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Recently, superconductivity has been observed in twisted WSe$_2$ moir\'{e} structures (Xia et al., arXiv:2405.14784; Guo et al., arXiv:2406.03418). Its transition temperature is high, reaching a few percent of the Fermi temperature scale. Here, we advance a mechanism for superconductivity based on the notion that electronic topology enables quantum fluctuations in a suitable regime of intermediate correlations. In this regime, the Coulomb interaction requires that an active topological flat band and nearby wider bands are considered together. Compact molecular orbitals arise, which experience quantum fluctuations through topology-dictated hybridization with the other molecular orbitals. The hybridization competes with the active flat band' natural tendency towards static electronic ordering, thereby weakening the latter; we link this effect with certain salient observations by experiments. Furthermore, the competition yields a quantum critical regime where quasiparticles are lost. The corresponding quantum critical fluctuations drive superconductivity. Broader implications and new connections among correlated materials platforms are discussed., Comment: 8 pages, 5 figures

The nature of charge carriers in strange metals has become a topic of intense current investigation. Recent shot noise measurements in the quantum critical heavy fermion metal YbRh$_2$Si$_2$ revealed a suppression of the Fano factor that cannot be understood from electron-phonon scattering or strong electron correlations in a Fermi liquid, indicating loss of quasiparticles. The experiment motivates the consideration of shot noise in a variety of theoretical models in which quasiparticles may be lost. Here we study shot noise in systems with co-existing itinerant electrons and dispersive bosons, going beyond the regime where the bosons are on their own in thermal equilibrium. We construct the Boltzmann-Langevin equations for the coupled system, and show that adequate electron-boson couplings restore the Fano factor to its Fermi liquid value. Our findings point to the beyond-Landau form of quantum criticality as underlying the suppressed shot noise of strange metals in heavy fermion metals and beyond., Comment: 13 pages, 4 figures

Kagome metals offer a unique platform for investigating robust electron-correlation effects because of their lattice geometry, flat bands and multi-orbital nature. In the cases with active flat bands, recent theoretical studies have pointed to a rich phase diagram that contains not only electronic orders but also quantum criticality. $\rm CsCr_3Sb_5$ has emerged as a strong candidate for exploring such new physics. Here, using effective tight-binding models obtained from ab initio calculations, we study the effects of electronic correlations and symmetries on the electronic structure of $\rm CsCr_3 Sb_5$. The effective tight-binding model and Fermi surface comprise multiple Cr-$d$ orbitals and Sb-$p$ orbitals. The introduction of Hubbard-Kanamori interactions leads to orbital-selective band renormalization dominated by the $d_{xz}$ band, concurrently producing emergent flat bands very close to the Fermi level. Our analysis sets the stage for further investigations into the electronic properties of $\rm CsCr_3Sb_5$, including electronic orders, quantum criticality and unconventional superconductivity, which promise to shed much new light into the electronic materials with frustrated lattices and bring about new connections with the correlation physics of a variety of strongly correlated systems., Comment: 6 + 6 pages, 4 + 5 figures

Despite much theoretical work, developing a comprehensive ab initio model for twisted bilayer graphene (TBG) has proven challenging due to the inherent trade-off between accurately describing the band structure and incorporating the interactions within the Hamiltonian, particularly given the topological obstruction -- so-called fragile topology -- to the description of the model in terms of localized symmetric Wannier functions within the flat band manifold. Here, we circumvent this obstruction by using an extended 8-orbital model, for which localized Wannier orbitals have been formulated by Carr et al. [1]. We constructed an extended multi-orbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings from -3 to 3. We found several nearly-degenerate insulating states at charge neutrality, all of which exhibit orbital orders. Crucially, TBG near magic angle is known to be particle-hole asymmetric, which is naturally captured by the single-particle band structure of our model and is reflected in the distinction between the symmetry broken states obtained at electron and hole dopings away from the charge neutral point. At filling -1 and +2, quantum anomalous hall states are obtained, while for the rest of the integer fillings away from charge neutrality, we found the system to realize metallic states with various orbital, valley and spin orderings. We also observed that most of the Hartree--Fock ground states exhibit a generalized valley Hund's-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intra-valley and inter-valley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.

The intersection of electronic topology and strong correlations offers a rich platform to discover exotic quantum phases of matter and unusual materials. An overarching challenge that impedes the discovery is how to diagnose strongly correlated electronic topology. Here, we develop a framework to address this outstanding question, and illustrate its power in the setting of electronic topology in Mott insulators. Based on single-particle Green's functions, the concept of a Green's function Berry curvature -- which is frequency dependent -- is introduced. We apply this notion in a system that contains symmetry-protected nodes in its noninteracting bandstructure; strong correlations drive the system into a Mott insulating state, creating contours in frequency-momentum space where the Green's function vanishes. The Green's function Berry flux of such zeros is found to be quantized, and is as such direct probe of the system's topology. Our framework allows for a systematic search of strongly correlated topological materials with Green's function topology., Comment: 38 pages, 13 figures including Supplemental Information

There is extensive current interest about electronic topology in correlated settings. In strongly correlated systems, contours of Green's function zeros may develop in frequency-momentum space, and their role in correlated topology has increasingly been recognized. However, whether and how the zeros contribute to electronic properties is a matter of uncertainty. Here we address the issue in an exactly solvable model for Mott insulator. We show that the Green's function zeros contribute to several physically measurable correlation functions, in a way that does not run into inconsistencies. In particular, the physical properties remain robust to chemical potential variations up to the Mott gap as it should be based on general considerations. Our work sets the stage for further understandings on the rich interplay among topology, symmetry and strong correlations., Comment: 17 pages, 4 figures

Strange metals arise in a variety of platforms for strongly correlated electrons, ranging from the cuprates, heavy fermions to flat band systems. Motivated by recent experiments in kagome metals, we study a Hubbard model on a kagome lattice whose noninteracting limit contains flat bands. A Kondo lattice description is constructed, in which the degrees of freedom are exponentially localized molecular orbitals. We identify an orbital-selective Mott transition through an extended dynamical mean field theory of the effective model. The transition describes a quantum critical point at which quasiparticles are lost and strange metallicity emerges. Our theoretical work opens up a new route for realizing beyond-Landau quantum criticality and emergent quantum phases that it nucleates., Comment: 38 pages, 11 figures

Lattice symmetries are central to the characterization of electronic topology. Recently, it was shown that Green's function eigenvectors form a representation of the space group. This formulation has allowed the identification of gapless topological states even when quasiparticles are absent. Here we demonstrate the profundity of the framework in the extreme case, when interactions lead to a Mott insulator, through a solvable model with long-range interactions. We find that both Mott poles and zeros are subject to the symmetry constraints, and relate the symmetry-enforced spectral crossings to degeneracies of the original non-interacting eigenstates. Our results lead to new understandings of topological quantum materials and highlight the utility of interacting Green's functions toward their symmetry-based design., Comment: To appear in PRR Letter. 7 pages, 2 figures + Supplemental Material

Flat electronic bands are expected to show proportionally enhanced electron correlations, which may generate a plethora of novel quantum phases and unusual low-energy excitations. They are increasingly being pursued in $d$-electron-based systems with crystalline lattices that feature destructive electronic interference, where they are often topological. Such flat bands, though, are generically located far away from the Fermi energy, which limits their capacity to partake in the low-energy physics. Here we show that electron correlations produce emergent flat bands that are pinned to the Fermi energy. We demonstrate this effect within a Hubbard model, in the regime described by Wannier orbitals where an effective Kondo description arises through orbital-selective Mott correlations. Moreover, the correlation effect cooperates with symmetry constraints to produce a topological Kondo semimetal. Our results motivate a novel design principle for Weyl Kondo semimetals in a new setting, viz. $d$-electron-based materials on suitable crystal lattices, and uncover interconnections among seemingly disparate systems that may inspire fresh understandings and realizations of correlated topological effects in quantum materials and beyond., Comment: To appear in Nature Communications; submitted version of the manuscript; 33 pages, 4 figures main text + 7 figures supplementary information

In time-reversal symmetry-broken Weyl semimetals, Weyl points act as monopoles and antimonopoles of the Berry curvature, with a monopole-antimonopole pair producing a net zero Berry flux. The two-dimensional (2D) planes that separate a monopole-antimonopole pair of Weyl points carry quantized Berry flux. In this work, we introduce a class of symmetry-protected Weyl semimetals which host monopole-antimonopole pairs of Weyl points that generate a quantized dipolar Berry flux. Consequently, topologically distinct 2D planes coexist in the Brillouin zone, carrying either quantized monopolar or dipolar flux. We construct a topological invariant -- the staggered Chern number -- to measure the quantized dipolar flux and employ it to topologically distinguish between various Weyl points. Finally, through a minimal two-band model, we investigate physical signatures of bulk topology, including surface Fermi arcs, zero-energy hinge states, and response to insertion of a $\pi$-flux vortex., Comment: 12 pages; 9 figures

Shot noise measures out-of-equilibrium current fluctuations and is a powerful tool to probe the nature of current-carrying excitations in quantum systems. Recent shot noise measurements in the heavy fermion strange metal YbRh$_2$Si$_2$ exhibit a strong suppression of the Fano factor ($F$) -- the ratio of the current noise to the average current in the DC limit. This system is representative of metals in which electron correlations are extremely strong. Here we carry out the first theoretical study on the shot noise of diffusive metals in the regime of strong correlations. A Boltzmann-Langevin equation formulation is constructed in a quasiparticle description in the presence of strong correlations. We find that $F = \sqrt{ 3}/{4}$ in such a correlation regime. Hence, the Fano factor suppression observed in experiments on YbRh$_2$Si$_2$ necessitates a loss of the quasiparticles. Our work opens the door to systematic theoretical studies of shot noise as a means of characterizing strongly correlated metallic phases and materials., Comment: 6+2 pages, 2+1 figures

Frustrated spin-systems have traditionally proven challenging to understand, owing to a scarcity of controlled methods for their analyses. By contrast, under strong magnetic fields, certain aspects of spin systems admit simpler and universal description in terms of hardcore bosons. The bosonic formalism is anchored by the phenomenon of Bose-Einstein condensation (BEC), which has helped explain the behaviors of a wide range of magnetic compounds under applied magnetic fields. Here, we focus on the interplay between frustration and externally applied magnetic field to identify instances where the BEC paradigm is no longer applicable. As a representative example, we consider the antiferromagnetic $J_1 - J_2 - J_3$ model on the square lattice in the presence of a uniform external magnetic field, and demonstrate that the frustration-driven suppression of the N\'{e}el order leads to a Lifshitz transition for the hardcore bosons. In the vicinity of the Lifshitz point, the physics becomes unmoored from the BEC paradigm, and the behavior of the system, both at and below the saturation field, is controlled by a Lifshitz multicritical point. We obtain the resultant universal scaling behaviors, and provide strong evidence for the existence of a frustration and magnetic-field driven correlated bosonic liquid state along the entire phase boundary separating the N\'{e}el phase from other magnetically ordered states., Comment: 14 pages; 9 figures; v3) published version

Strange-metal behavior has been observed in materials ranging from high-temperature superconductors to heavy fermion metals. In conventional metals, current is carried by quasiparticles; although it has been suggested that quasiparticles are absent in strange metals, direct experimental evidence is lacking. We measured shot noise to probe the granularity of the current-carrying excitations in nanowires of the heavy fermion strange metal YbRh2Si2. When compared with conventional metals, shot noise in these nanowires is strongly suppressed. This suppression cannot be attributed to either electron-phonon or electron-electron interactions in a Fermi liquid, which suggests that the current is not carried by well-defined quasiparticles in the strange-metal regime that we probed. Our work sets the stage for similar studies of other strange metals., Comment: 22 pages, 4 figures; 21 pages supplementary text, 11 supplementary figures

Benalcazar-Bernevig-Hughes (BBH) models, defined on $D$-dimensional simple cubic lattice, are paradigmatic toy models for studying $D$-th order topology and corner-localized, mid-gap states. Under periodic boundary conditions, the Wilson loops of non-Abelian Berry connection of BBH models along all high-symmetry axes have been argued to exhibit gapped spectra, which predict gapped surface-states under open boundary conditions. In this work, we identify 1D, 2D, and 3D topological invariants for characterizing higher order topological insulators. Further, we demonstrate the existence of cubic-symmetry-protected, gapless spectra of Wilson loops and surface-states along the body diagonal directions of the Brillouin zone of BBH models. We show the gapless surface-states are described by $2^{D-1}$-component, massless Dirac fermions. Thus, BBH models can exhibit the signatures of first and $D$-th order topological insulators, depending on the details of externally imposed boundary conditions., Comment: 13 pages; 7 figures. (v2) added discussions on 3D invariant, observables, and non-BBH class models; new figures; updated reference list; abstract updated accordingly

Exponentially localized surface states are the most distinctive property of a crystal with non-trivial band topology. Such surface states play a key role in characterizing topological insulators (TIs), both in theory and experiments. TIs resulting from the hybridization of heavy (or nearly flat) and light (or dispersive) bands are automatically tuned to the vicinity of an insulator-to-metal phase transition (IMT), which is not accompanied by a change in bulk band-topology. By formulating a scaling theory for IMTs in such "heavy" TIs, we show that the proximity to an IMT manifests most dramatically in the behavior of the surface states, viz. (i) the strength of spin-orbital locking is strongly suppressed; (ii) the surface conduction and valence bands support vastly different number of states; (iii) the surface states penetrate deep into the bulk and the penetration depth diverges at the IMT point. Thus, the surface states in heavy TIs coexist with bulk scattered states, and may no longer serve as an useful determinant of their bulk band-topology. The mechanism of degradation of surface states discussed here is generic, and expected to hold in both heavy TIs and semimetals., Comment: 6 pages; 4 figures

The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with two fold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number $C = 1$., Comment: 14 pages, 12 figures

Band topology of anomalous quantum Hall insulators can be precisely addressed by computing Chern numbers of constituent non-degenerate bands that describe quantized, Abelian Berry flux through two-dimensional Brillouin zone. Can Chern numbers be defined for $SU(2)$ Berry connection of two-fold degenerate bands of materials preserving space-inversion ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetries or combined $\mathcal{PT}$ symmetry, without detailed knowledge of underlying basis? We affirmatively answer this question by employing a non-Abelian generalization of Stokes' theorem and describe a manifestly gauge-invariant method for computing magnitudes of quantized $SU(2)$ Berry flux (spin-Chern number) from eigenvalues of Wilson loops. The power of this method is elucidated by performing $\mathbb{N}$-classification of \emph{ab initio} band structures of three-dimensional, Dirac materials. Our work outlines a unified framework for addressing first-order and higher-order topology of insulators and semimetals, without relying on detailed symmetry data., Comment: 17 pages, 11 figures; substantial revision of computational aspects; new data on ab initio band structure of Dirac materials

Usually the quantum spin Hall states are expected to possess gapless, helical edge modes. Are there clean, non-interacting, quantum spin Hall states without gapless, edge modes? We show the generic, $n$-fold-symmetric, momentum planes of three-dimensional, stable Dirac semi-metals, which are orthogonal to the direction of nodal separation are examples of such generalized quantum spin Hall systems. We demonstrate that the planes lying between two Dirac points and the celebrated Bernevig-Zhang-Hughes model support identical quantized, non-Abelian Berry flux of magnitude $2 \pi$. Consequently, both systems exhibit spin-charge separation in response to electromagnetic, $\pi$-flux vortex. The Dirac points are identified as the unit-strength, monopoles of $SO(5)$ Berry connection, describing topological quantum phase transitions between generalized, quantum spin Hall and trivial insulators. Our work identifies precise bulk invariant and quantized response of Dirac semimetals and shows that many two-dimensional higher-order topological insulators can be understood as generalized quantum spin Hall systems, possessing gapped edge states., Comment: 5 pages, 3 figures; concise presentation of bulk invariant and new results on spin-charge separation in higher-order topological insulators and Dirac semimetals

Recently, a new group of layered transition-metal tetra-chalcogenides were proposed, via first principles calculations, to correspond to a new family of Weyl type-II semimetals with promising topological properties in the bulk as well as in the monolayer limit. In this article, we present measurements of the Shubnikov-de Haas (SdH) and de Haas-van Alphen effects under high magnetic fields for the type-II Weyl semimetallic candidate NbIrTe$_{4}$. We find that the angular dependence of the observed Fermi surface extremal cross-sectional areas agree well with our DFT calculations supporting the existence of Weyl type-II points in this material. Although we observe a large and non-saturating magnetoresistivity in NbIrTe$_{4}$ under fields all the way up to 35 T, Hall-effect measurements indicate that NbIrTe$_{4}$ is not a compensated semimetal. The transverse magnetoresistivity displays a four-fold angular dependence akin to the so-called butterfly magnetoresistivity observed in nodal line semimetals. However, we conclude that its field and this unconventional angular-dependence are governed by the topography of the Fermi-surface and the resulting anisotropy in effective masses and in carrier mobilities., Comment: 8 pages, 6 figures

We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly ($d_L$) and (at most) quadratically ($d_Q$) dispersing directions. By virtue of such a unifying scheme, we identify a new perturbative route to access various strongly interacting non-Dirac semimetals with $d_Q>0$. As a demonstrative example, we relate a two dimensional anisotropic semimetal with $d_L=d_Q=1$, describing the topological transition between a Dirac semimetal and a normal insulator, and its three dimensional counterparts with $d_L=1$, $d_Q=2$. We address the quantum critical phenomena and emergence of non-Fermi liquid states with unusual dynamical structures within the framework of an $\epsilon$ expansion, where $\epsilon=2-d_Q$, when these systems reside at the brink of charge- or spin-density-wave orderings, or an $s$-wave pairing. Our results can be germane to two-dimensional uniaxially strained optical honeymcomb lattice, $\alpha$-(BEDT-TTF)$_2\text{I}_3$., Comment: 5 pages, 3 figures; Published version

We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak coupling renormalization group, we study a spinless fermion system on a checkerboard lattice at half-filling, which has a quadratic band touching in the absence of interaction. In the presence of strong nearest-neighbor ($V_1$) and next-nearest-neighbor ($V_2$) interactions, we identify a site nematic insulator phase, a stripe insulator phase, and a phase separation region, in agreement with the phase diagram obtained analytically in the strong coupling limit (i.e. in the absence of fermion hopping). In the intermediate interaction regime, we establish a quantum anomalous Hall phase in the DMRG as evidenced by the spontaneous time-reversal symmetry breaking and the appearance of a quantized Chern number $C = 1$. For weak interaction, we utilize the power expanded Gibbs potential method that treats $V_1$ and $V_2$ on equal footing, as well as the weak coupling renormalization group. Our analytical results reveal that not only the repulsive $V_1$ interaction, but also the $V_2$ interaction (both repulsive and attractive), can drive the quantum anomalous Hall phase. We also determine the phase boundary in the $V_1$-$V_2$ plane that separates the semimetal from the quantum anomalous Hall state. Finally, we show that the nematic semimetal, which was proposed for $|V_2| \gg V_1$ at weak coupling in a previous study, is absent, and the quantum anomalous Hall state is the only weak coupling instability of the spinless quadratic band touching semimetal., Comment: 25 pages, 19 figures

In systems above one dimension a continuously degenerate minimum of the single particle dispersion is realized due to one or a combination of system-parameters such as lattice structure, isotropic spin-orbit coupling, and interactions. A unit codimension of the dispersion-minima leads to a divergent density of states which enhances the effects of interactions, and may lead to novel states of matter as exemplified by Luttinger liquids in one dimensional bosonic systems. Here we show that in dilute, homogeneous bosonic systems above one dimension, weak, spin-independent, inter-particle interactions stabilize a metallic state at zero temperature in the presence of a curved manifold of dispersion minima. In this metallic phase the system possesses a quasi long-range order with non-universal scaling exponents. At a fixed positive curvature of the manifold, increasing either the dilution or the interaction strength destabilizes the metallic state towards charge density wave states that break one or more symmetries. The magnitude of the wave vector of the dominant charge density wave state is controlled by the product of the mean density of bosons and the curvature of the manifold. We obtain the zero temperature phase diagram, and identify the phase boundary., Comment: 17.1 + 13 pages; 11 figures; v2: Section I revised + Appendix A added + some typos fixed

We study systems made of periodic arrays of one dimensional quantum wires, coupled by Coulomb interaction. Using bosonization an interacting metallic fixed point is obtained, which is shown to be a higher dimensional analogue of the Tomonaga-Luttinger liquid, or a sliding Luttinger liquid. This non-Fermi liquid metallic state, however, is unstable in the presence of weak interwire backscatterings, which favor charge density wave states and suppress pairing. Depending on the effective strength of the Coulomb repulsion and the size of interwire spacing various charge density wave states are stabilized, including Wigner crystal states. Our method allows for the determination of the specific ordering patterns, and corresponding energy and temperature scales., Comment: 10 pages, 5 figures

We study Weyl-loop semi-metals with short range interactions, focusing on the possible interaction driven instabilities. We introduce an $\epsilon$ expansion regularization scheme by means of which the possible instabilities may be investigated in an unbiased manner through a controlled weak coupling renormalization group calculation. The problem has enough structure that a `functional' renormalization group calculation (necessary for an extended Fermi surface) can be carried out analytically. The leading instabilities are identified, and when there are competing degenerate instabilities a Landau-Ginzburg calculation is performed to determine the most likely phase. In the particle-particle channel, the leading instability is found to be to a fully gapped chiral superconducting phase which spontaneously breaks time reversal symmetry, in agreement with general symmetry arguments suggesting that Weyl loops should provide natural platforms for such exotic forms of superconductivity. In the particle hole channel, there are two potential instabilities - to a gapless Pomeranchuk phase which spontaneously breaks rotation symmetry, or to a fully gapped insulating phase which spontaneously breaks mirror symmetry. The dominant instability in the particle hole channel depends on the specific values of microscopic interaction parameters., Comment: 15+5 pages, 7 figures

We study non-Fermi liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in $3-\epsilon$ dimensional momentum space. In three dimensions, quasilocal marginal Fermi liquids arise both at the SDW and CDW critical points : the speed of the collective mode along the ordering wavevector is logarithmically renormalized to zero compared to that of Fermi velocity. Below three dimensions, however, the SDW and CDW critical points exhibit drastically different behaviors. At the SDW critical point, a stable anisotropic non-Fermi liquid state is realized for small $\epsilon$, where not only time but also different spatial coordinates develop distinct anomalous dimensions. The non-Fermi liquid exhibits an emergent algebraic nesting as the patches of Fermi surface are deformed into a universal power-law shape near the hot spots. Due to the anisotropic scaling, the energy of incoherent spin fluctuations disperse with different power laws in different momentum directions. At the CDW critical point, on the other hand, the perturbative expansion breaks down immediately below three dimensions as the interaction renormalizes the speed of charge fluctuations to zero within a finite renormalization group scale through a two-loop effect. The difference originates from the fact that the vertex correction anti-screens the coupling at the SDW critical point whereas it screens at the CDW critical point., Comment: 27 pages, 15 figures; v2) References & clarification added

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 is realized at the antiferromagnetic (AF) quantum critical point 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 the subtle dynamical balance between screening and infrared singularity caused by the spontaneous reduction of effective dimensionality., Comment: v2) minor revision; appendix A added

A non-Fermi liquid state without time-reversal and parity symmetries arises when a chiral Fermi surface is coupled with a soft collective mode in two space dimensions. The full Fermi surface is described by a direct sum of chiral patch theories, which are decoupled from each other in the low energy limit. Each patch includes low energy excitations near a set of points on the Fermi surface with a common tangent vector. General patch theories are classified by the local shape of the Fermi surface, the dispersion of the critical boson, and the symmetry group, which form the data for distinct universality classes. We prove that a large class of chiral non-Fermi liquid states exist as stable critical states of matter. For this, we use a renormalization group scheme where low energy excitations of the Fermi surface are interpreted as a collection of (1+1)-dimensional chiral fermions with a continuous flavor labelling the momentum along the Fermi surface. Due to chirality, the Wilsonian effective action is strictly UV finite. This allows one to extract the exact scaling exponents although the theories flow to strongly interacting field theories at low energies. In general, the low energy effective theory of the full Fermi surface includes patch theories of more than one universality classes. As a result, physical responses include multiple universal components at low temperatures. We also point out that, in quantum field theories with extended Fermi surface, a non-commutative structure naturally emerges between a coordinate and a momentum which are orthogonal to each other. We show that the invalidity of patch description for Fermi liquid states is tied with the presence of UV/IR mixing associated with the emergent non-commutativity. On the other hand, UV/IR mixing is suppressed in non-Fermi liquid states due to UV insensitivity, and the patch description is valid., Comment: 37 pages, 25 figures; v3) Typos fixed