Renormalization group for mixed fermion-boson systems

Yamamoto, Seiji J.; Si, Qimiao

doi:10.1103/physrevb.81.205106

Cited by 17 publications

(15 citation statements)

References 34 publications

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“…Using the procedure specified in Ref. 58, we found λ to be marginal at the leading order 55, just like in the paramagnetic case. The difference from the latter appears at the loop level: λ is exactly marginal to infinite loops 55.…”

Section: Antiferromagnetism and Fermi Surface In Kondo Latticesmentioning

confidence: 65%

Quantum criticality and global phase diagram of magnetic heavy fermions

2010

Physica Status Solidi (b)

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126

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Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. It is being discussed in a number of strongly correlated electron systems. A prototype case occurs in the heavy fermion metals, in which antiferromagnetic quantum critical points (QCPs) have been explicitly observed. Here, I address two types of antiferromagnetic QCPs. In addition to the standard description based on the fluctuations of the antiferromagnetic order, a local QCP is also considered. It contains inherently quantum modes that are associated with a critical breakdown of the Kondo effect. Across such a QCP, there is a sudden collapse of a large Fermi surface to a small one. I also consider the proximate antiferromagnetic and paramagnetic phases, and these considerations lead to a global phase diagram. Finally, I discuss the pertinent experiments and outline some directions for future studies. 1 Introduction A quantum critical point (QCP) refers to a second-order phase transition at zero temperature. The notion of quantum criticality is playing a central role in a number of strongly correlated systems, but this was not anticipated when the notion was first introduced. Indeed, the initial work of Hertz [1] was rather modest. From the critical phenomenon perspective, Hertz formulated a direct extension of Wilson's then-newly-completed renormalizationgroup (RG) theory of classical critical phenomena [2]. The formulation retained the basic property of the latter: the zerotemperature phases are still considered to be distinguished by an order parameter, a coarse-grained macroscopic variable characterizing the breaking of a global symmetry of the Hamiltonian, and the critical modes are the fluctuations of the order parameter. In this sense, it conforms to the Landau paradigm for phase transitions. From a microscopic perspective, Hertz's discussion built on the historical work about paramagnons, the overdamped magnons occurring in a paramagnetic metal as it becomes more and more ferromagnetic (for a review, see Ref. [3]). In hindsight, the convergence of these two lines of theoretical physics seems to be rather natural. For a Stoner ferromagnet, the fluctuations of the order parameter (magnetization) at its QCP is none other but the paramagnons. For a spin-densitywave (SDW) antiferromagnet, such fluctuations of the order

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Section: Antiferromagnetism and Fermi Surface In Kondo Latticesmentioning

confidence: 65%

Quantum criticality and global phase diagram of magnetic heavy fermions

2010

Physica Status Solidi (b)

Self Cite

126

111

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“…The tree level and one-loop analyses directly use the procedure of Ref. 70 , while the infinite-loop analysis was based on a decomposition of the Fermi surface into patches.…”

Section: The Case Of Fermi Surface Not Intersecting the Antiferromagnmentioning

confidence: 99%

Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators

Yamamoto

2010

J Low Temp Phys

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We discuss the general theoretical arguments advanced earlier for the T = 0 global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing between the established and the conjectured. In addition to the wellknown phase of a paramagnetic metal with a "large" Fermi surface (P L ), there is also an antiferromagnetic phase with a "small" Fermi surface (AF S ). We provide the details of the derivation of a quantum non-linear sigma-model (QNLσ M) representation of the Kondo lattice Hamiltonian, which leads to an effective field theory containing both low-energy fermions in the vicinity of a Fermi surface and low-energy bosons near zero momentum. An asymptotically exact analysis of this effective field theory is made possible through the development of a renormalization group procedure for mixed fermion-boson systems. Considerations on how to connect the AF S and P L phases lead to a global phase diagram, which not only puts into perspective the theory of local quantum criticality for antiferromagnetic heavy fermion metals, but also provides the basis to understand the surprising recent experiments in chemically-doped as well as pressurized YbRh 2 Si 2 . We point out that the AF S phase still occurs for the case of an equal number of spin-1/2 local moments and conduction electrons. This observation raises the prospect for a global phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally, we discuss the connection between the Kondo breakdown physics discussed

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“…Using the procedure specified in Ref. 39 , we found λ to be marginal at the leading order 34 , just like in the paramagnetic case. The difference from the latter appears at the loop level: λ is exactly marginal to infinite loops 34 .…”

Section: Antiferromagnetism and Fermi Surfaces In Kondo Lat-ticesmentioning

confidence: 66%

Entanglement Renormalization: An Introduction

Vidal¹

2010

Understanding Quantum Phase Transitions

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Quantum phase transitions (QPTs) arise as a result of competing interactions in a quantum many-body system. Kondo lattice models, containing a lattice of localized magnetic moments and a band of conduction electrons, naturally feature such competing interactions. A Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction among the local moments promotes magnetic ordering. However, a Kondo exchange interaction between the local moments and conduction electrons favors the Kondo-screened singlet ground state. This chapter summarizes the basic physics of QPTs in antiferromagnetic Kondo lattice systems. Two types of quantum critical points (QCPs) are considered. Spin-density-wave quantum criticality occurs at a conventional type of QCP, which invokes only the fluctuations of the antiferromagnetic order parameter. Local quantum criticality describes a new type of QCP, which goes beyond the Landau paradigm and involves a breakdown of the Kondo effect. This critical Kondo breakdown effect leads to non-Fermi liquid electronic excitations, which are part of the critical excitation spectrum and are in addition to the fluctuations of the magnetic order parameter. Across such a QCP, there is a sudden collapse of the Fermi surface from large to small. I close with a brief summary of relevant experiments, and outline a number of outstanding issues, including the global phase diagram.Comment: 27 pages, 6 figures; Chapter of the book "Understanding Quantum Phase Transitions", ed. Lincoln D. Carr (CRC Press/Taylor & Francis, Boca Raton, 2010

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Renormalization group for mixed fermion-boson systems

Cited by 17 publications

References 34 publications

Quantum criticality and global phase diagram of magnetic heavy fermions

Quantum criticality and global phase diagram of magnetic heavy fermions

Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators

Entanglement Renormalization: An Introduction

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