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Gu, Yingfei, Kitaev, Alexei, Sachdev, Subir, and Tarnopolsky, Grigory
 Subjects

High Energy Physics  Theory and Condensed Matter  Strongly Correlated Electrons
 Abstract

We describe numerous properties of the SachdevYeKitaev model for complex fermions with $N\gg 1$ flavors and a global U(1) charge. We provide a general definition of the charge in the $(G,\Sigma)$ formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the manybody density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.
Comment: 73 pages, 13 figures, 1 spooky propagator
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Gu, Yingfei and Qi, XiaoLiang
 Subjects

Condensed Matter  Statistical Mechanics, Condensed Matter  Strongly Correlated Electrons, Computer Science  Computational Complexity, and Mathematics  Combinatorics
 Abstract

Recently, Hao Huang proved the Sensitivity Conjecture, an important result about complexity measures of Boolean functions. We will discuss how this simple and elegant proof turns out to be closely related to physics concepts of the JordanWigner transformation and Majorana fermions. This note is not intended to contain original results. Instead, it is a translation of the math literature in a language that is more familiar to physicists, which helps our understanding and hopefully may inspire future works along this direction.
Comment: 13 pages, 7 figures
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3. Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory [2019]

Fan, Ruihua, Gu, Yingfei, Vishwanath, Ashvin, and Wen, Xueda
 Subjects

Condensed Matter  Strongly Correlated Electrons, Condensed Matter  Quantum Gases, and High Energy Physics  Theory
 Abstract

We study the energy and entanglement dynamics of $(1+1)$D conformal field theories (CFTs) under a Floquet drive with the sinesquare deformed (SSD) Hamiltonian. Previous work has shown this model supports both a nonheating and a heating phase. Here we analytically establish several robust and `superuniversal' features of the heating phase which rely on conformal invariance but not on the details of the CFT involved. First, we show the energy density is concentrated in two peaks in real space, a chiral and antichiral peak, which leads to an exponential growth in the total energy. The peak locations are set by fixed points of the M\"obius transformation. Second, all of the quantum entanglement is shared between these two peaks. In each driving period, a number of Bell pairs are generated, with one member pumped to the chiral peak, and the other member pumped to the antichiral peak. These Bell pairs are localized and accumulate at these two peaks, and can serve as a source of quantum entanglement. Third, in both the heating and nonheating phases we find that the total energy is related to the half system entanglement entropy by a simple relation $E(t)\propto c \exp \left( \frac{6}{c}S(t) \right)$ with $c$ being the central charge. In addition, we show that the nonheating phase, in which the energy and entanglement oscillate in time, is unstable to small fluctuations of the driving frequency in contrast to the heating phase. Finally, we point out an analogy to the periodically driven harmonic oscillator which allows us to understand global features of the phases, and introduce a quasiparticle picture to explain the spatial structure, which can be generalized to setups beyond the SSD construction.
Comment: 35 pages, 16 figures
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Guo, Haoyu, Gu, Yingfei, and Sachdev, Subir
 Phys. Rev. B 100, 045140 (2019)
 Subjects

Condensed Matter  Strongly Correlated Electrons, Condensed Matter  Disordered Systems and Neural Networks, Condensed Matter  Statistical Mechanics, and High Energy Physics  Theory
 Abstract

We compute the transport and chaos properties of lattices of quantum SachdevYeKitaev islands coupled by single fermion hopping, and with the islands coupled to a large number of local, low energy phonons. We find two distinct regimes of linearintemperature ($T$) resistivity, and describe the crossover between them. When the electronphonon coupling is weak, we obtain the `incoherent metal' regime, where there is nearmaximal chaos with front propagation at a butterfly velocity $v_B$, and the associated diffusivity $D_{\rm chaos} = v_B^2/(2 \pi T)$ closely tracks the energy diffusivity. On the other hand, when the electronphonon coupling is strong, and the linear resistivity is largely due to nearelastic scattering of electrons off nearly free phonons, we find that the chaos is far from maximal and spreads diffusively. We also describe the crossovers to low $T$ regimes where the electronic quasiparticles are well defined.
Comment: 25 pages, 26 figures; v2: Added a new Sec.II and a new figure; Added clarifications; Corrected Typos
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Gu, Yingfei and Kitaev, Alexei
 J. High Energ. Phys. (2019) 2019: 75
 Subjects

High Energy Physics  Theory and Condensed Matter  Strongly Correlated Electrons
 Abstract

We derive an identity relating the growth exponent of earlytime OTOCs, the preexponential factor, and a third number called "branching time". The latter is defined within the dynamical meanfield framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models, we also explicitly define "strings" in this context. As another application, we consider an SYK chain. If the coupling strength $\beta J$ is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly $2\pi/\beta$.
Comment: 20 pages, 7 figures
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Chaturvedi, Pankaj, Gu, Yingfei, Song, Wei, and Yu, Boyang
 Subjects

High Energy Physics  Theory
 Abstract

We discuss the connections between the complex SYK model at the conformal limit and warped conformal field theories. Both theories have an $SL(2,R) \times U(1)$ global symmetry. We present comparisons on symmetries, correlation functions, the effective action and the entropy formula. We also use modular covariance to reinterpret results in the complex SYK model.
Comment: 27 pages
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7. Fast scrambling on sparse graphs [2018]

Bentsen, Gregory, Gu, Yingfei, and Lucas, Andrew
 Proceedings of the National Academy of Sciences 116, 6689 (2019)
 Subjects

Condensed Matter  Strongly Correlated Electrons, Condensed Matter  Statistical Mechanics, High Energy Physics  Theory, and Quantum Physics
 Abstract

Given a quantum manybody system with fewbody interactions, how rapidly can quantum information be hidden during time evolution? The fast scrambling conjecture is that the time to thoroughly mix information among N degrees of freedom grows at least logarithmically in N. We derive this inequality for generic quantum systems at infinite temperature, bounding the scrambling time by a finite decay time of local quantum correlations at late times. Using LiebRobinson bounds, generalized SachdevYeKitaev models, and random unitary circuits, we propose that a logarithmic scrambling time can be achieved in most quantum systems with sparse connectivity. These models also elucidate how quantum chaos is not universally related to scrambling: we construct random fewbody circuits with infinite Lyapunov exponent but logarithmic scrambling time. We discuss analogies between quantum models on graphs and quantum black holes, and suggest methods to experimentally study scrambling with as many as 100 sparselyconnected quantum degrees of freedom.
Comment: 11+24 pages; 1+3 figures. v2: minor revisions, added references. v3: many revisions to improve presentation
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Fu, Wenbo, Gu, Yingfei, Sachdev, Subir, and Tarnopolsky, Grigory
 Phys. Rev. B 98, 075150 (2018)
 Subjects

Condensed Matter  Strongly Correlated Electrons and High Energy Physics  Theory
 Abstract

We describe the phases of a solvable $t$$J$ model of electrons with infiniterange, and random, hopping and exchange interactions, similar to those in the SachdevYeKitaev models. The electron fractionalizes, as in an `orthogonal metal', into a fermion $f$ which carries both the electron spin and charge, and a boson $\phi$. Both $f$ and $\phi$ carry emergent $\mathbb{Z}_2$ gauge charges. The model has a phase in which the $\phi$ bosons are gapped, and the $f$ fermions are gapless and critical, and so the electron spectral function is gapped. This phase can be considered as a toy model for the underdoped cuprates. The model also has an extended, critical, `quasiHiggs' phase where both $\phi$ and $f$ are gapless, and the electron operator $\sim f \phi$ has a Fermi liquidlike $1/\tau$ propagator in imaginary time, $\tau$. So while the electron spectral function has a Fermi liquid form, other properties are controlled by $\mathbb{Z}_2$ fractionalization and the anomalous exponents of the $f$ and $\phi$ excitations. This `quasiHiggs' phase is proposed as a toy model of the overdoped cuprates. We also describe the critical state separating these two phases.
Comment: 30 pages, 9 figures
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You, YiZhuang and Gu, Yingfei
 Phys. Rev. B 98, 014309 (2018)
 Subjects

Quantum Physics, Condensed Matter  Statistical Mechanics, and High Energy Physics  Theory
 Abstract

We introduce the concept of entanglement features of unitary gates, as a collection of exponentiated entanglement entropies over all bipartitions of input and output channels. We obtained the general formula for timedependent $n$thRenyi entanglement features for unitary gates generated by random Hamiltonian. In particular, we propose an Ising formulation for the 2ndRenyi entanglement features of random Hamiltonian dynamics, which admits a holographic tensor network interpretation. As a general description of entanglement properties, we show that the entanglement features can be applied to several dynamical measures of thermalization, including the outoftimeorder correlation and the entanglement growth after a quantum quench. We also analyze the YoshidaKitaev probabilistic protocol for random Hamiltonian dynamics.
Comment: 15 pages, 10 figures
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10. Fast scrambling on sparse graphs [2019]

Bentsen, Gregory, Gu, Yingfei, and Lucas, Andrew
 Proceedings of the National Academy of Sciences of the United States. April 2, 2019, Vol. 116 Issue 14, p6689, 6 p.
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Huang, Yichen and Gu, Yingfei
 Phys. Rev. D 100, 041901 (2019)
 Subjects

High Energy Physics  Theory, Condensed Matter  Statistical Mechanics, Condensed Matter  Strongly Correlated Electrons, and Quantum Physics
 Abstract

We study the entanglement entropy of eigenstates (including the ground state) of the SachdevYeKitaev model. We argue for a volume law, whose coefficient can be calculated analytically from the density of states. The coefficient depends on not only the energy density of the eigenstate but also the subsystem size. Very recent numerical results of Liu, Chen, and Balents confirm our analytical results.
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Gu, Yingfei, Lucas, Andrew, and Qi, XiaoLiang
 J. High Energ. Phys. (2017) 2017: 120
 Subjects

High Energy Physics  Theory and Condensed Matter  Strongly Correlated Electrons
 Abstract

We study the spread of R\'enyi entropy between two halves of a SachdevYeKitaev (SYK) chain of Majorana fermions, prepared in a thermofield double (TFD) state. The SYK chain model is a model of chaotic manybody systems, which describes a onedimensional lattice of Majorana fermions, with spatially local random quartic interaction. We find that for integer R\'enyi index $n>1$, the R\'enyi entanglement entropy saturates at a parametrically smaller value than expected. This implies that the TFD state of the SYK chain does not rapidly thermalize, despite being maximally chaotic: instead, it rapidly approaches a prethermal state. We compare our results to the signatures of thermalization observed in other quenches in the SYK model, and to intuition from nearly$\mathrm{AdS}_2$ gravity.
Comment: 1+46 pages, 11 figures
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Gu, Yingfei and Kitaev, Alexei
 Journal of High Energy Physics. Feb 2019, Vol. 2019 Issue 2, p1, 21 p.
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Chaturvedi, Pankaj, Gu, Yingfei, Song, Wei, and Yu, Boyang
 Journal of High Energy Physics. Dec 2018, Vol. 2018 Issue 12, p1, 24 p.
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Gu, Yingfei, Lucas, Andrew, and Qi, XiaoLiang
 SciPost Phys. 2, 018 (2017)
 Subjects

High Energy Physics  Theory and Condensed Matter  Strongly Correlated Electrons
 Abstract

We compute the energy diffusion constant $D$, Lyapunov time $\tau_{\text{L}}$ and butterfly velocity $v_{\text{B}}$ in an inhomogeneous chain of coupled Majorana SachdevYeKitaev (SYK) models in the large $N$ and strong coupling limit. We find $D\le v_{\text{B}}^2 \tau_{\text{L}}$ from a combination of analytical and numerical approaches. Our example necessitates the sharpening of postulated transport bounds based on quantum chaos.
Comment: 10+4 pages, 3 figures; v2: added appendix
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16. Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography [2016]

Davison, Richard A., Fu, Wenbo, Georges, Antoine, Gu, Yingfei, Jensen, Kristan, and Sachdev, Subir
 Phys. Rev. B 95, 155131 (2017)
 Subjects

Condensed Matter  Strongly Correlated Electrons and High Energy Physics  Theory
 Abstract

We compute the thermodynamic properties of the SachdevYeKitaev (SYK) models of fermions with a conserved fermion number, $\mathcal{Q}$. We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low temperature energy and $\mathcal{Q}$ fluctuations. We obtain higherdimensional generalizations of the SYK models which display disordered metallic states without quasiparticle excitations, and we deduce their thermoelectric transport coefficients. We also examine the corresponding properties of EinsteinMaxwellscalar theories on black brane geometries which interpolate from either AdS$_4$ or AdS$_5$ to an AdS$_2\times \mathbb{R}^2$ or AdS$_2\times \mathbb{R}^3$ nearhorizon geometry. These provide holographic descriptions of nonquasiparticle metallic states without momentum conservation. We find a precise match between low temperature transport and thermodynamics of the SYK and holographic models. In both models the Seebeck transport coefficient is exactly equal to the $\mathcal{Q}$derivative of the entropy. For the SYK models, quantum chaos, as characterized by the butterfly velocity and the Lyapunov rate, universally determines the thermal diffusivity, but not the charge diffusivity.
Comment: 57 pages, 6 figures; (v2) clarifications and refs
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Gu, Yingfei, Qi, XiaoLiang, and Stanford, Douglas
 J. High Energ. Phys. (2017) 2017: 125
 Subjects

High Energy Physics  Theory and Condensed Matter  Strongly Correlated Electrons
 Abstract

The SachdevYeKitaev model is a $(0+1)$dimensional model describing Majorana fermions or complex fermions with random interactions. This model has various interesting properties such as approximate local criticality (power law correlation in time), zero temperature entropy, and quantum chaos. In this article, we propose a higher dimensional generalization of the SachdevYeKitaev model, which is a lattice model with $N$ Majorana fermions at each site and random interactions between them. Our model can be defined on arbitrary lattices in arbitrary spatial dimensions. In the large $N$ limit, the higher dimensional model preserves many properties of the SachdevYeKitaev model such as local criticality in twopoint functions, zero temperature entropy and chaos measured by the outoftimeordered correlation functions. In addition, we obtain new properties unique to higher dimensions such as diffusive energy transport and a "butterfly velocity" describing the propagation of chaos in space. We mainly present results for a $(1+1)$dimensional example, and discuss the general case near the end.
Comment: 1+37 pages, published version
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Wen, Xueda, Cho, Gil Young, Lopes, Pedro L. S., Gu, Yingfei, Qi, XiaoLiang, and Ryu, Shinsei
 Phys. Rev. B 94, 075124 (2016)
 Subjects

Condensed Matter  Mesoscale and Nanoscale Physics, Condensed Matter  Strongly Correlated Electrons, and High Energy Physics  Theory
 Abstract

We study the realspace entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multiscale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the RG to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. I.e., if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA does not faithfully reproduce the exact ground state at all length scales.
Comment: 24 pages, many figures
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Gu, Yingfei, Lee, Ching Hua, Wen, Xueda, Cho, Gil Young, Ryu, Shinsei, and Qi, XiaoLiang
 Phys. Rev. B 94, 125107 (2016)
 Subjects

Condensed Matter  Mesoscale and Nanoscale Physics, Condensed Matter  Strongly Correlated Electrons, High Energy Physics  Theory, and Quantum Physics
 Abstract

In this paper, we study $(2+1)$dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$dimensional topological insulator. The dual description enables a new characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.
Comment: 10 pages, 9 figures
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Gu, Yingfei and Qi, XiaoLiang
 J. High Energ. Phys. (2016) 2016: 129
 Subjects

High Energy Physics  Theory, Condensed Matter  Statistical Mechanics, and Condensed Matter  Strongly Correlated Electrons
 Abstract

Fractional statistics and quantum chaos are both phenomena associated with the nonlocal storage of quantum information. In this article, we point out a connection between the butterfly effect in (1+1)dimensional rational conformal field theories and fractional statistics in (2+1)dimensional topologically ordered states. This connection comes from the characterization of the butterfly effect by the outoftimeordercorrelator proposed recently. We show that the latetime behavior of such correlators is determined by universal properties of the rational conformal field theory such as the modular Smatrix and conformal spins. Using the bulkboundary correspondence between rational conformal field theories and (2+1)dimensional topologically ordered states, we show that the late time behavior of outoftimeordercorrelators is intrinsically connected with fractional statistics in the topological order. We also propose a quantitative measure of chaos in a rational conformal field theory, which turns out to be determined by the topological entanglement entropy of the corresponding topological order.
Comment: Published version, 1+25 pages, 10 figures
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