Topology of the Fermi Surface Beyond the Quantum Critical Point

Abstract

We examine the nature of phase transitions occurring in strongly correlated Fermi systems at the quantum critical point (QCP) associated with a divergent effective mass. Conventional scenarios for the QCP involving collective degrees of freedom are shown to have serious shortcomings. Working within the original Landau quasiparticle picture, we propose an alternative topological scenario for the QCP, in systems that obey standard Fermi liquid (FL) theory in advance of the QCP. Applying the technique of Poincaré mapping, we analyze the sequence of iterative maps generated by the Landau equation for the single-particle spectrum at zero temperature. It is demonstrated that the Fermi surface is subject to rearrangement beyond the QCP. If the sequence of maps converges, a multi-connected Fermi surface is formed. If it fails to converge, the Fermi surface swells into a volume that provides a measure of entropy associated with formation of an exceptional state of the system characterized by partial occupation of single-particle states and dispersion of their spectrum proportional to temperature. Based on this dual scenario, the thermodynamics of Fermi systems beyond the QCP exhibits striking departures from the predictions of standard FL theory. Mechanisms for the release of the entropy excess of the exceptional state are discussed.

20 pages, 11 figures

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• Identification of Strongly Correlated Spin Liquid in Herbertsmithite
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• Conventional BCS, Unconventional BCS, and Non-BCS Hidden Dineutron Phases in Neutron Matter
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• Different scenarios of topological phase transitions in homogeneous neutron matter
• Fermi surface reconstruction in strongly correlated Fermi systems as a first order phase transition
• Phase Separation in Two-Dimensional Electron Systems: Experimental View
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• Discovering Strongly Correlated Quantum Spin Liquid
• Quantum critical point in high-temperature superconductors
• Magnetic-field-induced reentrance of Fermi-liquid behavior and spin-lattice relaxation rates in YbCu_{5-x}Au_x
• Spontaneous breaking of four-fold rotational symmetry in two-dimensional electronic systems explained as a continuous topological transition
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• Comment on Zeeman-Driven Lifshitz Transition: A Model for the Experimentally Observed Fermi-Surface Reconstruction in YbRh2Si2 (A. Hackl and M. Vojta, Phys. Rev. Lett. 106, 137002 (2011))
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• Fermion condensate generates a new state of matter by making flat bands
• The occurrence of a Mott-like gap in single-particle spectra of electron systems possessing flat bands
• Theory of fermion condensation as an analog of the liquid-drop theory of atomic nuclei
• Ultra spin liquid in $\mathrm{L}{\mathrm{u}}_3\mathrm{C}{\mathrm{u}}_2\mathrm{S}{\mathrm{b}}_3{\mathrm{O}}_{14}$
• A unified quasiparticle approach to the theory of strongly correlated electron liquids