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Spin-liquid Mott quantum criticality: Emergence of localized magnetic moments

Jae-Ho Han, Yong-Heum Cho, Ki‐Seok Kim

Published Jun 24, 2016• 0 citations
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Abstract

Emergence of localized magnetic moments in the vicinity of a metal-insulator transition is a non-perturbative phenomenon beyond the description based on the perturbative theoretical framework. Resorting to a recently developed theoretical device called dimensional regularization for the Fermi-surface problem, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Assuming that the spinon Fermi surface can be destabilized across the spin-liquid Mott quantum critical point, we show that such itinerant spinons become localized to result in localized magnetic moments near the spin-liquid Mott quantum critical point. The role of such emergent moments in non-Fermi liquid physics reveals the nature of spin-liquid Mott quantum criticality as novel local quantum criticality, where critical charge dynamics belongs to the inverted XY universality class and critical spin dynamics conforms to a locally critical universality class.

Related papers

Spin-liquid Mott quantum criticality in two dimensions: Destabilization of a spinon Fermi surface and emergence of one-dimensional spin dynamics

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Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted $XY$ universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a $2{k}_{F}$ transfer momentum, where ${k}_{F}$ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.

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Emergence of localized magnetic moments in the vicinity of a metal-insulator transition is a non-perturbative phenomenon beyond the description based on the perturbative theoretical framework. Resorting to a recently developed theoretical device called dimensional regularization for the Fermi-surface problem, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Assuming that the spinon Fermi surface can be destabilized across the spin-liquid Mott quantum critical point, we show that such itinerant spinons become localized to result in localized magnetic moments near the spin-liquid Mott quantum critical point. The role of such emergent moments in non-Fermi liquid physics reveals the nature of spin-liquid Mott quantum criticality as novel local quantum criticality, where critical charge dynamics belongs to the inverted XY universality class and critical spin dynamics conforms to a locally critical universality class.
Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted XYXYXY universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a 2kF2{k}_{F}2kF​ transfer momentum, where kF{k}_{F}kF​ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.
Gapless spin liquids have recently been observed in several frustrated Mott insulators, with elementary spin excitations-"spinons"-reminiscent of degenerate Fermi systems. However, their precise role at the Mott point, where charge fluctuations begin to proliferate, remains controversial and ill understood. Here we present the simplest theoretical framework that treats the dynamics of emergent spin and charge excitations on the same footing, providing a new physical picture of the Mott metal-to-insulator transition at half filing. We identify a generic orthogonality mechanism leading to strong damping of spinons, arising as soon as the Mott gap closes. Our results indicate that spinons should not play a significant role within the high-temperature quantum critical regime above the Mott point-in striking agreement with all available experiments.
This article is aimed at a pedagogical introduction to the physics of quantum phase transitions that is unique to metallic systems. It has been recognized for some time that quantum criticality can result in a breakdown of Landau's Fermi liquid theory. Its converse, however, has not been appreciated until very recently: non-Fermi liquid behavior can in turn lead to new classes of quantum phase transition. A concrete example is provided by ``local quantum critical points''. I summarize the theoretical reasoning and experimental evidence for local quantum criticality, in the context of heavy fermion metals. The underlying physics is likely to be relevant to other correlated electron systems including doped Mott insulators.
We study in this paper quantum spin liquid states (QSLs) at the vicinity of the metal-insulator transition. Assuming that the low-energy excitations in the QSLs are labeled by ``spinon'' occupation numbers with the same Fermi surface structure as in the corresponding metal (Fermi-liquid) side, we propose a phenomenological Landau-like low-energy theory for the QSLs and show that the usual U(1)U(1)U(1) QSLs is a representative member of this class of spin liquids. Based on our effective low-energy theory, an alternative picture to the Brinkman-Rice picture of the Mott metal-insulator transition is proposed. The charge, spin, and thermal responses of QSLs are discussed under such a phenomenology.
We revisit Stoner instability, an old problem but in a modern point of view. An idea is to extract out dynamics of directional fluctuations of spins explicitly, resorting to the CP1^{1}1 representation and integrating over their amplitude fluctuations. As a result, we derive an effective field theory for ferromagnetic quantum phase transitions in terms of bosonic spinons and fermionic holons. We show that this effective field theory reproduces overdamped spin dynamics in a paramagnetic Fermi liquid and magnon spectrum in a ferromagnetic Fermi liquid. An interesting observation is that the velocity of spinons becomes zero, approaching the ferromagnetic quantum critical point, which implies emergence of local quantum criticality. Based on this scenario, we predict the ω/Tω/Tω/T scaling behavior near ferromagnetic quantum criticality beyond the conventional scenario of the weak-coupling approach.
We present a theoretical approach to describing the Mott transition of electrons on a two-dimensional lattice that begins with the low-energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations that correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a priori assumptions about other Fermi surface shape fluctuations. Building on insights from the theory of the Mott transition of bosons, we implement this suppression by identifying and condensing vortex degrees of freedom in the phase of the low-energy electron operator. We show that the resulting Mott insulator is a quantum spin liquid with a spinon Fermi surface coupled to a U(1)U(1)U(1) gauge field, which is usually described within a slave particle formulation. Our approach thus provides a coarse-grained treatment of the Mott transition and the proximate spin liquid that is nevertheless equivalent to the standard slave particle construction. This alternate point of view provides further insight into the novel physics of the Mott transition and the spin liquid state that is potentially useful. We describe a generalization that suppresses spin antisymmetric fluctuations of the Fermi surface that leads to a spin-gapped charge metal previously also discussed in terms of slave particle constructions.