Search

Strange metals, heavy fermion metals, and quantum spin liquids are among the most intriguing and yet intellectually challenging topics in condensed matter physics. Here we report the experimental discovery of a perpetual heavy Fermi surface consisting of charge-neutral spinons that underpins both a heavy-fermion strange metal and a quantum spin liquid, which occur in an unlikely place, a 4d-electron trimer lattice Ba4Nb1-xRu3+xO12. Both states exhibit a universally large storage of entropy at the milli-Kelvin regime and a disassociation of charges and spins as such the heavy-fermion strange metal grossly violates the Wiedemann-Franz law, and the quantum spin liquid is a much better thermal conductor than the heavy-fermion strange metal. The novel phenomenology offers an unprecedented paradigm of correlated quantum matter., four main figures

Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the kagome and breathing kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct an effective Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two seemingly novel phenomena, including an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices., 23 pages, 9 figures

We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest non-trivial setting: a system with charge and dipole symmetry, but without momentum conservation. When no symmetries are broken, our formalism reproduces the quartic subdiffusion ($\omega \sim -i k^4$) characteristic of `fracton hydrodynamics' with conserved dipole moment. Our formalism also captures spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is spontaneously broken, the hydrodynamic modes are quadratically propagating and quartically relaxing ($\omega \sim \pm k^2 - ik^4$). When the dipole symmetry is spontaneously broken but the charge symmetry is preserved, then we find quadratically relaxing (diffusive) transverse modes, plus another mode which depending on parameters may be either purely diffusive ($\omega \sim -i k^2$) or quadratically propagating and quadratically relaxing ($\omega \sim \pm k^2 -i k^2$). Our work provides concrete predictions that may be tested in near-term cold atom experiments, and also lays out a general framework that may be applied to study systems with spontaneously broken multipolar symmetries., Comment: 4+2+epsilon pages, 3 figures

We present a set of generalized quantum loop models which provably exhibit topologically stable ergodicity breaking. These results hold for both periodic and open boundary conditions, and derive from a one-form symmetry (notably not being restricted to sectors of extremal one-form charge). We identify simple models in which this one-form symmetry can be emergent, giving rise to the aforementioned ergodicity breaking as an exponentially long-lived prethermal phenomenon. We unveil a web of dualities that connects these models, in certain limits, to models that have previously been discussed in the literature. We also identify nonlocal conserved quantities in such models that correspond to a pattern of system-spanning domain walls, and which are robust to the addition of arbitrary $k$-local perturbations., Comment: 22+8 pages, 8 figures; v2 includes minor revisions and additional references

Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit, is a key question in quantum condensed matter physics, quantum information, and quantum computation. It underpins classifications of topological phases, as well as the understanding of topological quantum codes, and has obvious relevance for device implementations. Traditionally, this question assumes that the quantum circuit is made up of unitary gates which are geometrically local. Inspired by the advent of noisy intermediate-scale quantum devices, we reconsider this question with $k$-local gates, i.e. gates that act on no more than $k$ degrees of freedom but are not restricted to be geometrically local. We show that symmetry-protected topological states (SPTs) can be produced by starting with a product state and acting with a finite-depth circuit of symmetric $k$-local gates, and are thus $k$-local trivial. These conclusions apply both to SPTs protected by global symmetries and subsystem symmetries, but seemingly not to higher-form symmetries. We also show that arbitrary translationally-invariant quantum cellular automata on periodic lattices in any dimension can be implemented by finite-depth $k$-local circuits. We conclude by discussing the implications for other phases, such as fracton phases, and surveying future directions. Our analysis opens a new experimentally motivated conceptual direction examining the feasibility of state preparation and the stability of phases without the assumption of geometric locality and has broad implications for condensed matter physics, quantum information, and quantum computation., 13+4 pages, 8 figures

The origin of the pseudogap in many strongly correlated materials has been a longstanding puzzle. Here, we uncover which many-body interactions underlie the pseudogap in quasi-one-dimensional (quasi-1D) material (TaSe4)2I by weak photo-excitation of the material to partially melt the ground state order and thereby reveal the underlying states in the gap. We observe the appearance of both dispersive and flat bands by using time- and angle-resolved photoemission spectroscopy. We assign the dispersive band to a single-particle bare band, while the flat band to a collection of single-polaron sub-bands. Our results provide direct experimental evidence that many-body interactions among small Holstein polarons i.e., the formation of bipolarons, are primarily responsible for the pseudogap in (TaSe4)2I. Recent theoretical studies of the Holstein model support the presence of such a bipolaron-to-polaron crossover. We also observe dramatically different relaxation times for the excited in-gap states in (TaSe4)2I (~600 fs) compared with another quasi-1D material Rb0.3MoO3 (~60 fs), which provides a new method for distinguishing between pseudogaps induced by polaronic or Luttinger-liquid many-body interactions.

We present a new route to ergodicity breaking via Hilbert space fragmentation that displays an unprecedented level of robustness. Our construction relies on a single emergent (prethermal) conservation law. In the limit when the conservation law is exact, we prove the emergence of Hilbert space fragmentation with an exponential number of frozen configurations. We further prove that every frozen configuration is absolutely stable to arbitrary perturbations, to all finite orders in perturbation theory. In particular, our proof is not limited to symmetric perturbations, or to perturbations with compact support, but also applies to perturbations with long-range tails, and even to arbitrary geometrically nonlocal $k$-body perturbations, as long as $k/L \rightarrow 0$ in the thermodynamic limit, where $L$ is linear system size. Additionally, we identify one-form $U(1)$ charges characterizing some non-frozen sectors, and discuss the dynamics starting from typical initial conditions, which we argue is best interpreted in terms of the magnetohydrodynamics of the emergent one-form symmetry., Comment: 5+9 pages, 2+10 figures; v2 includes updated supplement

We explore universality and phases of matter in hybrid quantum dynamics combining chaotic time evolution and projective measurements. We develop a unitary representation of measurements based on the Stinespring Theorem, which we crucially identify with the time evolution of the system and measurement apparatus, affording significant technical advantages and conceptual insight into hybrid dynamics. We diagnose spectral properties in the presence of measurements for the first time, along with standard, experimentally tractable probes of phase structure, finding no nontrivial effects due to measurements in the absence of feedback. We also establish that nonlinearity in the density matrix is neither sufficient nor necessary to see a transition, and instead identify utilization of the measurement outcomes (i.e., ``feedback'') as the crucial ingredient. After reviewing the definition of a phase of matter, we identify nontrivial orders in adaptive hybrid dynamics -- in which measurement outcomes determine future unitary gates -- finding a genuine measurement-induced absorbing-state phase transition in an adaptive quantum East model. In general, we find that only deterministic and constrained Haar-random dynamics with active feedback and without continuous symmetries can realize genuine, measurement-induced phases of matter., Comment: 36 + 8 pages, 9 figures; v2 includes numerical simulations of adaptive dynamics, clarifications throughout

We extend recent work on hydrodynamics with global multipolar symmetries -- known as "fracton hydrodynamics" -- to systems in which the multipolar symmetries are gauged. We refer to the latter as "fracton magnetohydrodynamics", in analogy to conventional magnetohydrodynamics (MHD), which governs systems with gauged charge conservation. We show that fracton MHD arises naturally from higher-rank Maxwell's equations and in systems with one-form symmetries obeying certain constraints; while we focus on "minimal" higher-rank generalizations of MHD that realize diffusion, our methods may also be used to identify other, more exotic hydrodynamic theories (e.g., with magnetic subdiffusion). In contrast to semi-microscopic derivations of MHD, our approach elucidates the origin of the hydrodynamic modes by identifying the corresponding higher-form symmetries. Being rooted in symmetries, the hydrodynamic modes may persist even when the semi-microscopic equations no longer provide an accurate description of the system., Comment: 44 pages, 2 figures; "Microscopic Hamiltonians" section added in v2

We investigate how the real and imaginary charge density waves interplay at the Van Hove singularity on the hexagonal lattices. A phenomenological analysis indicates the formation of $3Q$ complex orders at all three nesting momenta. Under a total phase condition, unequal phases at the three momenta break the rotation symmetry generally. The $3Q$ complex orders constitute a rich Haldane-model phase diagram. When effective time-reversal symmetries arise under 1-site translations, the Dirac semimetals are protected. The breakdown of these symmetries gaps the Dirac points and leads to the trivial and Chern insulator phases. These phases are deformations of purely real and imaginary orders, which exhibit trivial site and/or bond density and chiral flux orders, respectively. The exotic single-Dirac-point semimetals also appear along the gapless phase boundary. We further show that the theoretical model offers transparent interpretations of experimental observations in the kagome metals $\text{AV}_3\text{Sb}_5$ with $\text{A}=\text{K},\text{Rb},\text{Cs}$. The topological charge density waves may be identified with the complex orders in the Chern insulator phase. Meanwhile, the lower-temperature symmetry-breaking phenomena may be interpreted as the secondary orders from the complex order ground states. Our work sheds light on the nature of the topological charge density waves in the kagome metals $\text{AV}_3\text{Sb}_5$ and may offer useful indications to the experimentally observed charge orders in the future experiments., 14 pages, 9 figures. v3: Published version

We study the quantum dynamics of a simple translation invariant, center-of-mass (CoM) preserving model of interacting fermions in one dimension (1D), which arises in multiple experimentally realizable contexts. We show that this model naturally displays the phenomenology associated with fractonic systems, wherein single charges can only move by emitting dipoles. This allows us to demonstrate the rich Krylov fractured structure of this model, whose Hilbert space shatters into exponentially many dynamically disconnected subspaces. Focusing on exponentially large Krylov subspaces, we show that these can be either be integrable or non-integrable, thereby establishing the notion of Krylov-restricted thermalization. We analytically find a tower of integrable Krylov subspaces of this Hamiltonian, all of which map onto spin-1/2 XX models of various system sizes. We also discuss the physics of the non-integrable subspaces, where we show evidence for weak Eigenstate Thermalization Hypothesis (ETH) restricted to each non-integrable Krylov subspace. Further, we show that constraints in some of the thermal Krylov subspaces cause the long-time expectation values of local operators to deviate from behavior typically expected from translation-invariant systems. Finally, we show using a Schrieffer-Wolff transformation that such models naturally appear as effective Hamiltonians in the large electric field limit of the interacting Wannier-Stark problem, and comment on connections of our work with the phenomenon of Bloch many-body localization., Comment: 29 pages, 3 figures

We show that the large orbital degeneracy inherent in Moir�� heterostructures naturally gives rise to a `high-$T_c$' like phase diagram with a chiral twist - wherein an exotic $\textit{quantum anomalous Hall}$ insulator phase is flanked by chiral $d+id$ superconducting domes. Specifically, we analyze repulsively interacting fermions on hexagonal (triangular or honeycomb) lattices near Van Hove filling, with an ${\rm SU}(N_f)$ flavor degeneracy. This model is inspired by recent experiments on graphene Moir�� heterostructures. At this point, a nested Fermi surface and divergent density of states give rise to strong ($\ln^2$) instabilities to correlated phases, the competition between which can be controllably addressed through a combination of weak coupling parquet renormalization group and Landau-Ginzburg analysis. For $N_f=2$ (i.e. spin degeneracy only) it is known that chiral $d+id$ superconductivity is the unambiguously leading weak coupling instability. Here we show that $N_f\geq4$ leads to a richer (but still unambiguous and fully controllable) behavior, wherein at weak coupling the leading instability is to a fully gapped and chiral $\textit{Chern insulator}$, characterized by a spontaneous breaking of time reversal symmetry and a quantized Hall response. Upon doping this phase gives way to a chiral $d+id$ superconductor. We further consider deforming this minimal model by introducing an orbital splitting of the Van Hove singularities, and discuss the resulting RG flow and phase diagram. Our analysis thus bridges the minimal model and the practical Moir�� band structures, thereby providing a transparent picture of how the correlated phases arise under various circumstances. Meanwhile, a similar analysis on the square lattice predicts a phase diagram where (for $N_f>2$) a nodal staggered flux phase with `loop current' order gives way upon doping to a nodal $d$-wave superconductor., 20 pages, 8 figures. Add analysis of orbital splitting, bridging the minimal model and the practical Moire band structures

We show how local constraints can globally "shatter" Hilbert space into subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a "fractonic circuit" - a model of quantum circuit dynamics in one dimension constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic circuit dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. A large number of the emergent subsectors, exponentially many in the size of the system, have dimension one and exhibit strictly localized quantum dynamics---even in the absence of spatial disorder and in the presence of temporal noise. Exponentially large localized subspaces can be proven to exist for any one dimensional fractonic circuit with finite spatial range, and provide a potentially new route for the robust storage of quantum information. Other emergent subsectors display non-trivial dynamics and may be constructed by embedding finite sized non-trivial blocks into the localized subspace. The shattering of a particular symmetry sector into a distribution of dynamical subsectors with varying sizes leads to the coexistence of high and low entanglement states, i.e. this provides a general mechanism for the production of quantum many body scars. We discuss the detailed pattern of fracturing and its implications. We also discuss other mechanisms for similarly shattering Hilbert space., Comment: v3 - some discussions expanded and clarified

Measurement and control of magnetic order and correlations in real time is a rapidly developing scientific area relevant for magnetic memory and spintronics [1,15]. In these experiments an ultra-short laser pulse (pump) is first absorbed by excitations carrying electric dipole moment. These then give their energy to the magnetic subsystem monitored by a time-resolved probe. A lot of progress has been made in investigations of ferromagnets but antiferromagnets are more challenging. Here we introduce time-resolved two-magnon Raman scattering as a novel real time probe of magnetic correlations especially well-suited for antiferromagnets. Its application to the antiferromagnetic charge transfer insulator YBa$_2$Cu$_3$O$_{6+x}$ revealed rapid demagnetization within 90fs of photoexcitation. The relaxation back to thermal equilibrium is characterized by much slower timescales. We interpret these results in terms of slow relaxation of the charge sector and rapid equilibration of the magnetic sector to a prethermal state characterized by parameters that change slowly as the charge sector relaxes.

Three band crossings can arise in three dimensional quantum materials with certain space group symmetries. The low energy Hamiltonian supports spin $\textit{one}$ fermions and a flat band. We study the pairing problem in this setting. We write down a minimal BCS Hamiltonian and decompose it into spin-orbit coupled irreducible pairing channels. We then solve the resulting gap equations in channels with zero total angular momentum. We find that in the spin singlet channel (and also in an unusual `spin quintet' channel), superconductivity is enormously enhanced, with a possibility for the critical temperature to be $\textit{linear}$ in interaction strength. Meanwhile, in the spin triplet channel, the superconductivity exhibits features of conventional BCS theory due to the absence of flat band pairing. Three band crossings thus represent an exciting new platform for realizing exotic superconducting states with enhanced energy scales. We also discuss the effects of doping, nonzero temperature, and of retaining additional terms in the $\mathbf{k} \cdot \mathbf{p}$ expansion of the Hamiltonian., Comment: 17 pages, 8 figures. v2: Streamlined calculation, fixed a sign error that affected some quasiparticle dispersions, expanded discussions to include finite doping, temperature and band curvature

We review what is known about fracton phases of quantum matter. Fracton phases are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics, or mobile only in certain directions. They constitute a new class of quantum state of matter, which does not wholly fit into any of the existing paradigms, but which connects to areas including glassy quantum dynamics, topological order, spin liquids, elasticity theory, quantum information theory, and gravity. We begin by discussing gapped fracton phases, which may be described using exactly solvable lattice spin models. We introduce the basic phenomena, and discuss the geometric and topological response of fracton phases. We also discuss connections to generalized gauge theories, and explain how gapped fracton phases may be obtained from more familiar theories. We then introduce the framework of tensor gauge theory, which provides a powerful complementary perspective on fracton phases. We discuss how tensor gauge theory encodes the fracton phenomenon, and how it allows us to access gapless fracton phases. We discuss the basic properties of gapless fracton phases, and their connections to elasticity theory and gravity. We also discuss what is known about the dynamics and thermodynamics of fractons at non-zero density, before concluding with a brief survey of some open problems., Review article

We numerically explore the many body localization (MBL) transition through the lens of the {\it entanglement spectrum}. While a direct transition from localization to thermalization is believed to obtain in the thermodynamic limit (the exact details of which remain an open problem), in finite system sizes there exists an intermediate `quantum critical' regime. Previous numerical investigations have explored the crossover from thermalization to criticality, and have used this to place a numerical {\it lower} bound on the critical disorder strength for MBL. A careful analysis of the {\it high energy} part of the entanglement spectrum (which contains universal information about the critical point) allows us to make the first ever observation in exact numerics of the crossover from criticality to MBL and hence to place a numerical {\it upper bound} on the critical disorder strength for MBL., 4 pages+appendix

We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three dimensional systems where absent disorder the non-interacting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a 'non-Fermi liquid' phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled $\epsilon$-expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. We find that the non-Fermi liquid fixed point is unstable to disorder, and demonstrate that the problem inevitably flows to strong coupling, outside the regime of applicability of the perturbative RG. An examination of the flow to strong coupling suggests that disorder is asymptotically more important than interactions, so that the low energy behavior of the system can be described by a non-interacting sigma model in the appropriate symmetry class (which depends on whether exact particle-hole symmetry is imposed on the problem). We close with a discussion of general principles unveiled by our analysis that dictate the interplay of disorder and Coulomb interactions in gapless semiconductors, and of connections to many-body localized systems with long-range interactions., Comment: 15 pages, 4 figures

We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bath. Using general arguments and dimensional analysis, we constrain the overall phase diagram of the coupled system and bath. Our analysis incorporates all the previously discussed regimes, and also uncovers a new intrinsically quantum regime that has not hitherto been discussed. We discuss baths that are themselves near a localization transition, or are strongly disordered but protected against localization by symmetry or topology. We also discuss situations where the system and bath have different dimensionality (the case of `boundary MBL' and `boundary baths')., Updated references

We use exact diagonalization to study the breakdown of many-body localization in a strongly disordered and interacting system coupled to a thermalizing environment. We show that the many-body level statistics cross over from Poisson to GOE, and the localized eigenstates thermalize, with the crossover coupling decreasing with the size of the bath in a manner consistent with the hypothesis that an infinitesimally small coupling to a thermodynamic bath should destroy localization of the eigenstates. However, signatures of incomplete localization survive in spectral functions of local operators even when the coupling to the environment is non-zero. These include a discrete spectrum and a gap at zero frequency. Both features are washed out by line broadening as one increases the coupling to the bath., Some corrections made

We study three-dimensional Dirac fermions with weak finite-range scalar potential disorder. In the clean system, the density of states vanishes quadratically at the Dirac point. Disorder is known to be perturbatively irrelevant, and previous theoretical work has assumed that the Dirac semimetal phase, characterized by a vanishing density of states, survives at weak disorder, with a finite disorder phase transition to a diffusive metal with a non-vanishing density of states. In this paper we show that nonperturbative effects from rare regions, which are missed by conventional disorder-averaged calculations, instead give rise to a nonzero density of states for any nonzero disorder. Thus, there is no Dirac semimetal phase at non-zero disorder. The results are established both by a heuristic scaling argument and via a systematic saddle point analysis. We also discuss transport near the Dirac point. At the Dirac point, we argue that transport is diffusive, and proceeds via hopping between rare resonances. As one moves in chemical potential away from the Dirac point, there are interesting intermediate-energy regimes where the rare regions produce scattering resonances that determine the DC conductivity. We derive a scaling theory of transport near disordered 3D Dirac points. We also discuss the interplay of disorder with attractive interactions at the Dirac point, and the resulting granular superconducting and Bose glass phases. Our results are relevant for all 3D systems with Dirac points, including Weyl semimetals., Comment: Expanded version of 1307.3252 with many new results, including a new section showing how the results may be derived using a systematic saddle point calculation

We study three-dimensional Dirac fermions with weak finite-range scalar potential disorder. We show that even though disorder is perturbatively irrelevant at 3D Dirac points, nonperturbative effects from rare regions give rise to a nonzero density of states and a finite mean free path, with the transport at the Dirac point being dominated by hopping between rare regions. As one moves in chemical potential away from the Dirac point, there are interesting intermediate-energy regimes where the rare regions produce scattering resonances that determine the DC conductivity. We also discuss the interplay of disorder with interactions at the Dirac point. Attractive interactions drive a transition into a granular superconductor, with a critical temperature that depends strongly on the disorder distribution. In the presence of Coulomb repulsion and weak retarded attraction, the system can be a Bose glass. Our results apply to all 3D systems with Dirac points, including Weyl semimetals, and overturn a thirty year old consensus regarding the irrelevance of weak disorder at 3D Dirac points., Comment: minor changes

Interference and tunneling are two signature quantum effects that are often perceived as the yin and yang of quantum mechanics: particle simultaneously propagating along several distinct classical paths versus particle penetrating through a classically inaccessible region via a single least-action path. Here we demonstrate that the Dirac quasiparticles in graphene provide a dramatic departure from this paradigm. We show that Zener tunneling in gapped bilayer graphene (BLG), which governs transport through p-n heterojunctions, exhibits common-path interference that takes place under the tunnel barrier. Due to a symmetry peculiar to the BLG bandstructure, interfering tunneling paths form `conjugate pairs', giving rise to high-contrast oscillations in transmission as a function of the gate-tunable bandgap and other control parameters of the junction. The common-path interference is solely due to forward-propagating waves; in contrast to Fabry-Perot-type interference in resonant tunneling structures it does not rely on multiple backscattering. The oscillations manifest themselves in the junction I-V characteristic as N-shaped branches with negative differential conductivity, enabling new high-speed active-circuit devices with architectures which are not available in electronic semiconductor devices., Comment: 7 pgs, 5 fgs

We analyze competition between different ordered states in bilayer graphene (BLG). Combining arguments based on SU(4) spin-valley flavor symmetry with a mean field analysis, we identify the lowest energy state with the anomalous Hall insulator (AHI). This state is an SU(4) singlet excitonic insulator with broken time reversal symmetry, exhibiting quantized Hall effect in the absence of external magnetic field. Applied electric field drives an Ising-type phase transition, restoring time reversal symmetry. Applied magnetic field drives a transition from the AHI state to a quantum Hall ferromagnet state. We estimate energies of these states, taking full account of screening, and predict the phase diagram., 4.1 pgs

We analyze the many-body properties of bilayer graphene (BLG) at charge neutrality, governed by long range interactions between electrons. Perturbation theory in a large number of flavors is used in which the interactions are described within a random phase approximation, taking account of dynamical screening effect. Crucially, the dynamically screened interaction retains some long range character, resulting in $\log^2$ renormalization of key quantities. We carry out the perturbative renormalization group calculations to one loop order, and find that BLG behaves to leading order as a marginal Fermi liquid. Interactions produce a log squared renormalization of the quasiparticle residue and the interaction vertex function, while all other quantities renormalize only logarithmically. We solve the RG flow equation for the Green function with logarithmic accuracy, and find that the quasiparticle residue flows to zero under RG. At the same time, the gauge invariant quantities, such as the compressibility, remain finite to $\log^2$ order, with subleading logarithmic corrections. The key experimental signature of this marginal Fermi liquid behavior is a strong suppression of the tunneling density of states, which manifests itself as a zero bias anomaly in tunneling experiments in a regime where the compressibility is essentially unchanged from the non-interacting value., Comment: 12 pages, 3 figures

Electron interactions in undoped bilayer graphene lead to instability of the gapless state, `which-layer' symmetry breaking, and energy gap opening at the Dirac point. In contrast to single layer graphene, the bilayer system exhibits instability even for arbitrarily weak interaction. A controlled theory of this instability for realistic dynamically screened Coulomb interactions is developed, with full acount of dynamically generated ultraviolet cutoff. This leads to an energy gap that scales as a power law of the interaction strength, making the excitonic instability readily observable., Comment: 4 pgs, 2 fgs