Strongly correlated phases of matter are often described in terms of straightforward electronic patterns. This has so far been the basis for studying the Fermi-Hubbard model realized with ultracold atoms. Here, we show that artificial intelligence (AI) can provide an unbiased alternative to this paradigm for phases with subtle, or even unknown, patterns. Long- and short-range spin correlations spontaneously emerge in filters of a convolutional neural network trained on snapshots of single atomic species. In the less well-understood strange metallic phase of the model, we find that a more complex network trained on snapshots of local moments produces an effective order parameter for the non-Fermi-liquid behavior. Our technique can be employed to characterize correlations unique to other phases with no obvious order parameters or signatures in projective measurements, and has implications for science discovery through AI beyond strongly correlated systems.
Strange or bad metallic transport, defined by its incompatibility with conventional quasiparticle pictures, is a theme common to strongly correlated materials and ubiquitous in many high temperature superconductors. The Hubbard model represents a minimal starting point for modeling strongly correlated systems. Here we demonstrate strange metallic transport in the doped two-dimensional Hubbard model using determinantal quantum Monte Carlo calculations. Over a wide range of doping, we observe resistivities exceeding the Mott-Ioffe-Regel limit with linear temperature dependence. The temperatures …
We show exactly that small Hubbard rings exhibit unusual kink-like structures giving anomalous oscillations in persistent current. Singular behavior of persistent current disappears in some cases. In half-filled systems mobility gradually drops to zero with interaction, while it converges to some finite value in non-half-filled cases.
We show that the numerically exact bold-line diagrammatic theory for the $2d$ Hubbard model exhibits a non-Fermi-liquid (NFL) strange metal state, which is connected to the SYK NFL in the strong-interaction limit. The solution for the doped system features the expected phenomenology with the NFL near half-filling at strong couplings and in a wide temperature range enclosed by the atomic state at high temperatures and a Fermi liquid at low temperatures. We demonstrate, however, that this behavior in the weakly doped regime is due to the unphysical branch of the Luttinger-Ward functional. On the…
Strongly correlated electron systems host a variety of poorly understood correlations in their high temperature normal state. Unlike ordered phases defined by order parameters, these normal state phases are often defined through unconventional properties such as strange metallic transport or spectroscopic pseudogaps. Characterizing the microscopic correlations in the normal state is necessary to elucidate mechanisms that lead to these properties and their connection to ground state orders. Here we establish the presence of intertwined charge and spin stripes in the strange metal normal state o…
Extended strange metal and superconductivity in partially filled moiré Hubbard bands
Cornell University（康奈尔大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Kavli Institute at Cornell for Nanoscale Science（康奈尔纳米科学卡弗里研究所）；University of Delaware（特拉华大学）；National Institute for Materials Science（日本国立材料研究所）
The Sachdev-Ye-Kitaev (SYK) model describes a strange metal that shows peculiar non-Fermi liquid properties without quasiparticles. It exhibits a maximally chaotic behavior characterized by out-of-time-ordered correlators (OTOCs), and is expected to be a holographic dual to black holes. Recently, a striking similarity between the SYK model and the Hund-coupling induced spin-freezing crossover in multi-orbital Hubbard models has been pointed out. To further explore this connection, we study OTOCs for fermionic Hubbard models, which are prototypical models for strongly correlated electrons in so…
While a specific kind of strange metal is increasingly found to be the "normal" states in a wide variety of unconventional superconductors, its microscopic origin is presently a hotly debated enigma. Using dynamical mean-field theory (DMFT) based on hybridization expansion of continuous-time quantum Monte-Carlo (CTQMC) solver for an extended two-band Hubbard model (2BHM), we investigate the conditions underlying the emergence of such a metal. Specifically, we tie strange metallicity to an orbital-selective Mottness in 2BHM or momentum-selective Mott phase (OSMP) in 2D Hubbard models inspired b…
We propose that the non-equilibrium current measured in the $a-b$ plane of an underdoped cuprate (in either the strange metal or pseudogap regime) in contact with either an overdoped cuprate or a standard Fermi liquid can be used diagnose how different the pseudogap and strange metals are from a Fermi liquid. Naively one expects the strange metal to be more different from a Fermi liquid than is the pseudogap. We compute the expected non-equilibrium transport signal with the three Green functions that are available in the literature: 1) marginal Fermi liquid theory, 2) the phenomenological ansa…
Symmetry protected topological (SPT) phases in free fermion and interacting bosonic systems have been classified, but the physical phenomena of interacting fermionic SPT phases have not been fully explored. Here, employing large-scale quantum Monte Carlo simulation, we investigate the edge physics of a bilayer Kane-Mele-Hubbard model with zigzag ribbon geometry. Our unbiased numerical results show that the fermion edge modes are gapped out by interaction, while the bosonic edge modes remain gapless at the $(1+1)d$ boundary, before the bulk quantum phase transition to a topologically trivial ph…
The $U\rightarrow +\infty$ one-dimensional Hubbard model in an electric field has be exactly solved, with an emphasis on the charge current. It is found that undamped Bloch oscillations extensively exist in the system. Such conclusion has also been discussed for more general cases and we find that it is closely related to the temporal periodicity of the model Hamiltonian in electric field, rather than to the integrability of the model. As a comparison, we have also studied a model of electrons with $δ$-function interactions in continuous space, which is closely related to the Hubbard model, bu…
The origin of strange metallic phase is shown to exist due to these two conditions---(i) the electrons are strongly interacting such that there are no band and Mott-Hubbard gaps, and (ii) the electronic energy levels are crossed in such a way that there is an electronic energy gap between two energy levels associated to two different wave functions. The theory is also exploited to explain (i) the upward- and downward-shifts in the $T$-linear resistivity curves, and (ii) the spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements of the La-Sr-Cu-O Mott insulato…
Strong electron correlations lie at the origin of transformative phenomena such as colossal magneto-resistance and high-temperature superconductivity. Already near room temperature, doped copper oxide materials display remarkable features such as a pseudo-gap and a "strange metal" phase with unusual transport properties. The essence of this physics is believed to be captured by the Fermi-Hubbard model of repulsively interacting, itinerant fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realiz…
Distinguishing the nontrivial symmetry-protected topological (SPT) phase from the trivial insulator phase in the presence of electron-electron interaction is an urgent question to the study of topological insulators, due to the fact that most of the topological indices defined for free electron systems are very likely unsuitable for interacting cases. In this work, we demonstrate that the strange correlator is a sensitive diagnosis to detect SPT states in interacting systems. Employing large-scale quantum Monte Carlo (QMC) simulations, we investigate the interaction-driven quantum phase transi…
A one band Hubbard model with intermediate coupling is shown to describe the two most important unusual features of a normal state: linear resistivity strange metal and the pseudogap. Both the spectroscopic and transport properties of the cuprates are considered on the same footing by employing a relatively simple postgaussian approximation valid for the intermediate couplings $U/t=1.5-4$ in relevant temperatures $T>100{\rm K}.$ In the doping range $\ p=0.1-0.3$, the value of $U$ is smaller than that in the parent material. For a smaller doping, especially in the Mott insulator phase, the coup…
Understanding electronic properties that violate the Landau Fermi liquid paradigm in cuprate superconductors remains a major challenge in condensed matter physics. The strange metal state in overdoped cuprates that exhibits linear-in-temperature scattering rate and dc resistivity is a particularly puzzling example. Here, we compute the electronic scattering rate in the two-dimensional Hubbard model using cluster generalization of dynamical mean-field theory. We present a global phase diagram documenting an apparent non-Fermi liquid phase, in between the pseudogap and Fermi liquid phase in the …
Using two approaches to strongly correlated systems, the extremely correlated Fermi liquid theory and the dynamical mean field theory, we compute the transverse transport coefficients, namely the Hall constants $R_H$ and Hall angles $θ_H$, and also the longitudinal and transverse optical response of the $U=\infty$ Hubbard model in the limit of infinite dimensions. We focus on two successive low-temperature regimes, the Gutzwiller correlated Fermi liquid (GCFL) and the Gutzwiller correlated strange metal (GCSM). We find that the Hall angles $\cot θ_H \propto T^2$ in the GCFL regime, on warming …
Recent cold atom experiments have observed bad and strange metal behaviors in strongly-interacting Fermi-Hubbard systems. Motivated by these results, we calculate the thermoelectric transport properties of a 2D Fermi-Hubbard system in the weak coupling limit using quantum kinetic theory. We find that many features attributed to strong correlations are also found at weak coupling. In particular, for temperatures $T\gtrsim t$ the electrical resistivity is nearly linear in temperature despite the fact that the quasiparticle scattering rate is non-linear and changes by nearly an order of magnitude…
Recent progress in extremely correlated Fermi liquid theory (ECFL) and dynamical mean field theory (DMFT) enables us to compute in the $d \to \infty$ limit the resistivity of the $t-J$ model after setting $J\to0$. This is also the $U=\infty$ Hubbard model. We study three densities $n=.75,.8,.85$ that correspond to a range between the overdoped and optimally doped Mott insulating state. We delineate four distinct regimes characterized by different behaviors of the resistivity $ρ$. We find at the lowest $T$ a Gutzwiller Correlated Fermi Liquid regime with $ρ\propto T^2$ extending up to an effect…
Recent experiments on quantum degenerate gases give an opportunity for simulating strongly-correlated electronic systems in optical lattices. It may shed light on some long-standing puzzles in condensed-matter physics, like the nature of high-temperature superconductivity in cuprates that had baffled people over two decades. It is believed that the two-dimensional fermionic Hubbard model, or t-J model, contains the key to this problem; but the difficulty of unveiling the mystery of a strongly-interacting fermionic system is also generally acknowledged. Here, as a substitute, we systematically …
Anderson has recently proposed a theory of the strange metal state above Tc in the high Tc superconductors. [arXiv:cond-mat/0512471] It is based on the idea that the unusual transport properties and spectral functions are caused by the strong Mott- Hubbard interactions and can be computed by using the formal apparatus of Gutzwiller projection. In ref. 1 Anderson computed only the tunneling spectrum and the power-law exponent of the infrared conductivity. He had calculated the energy distribution curves (EDCs) in angle resolved photoemission spectroscopy (ARPES) but was discouraged when these d…
Hall conductivity reveals the nature of quantum coherence in strongly correlated metals
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；Department of Materials Science and Engineering, Stanford University（斯坦福大学材料科学与工程系）
