nontrivial band-structure topology in condensed matter systems leads to a topological insulator. Here, the authors make a connection between the seemingly disparate physics of these systems, showing that the Mott transition can be understood as a topological transition, and the Mott insulating state manifests a hitherto hidden topology in the interaction self-energy.

DOI
10.1103/physrevb.102.081110

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The Mott transition is a classic paradigm in quantum many-body physics, in which electronic interactions can produce an insulating state. By contrast, a nontrivial band-structure topology in condensed matter systems leads to a topological insulator. Here, the authors make a connection between the seemingly disparate physics of these systems, showing that the Mott transition can be understood as a topological transition, and the Mott insulating state manifests a hitherto hidden topology in the interaction self-energy.
Abstract: The metal–insulator transition (MIT) constitutes one of the most profound and persistent problems in condensed matter physics, sitting at the intersection of electronic structure theory, many-body physics, and emergent quantum phenomena. Conventional band theory, which successfully classifies materials as metals or insulators according to the filling of their electronic bands, fails dramatically when confronted with a class of compounds transition metal oxides chief among them that ought to be metallic by band-counting arguments yet are robustly insulating in the laboratory. The resolution of this paradox required abandoning the independent-electron picture entirely and recognizing that strong Coulomb repulsion between electrons can, by itself, drive localization. This insight, formalized by Mott and later distilled into the Hubbard model, established correlation-driven insulation as a phenomenon distinct from band insulation. The present paper offers a theoretical exploration of the MIT problem, tracing its conceptual development from the Mott criterion through the Hubbard Hamiltonian, the Brinkman–Rice scenario of quasiparticle mass divergence, and the watershed development of dynamical mean-field theory (DMFT), which rendered the Mott transition quantitatively tractable for the first time. We argue that the competition between the electronic bandwidth and the on-site interaction encoded in the ratio U/W provides the unifying organizing principle for the field. Building toward the modern frontier, we examine how the Mott transition connects to quantum phase transitions and quantum criticality, where zero-temperature instabilities governed by quantum rather than thermal fluctuations produce non-Fermi-liquid behavior and anomalous scaling. Case studies of vanadium oxides, rare-earth nickelates, and doped cuprates illustrate the diversity and subtlety of real correlated materials. We conclude that the MIT remains a central and unresolved problem whose continued study is increasingly entangled with the development of quantum materials and quantum technologies. Keywords: Metal–Insulator Transition; Mott Insulator; Strongly Correlated Electrons; Hubbard Model; DMFT; Quantum Criticality; Quantum Materials; Condensed Matter Physics
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting fermionic atoms in a disordered optical lattice. We find that the topological Anderson and Mott insulators in the noninteracting and clean limits can be adiabatically connected without gap closing in the phase diagram of our model. Lying between the two phases, we uncover a disordered correlated topological insulator, which is induced from a trivial band insulator by the combination of disorder and interaction, as the generalization of topological Anderson insulators to the many-body interacting regime. The phase diagram is determined by computing various topological properties and confirmed by unsupervised and automated machine learning. We develop an approach to provide a unified and clear description of topological phase transitions driven by interaction and disorder. The topological phases can be detected from disorder-/interaction-induced edge excitations and charge pumping in optical lattices.
A fundamental open problem in condensed-matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are six interacting electronic topological insulators that have no noninteracting counterpart. Combined with the previously known band insulators, these produce a total of eight topologically distinct phases. Two of the six interacting topological insulators can be described as Mott insulators in which the electron spins form spin analogs of the topological band insulator. The remaining phases are obtained as combinations of these two "topological paramagnets" and the topological band insulator. We prove that these eight phases form a complete list of all possible interacting topological insulators and discuss their experimental signatures.
We investigate properties of a topological Mott insulator in one dimension by examining the bulk topological invariant and the entanglement spectrum of a correlated electron model. We clarify how gapless edge states in a noninteracting topological band insulator evolve into spinon edge states in a topological Mott insulator. Furthermore, we propose a topological Mott transition, which is a new type of topological phase transition which has never been observed in free fermion systems. This unconventional transition occurs in spin liquid phases in the Mott insulator and is accompanied by zeros of the single-electron Green's function and a gap closing in the spin excitation spectrum.
Weyl semimetals are three-dimensional, topologically protected, gapless phases which show exotic phenomena such as Fermi arc surface states or negative magnetoresistance. It is an open question whether interparticle interactions can turn the topological semimetal into a topologically nontrivial Mott-insulating phase. We investigate an experimentally motivated model for Weyl physics of cold atoms in optical lattices, with the main focus on interaction effects and topological properties, by means of dynamical mean-field theory. We characterize topological phases by numerically evaluating the Chern number via the Ishikawa-Matsuyama formula for interacting phases. Within our studies, we find that the Chern numbers become trivial when interactions lead to insulating behavior. For a deeper understanding of the Weyl-semimetal-to-Mott-insulator topological phase transition, we evaluate the topological properties of quasiparticle bands as well as so-called blind bands. Finally, we consider a system with an open boundary along one spatial direction in order to study correlation effects of surface states. In a narrow regime close to the topological phase transition, we find a correlation-induced state in which the surface becomes metallic while the bulk is semimetallic.
Correlated electronic systems involve strong shortrange repulsion. At integer filling, the primary effect of correlation is the emergence of an insulating state where band theory predicts a metal. Understanding the transition from a metal to this ‘Mott insulator’, as interaction strength is increased, and the effect of doping the Mott state, are classic problems in quantum many-body physics. They have been explored for decades, starting with the approximate solutions of Hubbard. The real breakthrough came in the 1990s with the advent of dynamical mean field theory, which mapped the correlated system to an embedded single site, and described the detailed spectral evolution across the Mott transition. The only deficiency in this approach is the neglect of spatial correlations, and, possibly, the lack of some ‘visual intuition’ about the transition. We discuss a complementary approach, which provides a reasonable description of Mott physics in a real-space setting and allows a certain degree of visualization. This article provides a pedagogical review of our approach and presents some illustrative results.