Quasilocal strange metal

Abstract

One of the key factors that determine the fates of quantum many-body systems in the zero temperature limit is the competition between kinetic energy that delocalizes particles in space and interaction that promotes localization. While one dominates over the other in conventional metals and insulators, exotic states can arise at quantum critical points where none of them clearly wins. Here we present a novel metallic state that emerges at an antiferromagnetic (AF) quantum critical point in the presence of one-dimensional Fermi surfaces embedded in space dimensions three and below. At the critical point, interactions between particles are screened to zero in the low energy limit at the same time the kinetic energy is suppressed in certain spatial directions to the leading order in a perturbative expansion that becomes asymptotically exact in three dimensions. The resulting dispersionless and interactionless state exhibits distinct quasi-local strange metallic behaviors due to a subtle dynamical balance between screening and infrared singularity caused by spontaneous reduction of effective dimensionality. The strange metal, which is stable near three dimensions, shows enhanced fluctuations of bond density waves, d-wave pairing, and pair density waves. 1The richness of exotic zero-temperature states in condensed matter systems [1,2] can be attributed to quantum fluctuations driven by kinetic energy and interaction which can not be simultaneously minimized due to the uncertainty principle. In conventional metals, kinetic energy plays the dominant role, and interactions only dress electrons into quasiparticles which survive as coherent excitations in the absence of instabilities [3,4]. The existence of well defined quasiparticle excitations is the cornerstone of Landau Fermi liquid theory [5], which successfully explains a large class of metals. However, the Fermi liquid theory breaks down at the verge of spontaneous formation of order in metals [6][7][8]. Near continuous quantum phase transitions, new metallic states can arise as quantum fluctuations of order parameter destroy the coherence of quasiparticles through interactions that persist down to the zero energy limit [9,10]. Systematic understanding of the resulting strange metallic states is still lacking, although there exist some examples whose universal behaviors in the low energy limit can be understood within controlled theoretical frameworks [11][12][13][14][15].Antiferromagnetic (AF) quantum phase transition commonly arises in strongly correlated systems including electron doped cuprates [16], iron pnictides [17] and heavy fermion compounds [18].In two space dimensions, it has been shown that the interaction between the AF mode and itinerant electrons qualitatively modify the dynamics of the system at the critical point [19,20]. A recent numerical simulation shows a strong enhancement of superconducting correlations near the AF critical point [21]. However, the precise nature of the putative strange metallic state has not been understood yet due t...

Anisotropic non-Fermi liquids

“…We note that Fig. 3e does not contribute to the beta functions, because it is UV finite at d = 3 [37].…”

“…However, the effect of the interactions is rather limited in the presence of the C 4 symmetry, which constrains the x and y components of momentum to scale identically. Because the deviation from perfect nesting flows to zero only logarithmically in length scale [20,21,26,37,39], the Fermi surface nesting becomes noticeable only when the momentum is exponentially close to the hot spots. The situation is different when the C 4 symmetry is explicitly or spontaneously broken to two-fold rotational (C 2 ) symmetry [40][41][42][43][44][45][46][47][48].…”

Calculation of the magnetotransport for a spin-density-wave quantum critical theory in the presence of weak disorder

“…As a result, its expression can be written as J k /∂k x ∂k y ). In this way, we can conclude that, when the Fermi surface of a given model possesses flat regions -as it happens, e.g., in the so-called hot spot model 10,19,21,23 -both the Hall current and the Hall conductivity σ xy will not have contributions from these specific regions. This fact will be important for the considerations that follow in the present work.…”

“…This happens because of the emergent particle-hole symmetry at the low-energy fixed point in the model and the resulting dynamical nesting of the corresponding renormalized Fermi surface (for explanations about this change of topology of the underlying Fermi surface that was obtained by several RG approaches for the hot spot model, see the Refs. 10,19,21,23 ). This fact underscores the importance of the emergent charge conjugationĈ symmetry at the hot spots in the low-energy effective theory.…”

“…In the SDW quantum critical scenario, the underlying mechanism for the formation of Cooper pairs in the superconducting phase of these compounds is rooted in the exchange of antiferromagnetic short-range SDW fluctuations 20 , which are enhanced close to the quantum critical point 10 . On the theoretical side, many works have described several aspects of the properties of the Abanov-Chubukov spin-fermion model using various complementary analytical 10,15,19,[21][22][23][24][25][26] and numerical 27 techniques. In this respect, it is now clear that the quasiparticle excitations are destroyed at the socalled hot spots (i.e., the intersection of the underlying Fermi surface with the antiferromagnetic zone boundary) at low energies 19,27 .…”