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arXiv:1302.0157 · Physical Review B

Spin liquid states in the vicinity of a metal-insulator transition

Yi Zhou, Tai Kai Ng

Published Oct 21, 2013• 15 citations
arXivHTMLPDF

Abstract

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 $U(1)$ 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.

DOI
10.1103/physrevb.88.165130

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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 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.
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.
The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge-inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state-seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.
The quantum spin liquid (QSL) state of Kitaev-like materials, such as iridium oxides A 2IrO3 and α-RuCl3, has been explored in depth. The half-filled Kitaev–Hubbard model with bond-dependent hopping terms is used to describe the Kitaev-like materials, which is calculated using the state-of-the-art fermionic projected entangled pair states method. We find a QSL phase near the Mott insulator transition, which has a strong first-order transition to the semi-metal phase with the decrease of Hubbard U. We suggest that a promising approach to finding QSL states is by finding iridium oxides that are near the Mott insulator transition.
The quantum spin liquid (QSL) state has been searched intensively in Kitaev-like materials, such as the Iridium oxides A2A_2A2​IrO3_33​ and ααα-RuCl3_33​. The half-filled Kitaev-Hubbard model with bond dependent hopping terms is used to describe the Kitaev-like materials, which is calculated using the state-of-the-art fermionic projected entangled pair states (fPEPS) method. We find a QSL phase near the Mott insulator transition, which has a strong first-order transition to the semi-metal phase with the decrease of Hubbard UUU. We suggest that a promising routine to find the QSL is to find the Iridium oxides that are near the Mott insulator transitions.