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arXiv:2401.03013 · Physical review. B./Physical review. B

Impact of a Lifshitz transition on the onset of spontaneous coherence

Adam Eaton, Dibya Kanti Mukherjee, H. A. Fertig

Published Jul 11, 2024• 1 citation
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Abstract

Lifshitz transitions are topological transitions of a Fermi surface, whose signatures typically appear in the conduction properties of a host metal. Here, we demonstrate, using an extended Falicov-Kimball model of a two-flavor fermion system, that a Lifshitz transition which occurs in the noninteracting limit impacts interaction-induced insulating phases, even though they do not host Fermi surfaces. For strong interactions we find a first-order transition between states of different polarization. This transition line ends in a very unusual quantum critical endpoint, whose presence is stabilized by the onset of interflavor coherence. We demonstrate that the surfaces of maximum coherence in these states reflect the distinct Fermi-surface topologies of the states separated by the noninteracting Lifshitz transition. Experimental realizations of our results are discussed for both electronic and optical lattice systems.

DOI
10.1103/physrevb.110.035132

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Lifshitz transitions are topological transitions of a Fermi surface, whose signatures typically appear in the conduction properties of a host metal. Here, we demonstrate, using an extended Falicov-Kimball model of a two-flavor fermion system, that a Lifshitz transition which occurs in the noninteracting limit impacts interaction-induced insulating phases, even though they do not host Fermi surfaces. For strong interactions we find a first-order transition between states of different polarization. This transition line ends in a very unusual quantum critical endpoint, whose presence is stabilized by the onset of interflavor coherence. We demonstrate that the surfaces of maximum coherence in these states reflect the distinct Fermi-surface topologies of the states separated by the noninteracting Lifshitz transition. Experimental realizations of our results are discussed for both electronic and optical lattice systems.
We consider a two-dimensional model of noninteracting chains of spinless fermions weakly coupled via a small interchain hopping and a repulsive interchain interaction. The phase diagram of this model has a surprising feature: an abrupt change in the Fermi surface as the interaction is increased. We study in detail this metanematic transition and show that the well-known 2122\frac{1}{2}221​-order Lifshitz transition is the critical end point of this first-order quantum phase transition. Furthermore, in the vicinity of the end point, the order parameter has a nonperturbative BCS-type form. We also study a competing crystallization transition in this model and derive the full phase diagram. This physics can be demonstrated experimentally in dipolar ultracold atomic or molecular gases. In the presence of a harmonic trap, it manifests itself as a sharp jump in the density profile.
Anisotropic dipole-dipole interactions between ultracold dipolar fermions break the symmetry of the Fermi surface and thereby deform it. Here we demonstrate that such a Fermi surface deformation induces a topological phase transition---the so-called Lifshitz transition---in the regime accessible to present-day experiments. We describe the impact of the Lifshitz transition on observable quantities such as the Fermi surface topology, the density-density correlation function, and the excitation spectrum of the system. The Lifshitz transition in ultracold atoms can be controlled by tuning the dipole orientation and, in contrast to the transition studied in crystalline solids, is completely interaction driven.
Topological quantum phase transitions are characterized by changes in global topological invariants. These invariants classify many-body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry breaking. For noninteracting electrons, it is well understood that such transitions are continuous and always accompanied by a gap closing in the energy spectrum, given that the symmetries protecting the topological phase are maintained. Here, we demonstrate that a sufficiently strong electron-electron interaction can fundamentally change the situation: we discover a topological quantum phase transition of first-order character in the genuine thermodynamic sense that occurs without a gap closing. Our theoretical study reveals the existence of a quantum critical endpoint associated with an orbital instability on the transition line between a 2D topological insulator and a trivial band insulator. Remarkably, this phenomenon entails unambiguous signatures related to the orbital occupations that can be detected experimentally.
We study the quantum phase transition in f -electron systems as a quantum Lifshitz transition driven by selective Mott localization in a realistic extended Anderson lattice model.Using DMFT, we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s).Fermi surface reconstruction occurs via the interplay between, and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the selective-Mott phase .We show how this naturally leads to scale-invariant responses in transport.Our work is represents a specific (DMFT) realization of the hidden-FL and FL * theories, and holds promise for study of "strange" metal phases in quantum matter.
We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of 'strange' metal phases in quantum matter.
Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two-dimensional Hubbard model with next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. At ${t}^{\ensuremath{'}}\ensuremath{\le}0$, we identify a line of Lifshitz transition points associated with a change in the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects and becomes more singular when ${t}^{\ensuremath{'}}$ becomes more negative. The resulting temperature dependence on the bare ddd-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at ${t}^{\ensuremath{'}}\ensuremath{\le}0$ extends our understanding of the quantum critical region in the phase diagram and shines lights on future investigations of the nature of the quantum critical point in the two-dimensional Hubbard model.