SU(2) slave-rotor theory of the attractive Hubbard model

Extending the U(1) slave-rotor representation\cite{FG_SRR} of the repulsive Hubbard model, we propose an SU(2) slave-rotor decomposition for the attractive Hubbard model, where the SU(2) slave-rotor variables represent order parameter fluctuations associated with superconductivity and charge density wave. This decomposition method allows us to modify the standard Hartree-Fock mean field theory by incorporating order parameter fluctuations on an equal footing. Deriving an effective SU(2) slave-rotor action from the attractive Hubbard model, and analyzing it at the mean field level, we demonstrate a second order phase transition driven by softening of the slave-rotor variables

Role of non-magnetic disorder in a doped U(1) spin liquid

Recently we investigated a role of non-magnetic disorder on the stability of a U(1) spin liquid ($U1SL$) [cond-mat/0407151; Phys. Rev. B (R) accepted]. In the present paper we examine an effect of the non-magnetic disorder on a doped $U1SL$. In a recent study [cond-mat/0408236] we have shown that the doped $U1SL$ shows deconfined massive spinon excitations in the superconducting phase as a result of holon condensation. We find that the massive spinon is trapped by the non-magnetic disorder. Owing to the localized spin the non-magnetic disorder acts as magnetic one

Role of vertex corrections in the TT-linear resistivity at the Kondo breakdown quantum critical point

The Kondo breakdown scenario has been claimed to allow the $T$-linear resistivity in the vicinity of the Kondo breakdown quantum critical point, two cornerstones of which are the dynamical exponent $z = 3$ quantum criticality for hybridization fluctuations in three dimensions and irrelevance of vertex corrections for transport due to the presence of localized electrons. We revisit the issue of vertex corrections in electrical transport coefficients. Assuming that two kinds of bosonic degrees of freedom, hybridization excitations and gauge fluctuations, are in equilibrium, we derive coupled quantum Boltzmann equations for two kinds of fermions, conduction electrons and spinons. We reveal that vertex corrections play a certain role, changing the $T$-linear behavior into $T^{5/3}$ in three dimensions. However, the $T^{5/3}$ regime turns out to be narrow, and the $T$-linear resistivity is still expected in most temperature ranges at the Kondo breakdown quantum critical point in spite of the presence of vertex corrections. We justify our evaluation, showing that the Hall coefficient is not renormalized to remain as the Fermi-liquid value at the Kondo breakdown quantum critical point

Heavy-fermion spin liquid in the strong hybridization limit of the finite-U Anderson lattice model

Studying the finite-U Anderson lattice model in the strong hybridization limit, we find a heavy-fermion spin liquid phase, where both conduction and localized fermions are strongly hybridized to form heavy fermions but this heavy-fermion phase corresponds to a symmetric Mott insulating state owing to the presence of charge gap, resulting from large Hubbard-U interactions in localized fermions. We show that this heavy-fermion spin liquid phase differs from the "fractionalized" Fermi liquid state, where the latter corresponds to a metallic state with a small Fermi surface of conduction electrons while localized fermions decouple from conduction electrons to form a spin liquid state. We discuss the stability of this anomalous spin liquid phase against antiferromagnetic ordering and gauge fluctuations, in particular, instanton effects associated with confinement of slave particles. Furthermore, we propose a variational wave function to check its existence from the microscopic model

Deconfined Quantum Criticality at the Quantum Phase Transition from Antiferromagnetism to Algebraic Spin Liquid

We investigate the quantum phase transition from antiferromagnetism ($AF$) to algebraic spin liquid ($ASL$). {\it We propose that spin 1/2 fermionic spinons in the $ASL$ fractionalize into spin 1/2 bosonic spinons and spinless fermions at the quantum critical point ($QCP$) between the $AF$ and the $ASL$}. Condensation of the bosonic spinons leads to the $AF$, where the condensed bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are also confined to make antiferromagnons as elementary excitations in the $AF$. {\it Approaching the $QCP$ from the $AF$, spin 1 critical antiferromagnetic fluctuations are expected to break up into spin 1/2 critical bosonic spinons. Then, these bosonic spinons hybridize with spin 1/2 fermionic spinons, making spinless fermions}. As a result the fermionic spinons decay into the bosonic spinons and the spinless fermions. But, the spinless fermions are confined and thus, only the bosonic spinons emerge at the $QCP$. This coincides with the recent studies of {\it deconfined quantum criticality}\cite{Laughlin_deconfinement,Senthil_deconfinement,Kim1,Ichinose_de confinement}. When the bosonic spinons are gapped, the $ASL$ is realized. The bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are deconfined to describe the $ASL$

Quantum phase transition in one dimensional extended Kondo lattice model away from half filling

We study one dimensional {\it extended} Kondo lattice model, described by the $t-J$ Hamiltonian for conduction electrons away from half filling and the Heisenberg Hamiltonian for localized spins at half filling. Following Shankar,\cite{Shankar} we find an effective field theory for this model, where doped holes are represented by massless Dirac fermions (holons) and spin excitations are fractionalized into relativistic bosons (spinons). These holons and spinons interact via U(1) gauge fluctuations. Effects of Berry phase to the localized spins disappear due to the presence of Kondo couplings, causing the spinon excitations gapped. Furthermore, the gauge fluctuations are suppressed by hole doping. As a result, massive spinons are deconfined to arise in the localized spins unless the Kondo hybridization is strong enough. When the Kondo hybridization strength exceeds a certain value, we find that the localized spin chain becomes critical. This indicates that the present one dimensional Kondo lattice model exhibits a phase transition from a spin-gapped phase to a critical state in the localized spin chain, driven by the Kondo interaction

An effective Lagrangian for the continuous transition in an extended Kondo lattice model

We propose an effective Lagrangian for the continuous transition from the heavy fermion metal to the antiferromagnetic metal in an extended Kondo lattice model. Based on the slave-boson representation we introduce an additional new order parameter associated with difference of the chemical potential between conduction electrons $c_{i\sigma}$ and local spinons $f_{i\sigma}$. This order parameter allows pseudospin construction $T_{ix} = {1/2}$, $T_{iy} = - \frac{i}{2}<{c}_{i\alpha}^{\dagger}f_{i\alpha} - f_{i\alpha}^{\dagger}c_{i\alpha}>$, and $T_{iz} = {1/2}$, where $T_{i\pm} = T_{ix} \pm iT_{iy}$ corresponds to the usual hybridization order parameter in the slave-boson representation of the Kondo lattice model. The resulting effective action is shown to be an anisotropic pseudospin model with a Landau damping term for the screened-unscreened (XY$-$Ising) phase transition. To describe the emergence of antiferromagnetic order in the unscreened (Ising) phase, we phenomenologically introduce the antiferromagnetic Heisenberg model for the localized spins, where the effective coupling strength is given by $J_{eff} = J||^{2}$. This ad-hoc construction allows the continuous transition from the heavy fermion phase to the antiferromagnetic phase because breakdown of Kondo screening ($= 0$ and $\not= 0$) causes effective exchange interactions between unscreened local moments

Role of axion electrodynamics in Weyl metal: Violation of Wiedemann-Franz law

Recently, enhancement of the longitudinal magneto-electrical conductivity (LMEC) has been observed in Bi$_{1-x}$Sb$_{x}$ around $x \sim 3\%$ under $\bm{E} \parallel \bm{B}$ ($\bm{E}$: external electric field and $\bm{B}$: external magnetic field) [Phys. Rev. Lett. {\bf 111}, 246603 (2013)], where an enhancement factor proportional to $B^{2}$ is suggested to result from the $\bm{E} \cdot \bm{B}$ term. In the present study, we show that this $B^{2}$ enhancement is not limited on the LMEC, where both the Seebeck and thermal conductivities in the longitudinal setup ($\bm{E} \parallel \bm{B}$) are predicted to show essentially the same enhancement proportional to $B^{2}$. In particular, the $B^{2}$ enhancement factor of the LMEC turns out to differ from that of the longitudinal thermal conductivity, responsible for breakdown of Wiedemann-Franz (WF) law, which means that anomalous currents flowing through the dissipationless channel differ from each other. Since the breakdown of the WF law appears in spite of the existence of electron quasiparticles, regarded to be a purely topological character (chiral anomaly), the Weyl metallic state cannot be identified with the Landau's Fermi-liquid fixed point. We propose the violation of the WF law as another hallmark of the Weyl metallic phase, which originates from axion electrodynamics

Role of doped holes in a U(1) spin liquid

In the context of the SU(2) slave boson theory we show that condensation of holons can result in the zero mode of a nodal spinon in a single instanton potential. Instanton contribution in the presence of the zero mode induces the 't Hooft effective interaction, here mass to the spinon. We find that the spinon mass is determined by the state of instantons in the presence of the zero mode. The mass corresponds to antiferromagnetic moment of the nodal spinon. Considering the state of instantons, we discuss the possibility of coexistence between antiferromagnetism and $d-wave$ superconductivity in underdoped cuprates

Spin-gapped incoherent metal with preformed pairing in the doped antiferromagnetic Mott insulator

We investigate how the antiferromagnetic Mott insulator evolves into the d-wave BCS superconductor through hole doping. Allowing spin fluctuations in the strong coupling approach, we find a spin-gapped incoherent metal with preformed pairing as an intermediate phase between the antiferromagnetic Mott insulator and d-wave superconductor. This non-Fermi liquid metal is identified with an infrared stable fixed point in the spin-decomposition gauge theory, analogous to the spin liquid insulator in the slave-boson gauge theory. We consider the single particle spectrum and dynamical spin susceptibility in the anomalous metallic phase, and discuss physical implications