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Under the restrictionˆK1restrictionˆ restrictionˆK1 = ˆ K2, the boson momentum q can still have a non-zero modulus, but it loses its angular freedom and is forced to point exactly normal to the Fermi surface. This constraint does not allow the boson field φ to transform in a homogeneous fashion.
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We formulate a momentum-shell renormalization group (RG) procedure that can be used in theories containing both bosons and fermions with a Fermi surface. We focus on boson-fermion couplings that are nearly forward-scattering, {\it i.e.} involving small momentum transfer ($\vec{q} \approx 0$) for the fermions. Special consideration is given to phase...
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Recent discovery of transport anomaly in graphene demonstrated that a system known to be weakly interacting may become strongly correlated if system parameter(s) can be tuned such that fermi surface is sufficiently small. We study the strong correlation effects in the transport coefficients of Dirac materials doped with magnetic impurity under the...
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... In this section, we provide details of the RG analysis of our slave-boson approach to the Kondo-Heisenberg-like t-J model. The RG procedure is primarily based on Ref. [60][61][62] . ...
... The scaling dimension for the measure d d k for fermions with scale-invariant Fermi velocity is given by [60] [ ...
... with k = (ω, k) and p = (ν, p). From Ref. [60], for a special case z = 1, the calculation of the scaling dimension for a boson-fermion coupling term can be performed via the usual way without invoking the patch scheme. The scaling dimension ofḡ can be obtained similarly by simple power-counting, 0 = [ḡ] + 2z ...
The mysterious metallic phase showing perfect $T$-linear resistivity and a universal scattering rate $1/\tau = \alpha_P k_B T /\hbar$ with a universal prefactor $\alpha_P \sim 1$ and logarithmic-in-temperature singular specific heat coefficient, so-called Planckian metal phase was observed in various overdoped high-$T_c$ cuprate superconductors over a finite range in doping. Here, we propose a microscopic mechanism for this exotic state based on quantum-critical bosonic charge Kondo fluctuations coupled to both spinon and a heavy conduction-electron Fermi surfaces within the heavy-fermion formulation of the slave-boson $t$-$J$ model. Using a controlled perturbative renormalization group (RG) analysis, we examine the competition between the pseudogap phase, characterized by Anderson's Resonating-Valence-Bond spin-liquid, and the Fermi-liquid state, characterized by the electron hoping (effective charge Kondo effect). We find a quantum-critical metallic phase with a universal Planckian $\hbar \omega/k_B T$ scaling in scattering rate near a localized-delocalized (pseudogap-to-Fermi liquid) charge Kondo breakdown transition. Our results are in excellent agreement with the recent experimental observations on optical conductivity (without fine-tuning) in Nat. Commun. 14, 3033 (2023), universal doping-independent field-to-temperature scaling in magnetoresistance in Nature 595, 661 (2021), and the marginal Fermi-liquid spectral function observed in ARPES (Science 366, 1099 (2019)) as well as Hall coefficient in various overdoped cuprates in Nature 595, 661 (2021) and Annu. Rev. Condens. Matter Phys. 10, 409 (2019). Our mechanism offers a microscopic understanding of the quantum-critical Planckian metal phase observed in cuprates d-wave superconducting, and Fermi liquid phases.
... Dynamical Kondo effectKondo destruction in Kondo lattice models originates from the dynamical competition between the Kondo and RKKY exchange interactions. The exact marginality of the Kondo coupling inside the AF order phase has been demonstrated based on an RG analysis within a quantum nonlinear sigma model analysis[45,46]. Indeed, the dynamical Kondo effect allows the gain of a Kondo exchange energy in the absence of static Kondo singlet formation, which is important to help stabilize a Kondo-destroyed phase and allows for the quantum Dynamical local spin susceptibility for SU(2) Anderson lattice model in the magnetic ordered side[43].phase ...
An overarching question in strongly correlated electron systems is how the landscape of quantum phases emerges from electron correlations. The method of extended dynamical mean field theory (EDMFT) has been developed for clean lattice models of the correlated electrons. For such models, not only onsite Hubbard-like interactions are important, but so are intersite interactions. Importantly, the EDMFT method treats the interplay between the onsite and intersite interactions dynamically. It was initially formulated for models of the two-band Anderson-lattice type with intersite interactions, as well as for the one-band Hubbard type with intersite Heisenberg-like terms that are often called Hubbard-Heisenberg models. In the case of Kondo lattice models, the EDMFT method incorporates a dynamical competition between the local Kondo and intersite Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. In these models, the EDMFT-based analyses led to the notion of Kondo destruction, which has played a central role in the understanding of quantum critical heavy fermion metals. In this article, we summarize the EDMFT method, and survey its applications, particularly for Kondo/Anderson lattice models. We also discuss the prospect for further developing the EDMFT method, as well as for applying it to address the correlation physics in a variety of new settings. Among the latter are the orbital-selective Mott physics that arises both in iron-based superconductors and in frustrated bulk systems with topological flat bands.
... Q 0 = (π, π, π) in 3D], only fermions around the Fermi surface points connected by Q 0 are coupled to the critical mode. However, performing the scaling analysis for the resulting fermion-boson theory assuming z = 2 [27,38], we have found that this coupling (due to the factor f (k, q)), as well as the Ising one in Eq. (2), are both irrelevant in d > 1. This provides a strong indication that the BEC transition should retain its universality class in the one-band case. ...
... [37] Pasquale Calabrese and John Cardy, "Entanglement entropy and conformal field theory," Journal of Physics A: Mathematical and Theoretical 42, 504005 (2009). [38] Seiji J. Yamamoto and Qimiao Si, "Renormalization group for mixed fermion-boson systems," Phys. Rev. B 81, 205106 (2010). ...
... , only fermions around the Fermi surface points connected by Q 0 are coupled to the critical mode. However, performing the scaling analysis for the resulting fermion-boson theory assuming z = 2 [27,38], we have found that this coupling (due to the factor f (k, q)), as well as the Ising one in Eq. (2), are both irrelevant in d > 1. This provides a strong indication that the BEC transition should retain its universality class in the one-band case. ...
Motivated by recent experiments on magnetically frustrated heavy fermion metals, we theoretically study the phase diagram of the Kondo lattice model with a nonmagnetic valence bond solid ground state on a ladder. A similar physical setting may be naturally occurring in YbAl$_3$C$_3$, CeAgBi$_2$, and TmB$_4$ compounds. In the insulating limit, the application of a magnetic field drives a quantum phase transition to an easy-plane antiferromagnet, which is described by a Bose-Einstein condensation of magnons. Using a combination of field theoretical techniques and density matrix renormalization group calculations we demonstrate that in one dimension this transition is stable in the presence of a metallic Fermi sea and its universality class in the local magnetic response is unaffected by the itinerant gapless fermions. Moreover, we find that fluctuations about the valence bond solid ground state can mediate an attractive interaction that drives unconventional superconducting correlations. We discuss the extensions of our findings to higher dimensions and argue that, depending on the filling of conduction electrons, the magnon Bose-Einstein condensation transition can remain stable in a metal also in dimensions two and three.
... [43,59]. This approach is distinct from the patch RG scheme on a two dimensional Fermi surface [60] at which the Fermi volume is conserved due to the Luttinger theorem. We also assume that the self-energy only depends on external frequency but is independent of external momentum. ...
The heavy fermion systems CeMIn5 with M=Co, Rh, Ir, the “115” family, provide a prototypical example of strange superconductivity with unconventional d-wave pairing and strange metal normal state, emerged near an antiferromagnetic quantum critical point. The microscopic origin of strange superconductivity and its link to antiferromagnetic quantum criticality of the strange metal state are still long-standing open issues. We propose a microscopic mechanism for strange superconductors, based on the coexistence and competition between the Kondo correlation and the quasi-2d short-ranged antiferromagnetic resonating-valence-bond spin-liquid near the antiferromagnetic quantum critical point via a large-N Kondo-Heisenberg model and renormalization group analysis beyond the mean-field level. The interplay of these two effects provides a qualitative understanding on how superconductivity emerges from the strange metal state and the observed superconducting phase diagrams for CeMIn5.
... The RG analysis near the QCP stems from the competing J χ and J terms in Eq. (1). Within our RG scheme k, k F , and ω are rescaled as follows: k = e l k; k F = e l k F ; ω = e zl ω, where the dynamical exponent z is set to 2. This scheme, distinct from the conventional one [46,47], allows the Fermi momentum k F to flow in the same way as the momentum variable k: [k] = [k F ] = 1, effectively capturing the continuous small-to-large evolution of the electron density seen in the Hall coefficient measurement at finite temperatures across the transition [36,47,48]. At bare level, J χ , J , u χ , and u are irrelevant couplings for d > z = 2, while J χ , u χ , and u become marginal for d = z = 2 ([J χ ] = (z − d)/2,[u χ ] = [u ] = z − d), which allows a controlled perturbative RG analysis on the effective action on a quasi-2d lattice: d = 2 + η with η = 0 + [49]. ...
... In the following, we shall prove that, for z = d = 2 with z being the dynamical exponent and d being the spatial dimension, the wave vectors for bosons and fermions share the same scaling dimension. Therefore, we do not need to apply the patch RG scheme as being used in Ref. [46]. We start with the action for free bosons with z = 2 as an example, which is given by ...
... where the subscript f in Eq. (A2) denoted "fermion." Here, we denote k as the wave vector for fermions (to distinguish the fermion wave vector k from the boson wave vector q), m the mass, the frequency, f the fermion field, There exists a fundamental difference between the scaling scheme being used in Ref. [46] and ours. Fermi wave vector k F in Ref. [46] is considered to be scale invariant by Luttinger theorem, the conservation of Fermi volume under RG. ...
Unconventional metallic or strange metal (SM) behavior with non-Fermi liquid (NFL) properties, generic features of heavy-fermion systems near quantum phase transitions, are yet to be understood microscopically. A paradigmatic example is the magnetic field-tuned quantum critical heavy-fermion metal YbRh2Si2, revealing a possible SM state over a finite range of fields at low temperatures when substituted with Ge. Above a critical
field, the SM state gives way to a heavy Fermi liquid with Kondo correlation. The NFL behavior, most notably a linear-in-temperature electrical resistivity and a logarithmic-in-temperature followed by a power-law singularity in the specific heat coefficient at low temperatures, still lacks a definite understanding.We propose the following mechanism as origin of the experimentally observed behavior: a quasi-2d fluctuating short-ranged resonating-valence-bond spin liquid competing with the Kondo correlation. Applying a field-theoretical renormalization group analysis on an effective field theory beyond a large-N approach to an antiferromagnetic Kondo-Heisenberg model, we identify the critical point and explain remarkably well the SM behavior. Our theory goes beyond the
well-established framework of quantum phase transitions and serves as a basis to address open issues in quantum critical heavy-fermion systems.
... It is possible to use the RG, even if bosons are simultaneously present, provided the dynamical exponent z = 1 [35]. ...
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.
... A momentum-shell RG treatment requires a procedure that mixes bosons, which scale along all directions in momentum space [2] , and fermions, which scale along the radial direction perpendicular to the Fermi surface [57] . 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]. ...
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 have been explicitly observed. Here, I address two types of
antiferromagnetic quantum critical points. In addition to the standard
description based on the fluctuations of the antiferromagnetic order, a local
quantum critical point is also considered. It contains inherently quantum modes
that are associated with a critical breakdown of the Kondo effect. Across such
a quantum critical point, 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 on the antiferromagnetic heavy
fermions, briefly address the case of ferromagnetic heavy fermions, and outline
some directions for future studies.
Multiple-band nature of electronic energy bands leads to novel physical effects in solids. In this paper, we clarify physical properties of a Fermi system with a pair of electron and hole Fermi surfaces (FSs), whose coupling is mediated by a critical U(1) boson field. By using a one-loop renormalization group analysis, we show that when the boson field undergoes a quantum phase transition with broken U(1) symmetry, the multiple-band Fermi system shows a non-Fermi liquid (non-FL) behavior in its thermodynamic and magnetic properties. At a quantum critical point (QCP), Fermi velocities of the two FSs are renormalized into the same critical velocity as a boson velocity, and the fermion's density of states (DOS) shows a pseudogap behavior with a logarithmic energy dependence at the QCP.
Significance
Magnetically frustrated Kondo lattices are correlated metals not governed by symmetry-breaking quantum criticality, offering a new perspective on the puzzling phenomenology of strange metal behavior and unconventional superconductivity. While this concept is likely to be realized in certain heavy-fermion compounds, the corresponding models are notoriously difficult to solve, hindering robust theoretical predictions. Here we provide a comprehensive solution for a 1D Kondo ladder with a frustrated valence bond solid ground state in the presence of a magnetic field. We prove the stability of the field-induced magnon Bose–Einstein condensation and demonstrate the emergence of unconventional superconductivity. We also present strong evidence that our results carry over to two and three dimensions. These findings anchor future studies of frustrated heavy fermion systems.
Recent experiments on quantum criticality in the Ge-substituted heavy-electron material YbRh2Si2 under magnetic field have revealed a possible non-Fermi liquid (NFL) strange metal (SM) state over a finite range of fields at low temperatures, which still remains a puzzle. In the SM region, the zero-field antiferromagnetism is suppressed. Above a critical field, it gives way to a heavy Fermi liquid with Kondo correlation. The T (temperature)-linear resistivity and the T-logarithmic followed by a power-law singularity in the specific heat coefficient at low T, salient NFL behaviours in the SM region, are un-explained. We offer a mechanism to address these open issues theoretically based on the competition between a quasi-2d fluctuating short-ranged resonant- valence-bonds (RVB) spin-liquid and the Kondo correlation near criticality. Via a field-theoretical renormalization group analysis on an effective field theory beyond a large-N approach to an anti- ferromagnetic Kondo-Heisenberg model, we identify the critical point, and explain remarkably well both the crossovers and the SM behaviour.
