Quantum criticality, a manifestation of emergent scale invariance in electron wavefunctions arises from intricate many-body quantum entanglement. One of the natural venues for the criticality is clean undoped Dirac semimetals, known as a marginally-renormalized critical phase. The ground state is only slightly modified from the Slater-type product wavefunction because the scatterings from weak disorder and Coulomb interactions are suppressed. Here, using the renormalization group (RG) analysis, we show that a novel class of quantum criticality appears in Dirac semimetals when the disorder strength becomes sufficiently strong in the presence of Coulomb interactions so that a quantum phase transition from the marginally-renormalized critical phase to a disorder-dominated phase arises. The ground state at the critical point is a quantum critical non-Fermi liquid (NFL), characterized by the properties of strongly entangled low-energy states such as the absence of quasi-particles. Near the critical point, unusually wide temperature regions with NFL behaviors emerge.
Quantum criticality, a manifestation of emergent scale invariance in electron wavefunctions arises from intricate many-body quantum entanglement. One of the natural venues for the criticality is clean undoped Dirac semimetals, known as a marginally-renormalized critical phase. The ground state is only slightly modified from the Slater-type product wavefunction because the scatterings from weak disorder and Coulomb interactions are suppressed. Here, using the renormalization group (RG) analysis, we show that a novel class of quantum criticality appears in Dirac semimetals when the disorder strength becomes sufficiently strong in the presence of Coulomb interactions so that a quantum phase transition from the marginally-renormalized critical phase to a disorder-dominated phase arises. The ground state at the critical point is a quantum critical non-Fermi liquid (NFL), characterized by the properties of strongly entangled low-energy states such as the absence of quasi-particles. Near the critical point, unusually wide temperature regions with NFL behaviors emerge.
Non-Fermi liquid (NFL) behavior and strange metallicity, often marked by resistivity linear in temperature and the breakdown of Fermi liquid quasiparticles, are recurring themes in strongly correlated quantum materials, ranging from high-temperature cuprates to twisted van der Waals heterostructures. Enormous efforts are being made to uncover the origin of NFL underlying strange metallicity, yet progress remains slow. Here, we report appearance of an NFL phase in a discontinuous metal-NFL-insulator transition of the Holstein model away from half-filling. The NFL appears as a distinct ground state of finite regime in addition to the metal and insulator states in a phase diagram, not as a consequence of quantum criticality of a continuous transition. Also, the discontinuity of the metal-NFL transition produces a mixture between the two phases along the phase boundary to exhibit a two-fluid kind strange metallicity. The dynamical mean-field theory was employed with Wilson’s numerical renormalization group in infinite dimensions. We trace the NFL phase to a spin gap opening in the absence of a charge gap. This offers an intriguing route to understanding the NFL and intertwined superconductivity in correlated quantum materials.
We study a non-Anderson disorder driven quantum phase transition in a semi-infinite Dirac semimetal with a flat boundary. The conformally invariant boundary conditions, which include those that are time-reversal invariant, lead to nodal-like surface states on the boundary. In this case the boundary becomes metallic at a critical disorder that is weaker than that for the semimetal-diffusive metal transition in the bulk. The latter transition takes place in the presence of a metallic surface; in the language of surface critical phenomena this corresponds to the so-called extraordinary transition. The lines of the surface and the extraordinary transitions meet at the special transition point. To elucidate universal properties at different transitions on the phase diagram, we employ renormalization group methods and compute the corresponding surface critical exponents using $\ensuremath{\varepsilon}$ expansion.
A strange metal state appears in many strongly correlated materials from the cuprates, pnictides, and twisted bilayer graphenes to even bosonic systems. Enormous efforts are being made to unravel the nature of the non-Fermi liquid (NFL) which underlies the strange metallicity, yet progress is rather slow. Understanding the NFL behavior is crucial, in addition to its importance in replacing the Fermi liquid paradigm, in that NFL is the normal state from which new states of matter emerge like high temperature superconductivity. Here, we report the appearance of an NFL phase in a discontinuous metal-NFL-insulator transition in a ``non-engineered'' Hamiltonian of the Holstein model away from half-filling. The discontinuity of the phase transition between NFL and Fermi liquid metal renders the ground state at the phase boundary a mixture between them over an extended range like the extended criticality observed in cuprates and other quantum materials. The dynamical mean-field theory was employed in combination with Wilson's numerical renormalization group technique. We identify the origin of the NFL metal phase as the opening of a spin gap in the absence of a charge gap. Also, strong lattice fluctuations emerge at the boundary which should enhance superconductivity.
Understanding correlation effects in topological phases and their transitions is a cutting-edge area of research in recent condensed matter physics. We study topological quantum phase transitions (TQPTs) between double-Weyl semimetals (DWSMs) and insulators, and argue that a novel class of quantum criticality appears at the TQPT characterized by emergent anisotropic non-Fermi-liquid behaviors, in which the interplay between the Coulomb interaction and electronic critical modes induces not only anisotropic renormalization of the Coulomb interaction but also strongly correlated electronic excitation in three spatial dimensions. Using the standard renormalization group methods, large N_{f} theory, and the ε=4-d method with a fermion flavor number N_{f} and spatial dimension d, we obtain the anomalous dimensions of electrons (η_{f}=0.366/N_{f}) in large N_{f} theory and the associated anisotropic scaling relations of various physical observables. Our results may be observed in candidate materials for DWSMs such as HgCr_{2}Se_{4} or SrSi_{2} when the system undergoes a TQPT.
Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system.The generalized Harris criterion, augmented by a perturbative renormalization-group analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal (WSM)-insulator quantum-critical point.But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point.The field-theoretic predictions for the correlation length exponent ν ¼ 2 and dynamic scaling exponent z ¼ 5=4 at this multicritical point are in good agreement with the ones extracted numerically, yielding ν ¼ 1.98 Æ 0.10 and z ¼ 1.26 Æ 0.05, from the scaling of the average density of states (DOS).Deep inside the WSM phase, generic disorder is also an irrelevant perturbation, while a metallic phase appears at strong disorder through a QPT.We here demonstrate that in the presence of generic but strong disorder, the WSM-metal QPT is ultimately always characterized by the exponents ν ¼ 1 and z ¼ 3=2 (to one-loop order), originating from intranode or chiralsymmetric (e.g., regular and axial potential) disorder.We here anchor such emergent chiral superuniversality through complementary renormalization-group calculations, controlled via ϵ expansions, and numerical analysis of average DOS across WSM-metal QPT.In addition, we also discuss a subsequent QPT (at even stronger disorder) of a Weyl metal into an Anderson insulator by numerically computing the typical DOS at zero energy.The scaling behavior of various physical observables, such as residue of quasiparticle pole, dynamic conductivity, specific heat, Grüneisen ratio, inside various phases as well as across various QPTs in the global phase diagram of a dirty Weyl liquid, are discussed.
We develop a theoretical framework based on the nonperturvative renormalization group (RG) in the one-particle irreducible (Wetterich) formulation to tackle the interplay of coupled fermionic and order-parameter fluctuations at metallic quantum critical points (QCPs) with ordering wavevector Q=0. We consistently treat the dynamical emergence of the Landau damping of the bosonic mode and non-Fermi liquid scaling of fermions upon lowering the cutoff scale. The loop integrals of the present theory involve only contributions from fluctuations above the cutoff scale, which protects the system from developing singular bosonic interactions. We emphasize the importance of the nontrivial relative scaling of the bosonic and fermionic cutoffs Λ and Λf, which we fix by analyzing the RG flow of the scale-dependent ordering wave-vector QΛ. Upon neglecting Fermi self-energy in the loop integrals of the functional RG flow, we identify a non-Fermi liquid RG fixed point and recover the features obtained earlier within RPA-type approaches. In a subsequent step, we self-consistently include the scaling of the self-energy and the Yukawa coupling. We find a generic instability of the non-Fermi liquid RG fixed point. This implies, at least at this truncation level, absence of the QCP with Q=0 and development of a first-order phase transition or a phase characterized by Q=0.