Critical-field theory of the Kondo lattice model in two dimensions

2005

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We investigate the quantum phase transition of the O(3) nonlinear σ model without Berry phase in two spacial dimensions. Utilizing the CP 1 representation of the nonlinear σ model, we obtain an effective action in terms of bosonic spinons interacting via compact U(1) gauge fields. Based on the effective field theory, we find that the bosonic spinons are deconfined to emerge at the quantum critical point of the nonlinear σ model. It is emphasized that the deconfinement of spinons is realized in the absence of Berry phase. This is in contrast to the previous study of Senthil et al. [Science 303, 1490[Science 303, (2004], where the Berry phase plays a crucial role, resulting in the deconfinement of spinons. It is the reason why the deconfinement is obtained even in the absence of the Berry phase effect that the quantum critical point is described by the XY ("neutral") fixed point, not the IXY ("charged") fixed point. The IXY fixed point is shown to be unstable against instanton excitations and the instanton excitations are proliferated. At the IXY fixed point it is the Berry phase effect that suppresses the instanton excitations, causing the deconfinement of spinons. On the other hand, the XY fixed point is found to be stable against instanton excitations because an effective internal charge is zero at the neutral XY fixed point. As a result the deconfinement of spinons occurs at the quantum critical point of the O(3) nonlinear σ model in two dimensions.PACS numbers: 75.10. Jm, 71.27.+a, 71.10.Hf, 11.10.Kk I. MOTIVATION AND SUMMARYNature of quantum criticality is one of the central interests in modern condensed matter physics. Especially, deconfined quantum criticality has been proposed in various strongly correlated electron systems such as low dimensional quantum antiferromagnets [1,2,3,4,5,6,7,8] and Kondo systems [9,10,11,12]. In the present paper we investigate one deconfined quantum criticality based on the O(3) nonlinear σ model describing a quantum phase transition from antiferromagnetism to quantum disordered paramagnetism on two dimensional square lattices. This phase transition has been originally analyzed by Bernevig et al. [1]. In the study the authors got to the conclusion that although the appropriate "off-critical" elementary degrees of freedom are given by either spin 1 excitons (gapped paramagnons) in the quantum disordered paramagnetism and spin 1 antiferromagnons in the antiferromagnetism, at the quantum critical point such excitations should break up into more elementary spin 1/2 excitations usually called spinons [1]. Thus, spinons emerge as true, deconfined, elementary excitations right at the quantum critical point. This is the precise meaning of the deconfined quantum criticality in the context of quantum antiferromagnetism. In Fig. 1 schematic phase diagram and proposed elementary excitations in the O(3) nonlinear σ model are shown.This was challenged by Senthil et al. [2]. They claimed that since the phase transition in Ref.[1] is supposed to fall into Landau-Ginzburg-Wilson (LGW ...

Deconfined quantum criticality of theO(3)nonlinearσmodel in two spatial dimensions: A renormalization-group study

2005

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Deconfined quantum criticality in the two-dimensional Kondo lattice model

2005

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We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.PACS numbers: 71.10.Hf, 71.27.+a, 75.30.Mb Nature of quantum criticality is one of the central interests in modern condensed matter physics. Especially, deconfined quantum criticality has been proposed in various strongly correlated electron systems such as low dimensional quantum antiferromagnetism [1,2,3,4,5,6,7,8,9] and heavy fermion liquids [10,11,12,13]. In the present paper we focus our attention on the quantum phase transition from an antiferromagnetic metal to a heavy fermion liquid in the two dimensional Kondo lattice model. In the Landau-Ginzburg-Wilson theoretical frame work the quantum phase transition would belong to the first order because the two phases are characterized by two different order parameters [1]. However, it is well known that there exists a continuous quantum phase transition between the two phases [10,11,12,13]. In this paper we propose that the continuous quantum phase transition can be realized via deconfined quantum criticality, where antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. Near the quantum critical point two kinds of critical fluctuations are expected to arise. One would correspond to critical fluctuations of Kondo singlets and the other, critical antiferromagnetic spin fluctuations. Remarkably, the emergent spinless fermions are associated with critical fluctuations of the Kondo singlets while the critical bosonic spinons result from critical spin fluctuations.We consider the Kondo lattice model in two dimensions [14,15]. In this mapping high energy antiferromagnetic spin fluctuations would induce new interactions between low energy spin degrees of freedom and conduction electrons. We can derive the following expression for the Kondo lattice modelThe local spins are described by the O(3) nonlinear σ model of a low energy spin variable n, where g = 2 √ 2d S a d−1 is a spin stiffness parameter (g −1 ) and c = √ 2dJSa, a velocity of spin waves [14,15]. a is a lattice spacing, S, the value of localized spins, and d, a spatial dimension. Here S = 1/2 and d = 2. The first term in S m is a Berry phase action, where u and x 0 are two parameters in a unit sphere [14,15]. x 0 = cτ is considered to be a rescaled time. The mapping to the nonlinear σ model results in nontrivial couplings b...

Deconfinement in the presence of a Fermi surface

2005

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U(1) gauge theory of non-relativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions ($QED_3$) by Hermele et al. [Phys. Rev. B {\bf 70}, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ (the coupling strength between non-relativistic fermions and U(1) gauge fields) reveals that the conductivity $\sigma$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in $QED_3$. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the non-relativistic fermions at the charged fixed point. As a result a critical field theory of non-relativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point