Search

We examine the orbital-selective Mott transition in the non-hybridized two-band Hubbard model using the dynamical mean-field theory. We find that the orbital-selective Mott transition could be quantitatively depicted by the {local two-qubit fidelity}. Furthermore, within the orbital-selective Mott phase, the combined characteristics of the two orbitals lead to the presence of quantum entanglement, which is characterized by the non-semi-integer values of local two-qubit fidelity. It is demonstrated that the Hund's coupling results in the ground states of both wide and narrow bands exhibiting the specific superposition states, indicating the existence of quantum entanglement within orbital-selective Mott phase. Without Hund's coupling, there are no specific superposition states, nor does quantum entanglement occur within the orbital-selective Mott phase. The mechanisms underlying the orbital-selective Mott transition show prominent variations depending on the presence or absence of Hund's coupling and its transverse terms., Comment: 6 pages, 4 figures

Traditional federated learning uses the number of samples to calculate the weights of each client model and uses this fixed weight value to fusion the global model. However, in practical scenarios, each client's device and data heterogeneity leads to differences in the quality of each client's model. Thus the contribution to the global model is not wholly determined by the sample size. In addition, if clients intentionally upload low-quality or malicious models, using these models for aggregation will lead to a severe decrease in global model accuracy. Traditional federated learning algorithms do not address these issues. To solve this probelm, we propose FedDRL, a model fusion approach using reinforcement learning based on a two staged approach. In the first stage, Our method could filter out malicious models and selects trusted client models to participate in the model fusion. In the second stage, the FedDRL algorithm adaptively adjusts the weights of the trusted client models and aggregates the optimal global model. We also define five model fusion scenarios and compare our method with two baseline algorithms in those scenarios. The experimental results show that our algorithm has higher reliability than other algorithms while maintaining accuracy.

We analytically calculate the scaling exponents of a two-dimensional KPZ-like system: coherently moving incompressible polar active fluids. Using three different renormalization group approximation schemes, we obtain values for the ``roughness" exponent $\chi$ and anisotropy exponent $\zeta$ that are extremely near the known exact results. This implies our prediction for the previously completely unknown dynamic exponent $z$ is quantitatively accurate.

We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We obtain the large-distance, long-time scaling laws of the velocity fluctuations using three distinct dynamic renormalization group schemes. These are an uncontrolled one-loop calculation in exactly two dimensions, and two $d=(d_c-\epsilon)$-expansions to $O(\epsilon)$, obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a ``hard" continuation which has $d_c={7\over 3}$, and a ``soft" continuation with $d_c={5\over 2}$. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and, therefore, we expect the numerical values we predict for them to be highly accurate., Comment: 39 pages, 11 figures

We present a hydrodynamic theory of incompressible polar active fluids with quenched disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a non-zero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions., Comment: 10 pages, 1 figure

We show that incompressible polar active fluids can exhibit an ordered, coherently moving phase even in the presence of quenched disorder in two dimensions. Unlike such active fluids with annealed (i.e., time-dependent) disorder only, which behave like equilibrium ferromagnets with long-range interactions, this robustness against quenched disorder is a fundamentally non-equilibrium phenomenon. The ordered state belongs to a new universality class, whose scaling laws we calculate using three different renormalization group schemes, which all give scaling exponents within 0.02 of each other, indicating that our results are quite accurate. Our predictions can be quantitatively tested in readily available artificial active systems, and imply that biological systems such as cell layers can move coherently in vivo, where disorder is inevitable., Comment: 6 pages

The Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur at the metallic phase near the Mott metal-insulator transition. We investigate the Mott metal-insulator transition in a strongly-correlated electron system based on the Hubbard model. The on-site moment evaluated by the dynamical mean-field theory is employed to depict the Mott metal-insulator transition. Conveniently, the on-site moment is a more proper order parameter to quantitatively determine the Mott critical point, in comparison with the corresponding quasiparticle coherent weight. Moreover, this order parameter also gives a consistent description of two distinct forms of the critical points of the Mott metal-insulator transition., Comment: 6 pages, 4 figures

We combine numerical and analytical methods to study two dimensional active crystals formed by permanently linked swimmers and with two distinct alignment interactions. The system admits a stationary phase with quasi long range translational order, as well as a moving phase with quasi-long range velocity order. The translational order in the moving phase is significantly influenced by alignment interaction. For Vicsek-like alignment, the translational order is short-ranged, whereas the bond-orientational order is quasi-long ranged, implying a moving hexatic phase. For elasticity-based alignment, the translational order is quasi-long ranged parallel to the motion and short-ranged in perpendicular direction, whereas the bond orientational order is long-ranged. We also generalize these results to higher dimensions.

We show that "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calculate the universal exponents and scaling laws of this new universality class to $O(\epsilon)$ in a $d=4-\epsilon$ expansion, and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of $2 < d \leq 4$. We also obtain a universal amplitude ratio relating the damping of transverse and longitudinal velocity and density fluctuations in these systems. Furthermore, we find a universal separatrix in real (${\bf r}$) space between two regions in which the equal time density correlation $\langle\delta\rho({\bf r}, t)\delta\rho(0, t)\rangle$ has opposite signs. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments., Comment: 48 pages, 7 figures. This is the long paper accompanying the short paper "Moving, reproducing, and dying beyond Flatland: Malthusian flocks in dimensions $d> 2$" [arXiv:2001.01300]

The van der Waals ferromagnet Fe5GeTe2 has a Curie temperature TC of about 270 K, which can be raised above room temperature by tuning the Fe deficiency content. To achieve insights into its ferromagnetic exchange, we have studied the critical behavior by measuring the magnetization in bulk Fe5GeTe2 crystal around the ferromagnetic to paramagnetic phase transition. The analysis of the magnetization by employing various techniques including the modified Arrott plot, Kouvel-Fisher plot and critical isotherm analysis achieved a set of reliable critical exponents with TC = 273.7 K, beta = 0.3457, gamma = 1.40617, and delta = 5.021, suggesting a three-dimensional magnetic exchange with the distance decaying as J(r) ~ (r)$^-4.916, which is close to that of a three-dimensional Heisenberg model with long-range magnetic coupling., Comment: 22 pages, 2 tables, 6 figures

By measuring the de Hass-van Alphen effect and calculating the electronic band structure, we have investigated the bulk Fermi surface of the BaSn3 superconductor with a transition temperature of ~ 4.4 K. Striking de Haas-van Alphen (dHvA) quantum oscillations are observed when the magnetic field B is perpendicular to both (100) and (001) planes. Our analysis unveiled nontrivial Berry phase imposed in the quantum oscillations when B is perpendicular to (100), with two fundamental frequencies at 31.5 T and 306.7 T, which likely arise from two corresponding hole pockets of the bands forming a type-II Dirac point. The results are supported by the ab initio calculations indicating a type-II Dirac point setting and tilting along the high symmetric K-H line of the Brillouin zone, about 0.13 eV above the Fermi level. Moreover, the calculations also revealed other two type-I Dirac points on the high symmetric {\Gamma}-A direction, but slightly far below the Fermi level. The results demonstrate BaSn3 as an excellent platform for the study of not only exotic properties of different types of Dirac fermions in a single material, but also the interplay between nontrivial topological states and superconductivity., Comment: 15 pages, 1 table, 4 figures

We show that "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calculate the universal exponents and scaling laws of this new universality class to $O(\epsilon)$ in an $\epsilon=4-d$ expansion, and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks in $d>2$. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments., Comment: 5 pges, 2 figures. This new version has essentially the same content as the earlier one, but differs cosmetically, and is the version actually submitted to PRL. The accompanying long paper is titled "A novel nonequilibrium state of matter: a $d=4-\epsilon$ expansion study of Malthusian flocks"

High magnetic field transport measurements and ab initio calculations on the layered superconductor TaSe3 have provided compelling evidences for the existence of a three-dimensional strong topological insulator state. Longitudinal magnetotransport measurements up to ~ 33 T unveiled striking Shubnikov-de Hass oscillations with two fundamental frequencies at 100 T and 175 T corresponding to a nontrivial electron Fermi pocket at the B point and a nontrivial hole Fermi pocket at the {\Gamma} point respectively in the Brillouin zone. However, calculations revealed one more electron pocket at the B point, which was not detected by the magnetotransport measurements, presumably due to the limited carrier momentum relaxation time. Angle dependent quantum oscillations by rotating the sample with respect to the magnetic field revealed clear changes in the two fundamental frequencies, indicating anisotropic electronic Fermi pockets. The ab initio calculations gave the topological Z2 invariants of (1; 100) and revealed a single Dirac cone on the (1 0 -1) surface at the X point with helical spin texture at a constant-energy contour, suggesting a strong topological insulator state. The results demonstrate TaSe3 an excellent platform to study the interplay between topological phase and superconductivity and a promising system for the exploration of topological superconductivity., Comment: 16 pages, 4 figures, 1 table. arXiv admin note: text overlap with arXiv:1911.03844

We study universal behavior in the moving phase of a generic system of motile particles with alignment interactions in the incompressible limit for spatial dimensions $d>2$. Using a dynamical renormalization group analysis, we obtain the exact dynamic, roughness, and anisotropy exponents that describe the scaling behavior of such incompressible systems. This is the first time a compelling argument has been given for the exact values of the anomalous scaling exponents of a flock moving through an isotropic medium in $d>2$.

We study the hydrodynamic behavior of three dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with non-zero average velocity, hereafter called 3D easy-plane incompressible polar active fluids. We show that the hydrodynamic model for this system belongs to the same universality class as that of an equilibrium system, namely a special 3D anisotropic magnet. The latter can be further mapped onto yet another equilibrium system, a DNA-lipid mixture in the sliding columnar phase. Through these connections we find a divergent renormalization of the damping coefficients in 3D easy-plane incompressible polar active fluids, and obtain their equal-time velocity correlation functions.

Novel "smectic-P" behavior, in which self-propelled particles form rows and move on average along them, occurs generically within the orientationally-ordered phase of simple models that we simulate. Both apolar (head-tail symmetric) and polar (head-tail asymmetric) models with aligning and repulsive interactions exhibit slow algebraic decay of smectic order with system size up to some finite length scale, after which faster decay occurs. In the apolar case, this scale is that of an undulation instability of the rows. In the polar case, this instability is absent, but traveling fluctuations disrupt the rows in large systems and motion and smectic order may spontaneously globally rotate. These observations agree with a new hydrodynamic theory which we present here. Variants of our models also exhibit active smectic "A" and "C" order, with motion orthogonal and oblique to the layers respectively., Comment: revised version

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behavior quite different from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems : two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent $\zeta$ and the roughness exponents $\chi_{_{x,y}}$ that characterize these correlations., Comment: 14 pages, 3 figures, to appear in Nature Communications

We study incompressible systems of motile particles with alignment interactions. Unlike their compressible counterparts, in which the order-disorder (i.e., moving to static) transition, tuned by either noise or number density, is discontinuous, in incompressible systems this transition can be continuous, and belongs to a new universality class. We calculate the critical exponents to $O(\epsilon)$in an $\epsilon=4-d$ expansion, and derive two exact scaling relations. This is the first analytic treatment of a phase transition in a new universality class in an active system., Comment: 17pages, 4 figures

Fluids of exciton-polaritons, excitations of two dimensional quantum wells in optical cavities, show collective phenomena akin to Bose condensation. However, a fundamental difference from standard condensates stems from the finite life-time of these excitations, which necessitate continuous driving to maintain a steady state. A basic question is whether a two dimensional condensate with long range algebraic correlations can exist under these non-equilibrium conditions. Here we show that such driven two-dimensional Bose systems cannot exhibit algebraic superfluid order except in low-symmetry, anisotropic systems. Our result implies, in particular, that recent apparent evidence for Bose condensation of exciton-polaritons must be an intermediate scale crossover phenomenon, while the true long distance correlations fall off exponentially. We obtain these results through a mapping of the long-wavelength condensate dynamics onto the anisotropic Kardar-Parisi-Zhang equation.

We present a hydrodynamic theory of polar active smectics, for systems both with and without number conservation. For the latter, we find quasi long-ranged smectic order in d=2 and long-ranged smectic order in d=3. In d=2 there is a Kosterlitz-Thouless type phase transition from the smectic phase to the ordered fluid phase driven by increasing the noise strength. For the number conserving case, we find that giant number fluctuations are greatly suppressed by the smectic order; that smectic order is long-ranged in d=3; and that nonlinear effects become important in d=2., Comment: 6 pages, 2 figures

We study theoretically the smectic A to C phase transition in isotropic disordered environments. Surprisingly, we find that, as in the clean smectic A to C phase transition, smectic layer fluctuations do not affect the nature of the transition, in spite of the fact that they are much stronger in the presence of the disorder. As a result, we find that the universality class of the transition is that of the "Random field XY model" (RFXY).

We study the smectic $A$-$C$ phase transition in biaxial disordered environments, e.g. fully anisotropic aerogel. We find that both the $A$ and $C$ phases belong to the universality class of the "XY Bragg glass", and therefore have quasi-long-ranged translational smectic order. The phase transition itself belongs to a new universality class, which we study using an $\epsilon=7/2-d$ expansion. We find a stable fixed point, which implies a continuous transition, the critical exponents of which we calculate.

We show that in suitable anisotropic ferromagnets, both stable and metastable ``tilted'' phases occur, in which the magnetization ${\vec M}$ makes an angle between zero and $180$ degrees with the externally applied ${\vec H}$. Tuning either the magnitude of the external field or the temperature can lead to continuous transitions between these states. A unique feature is that one of these transitions is between two {\it metastable} states. Near the transitions the longitudinal susceptibility becomes anomalous with an exponent which has an {\it exact} scaling relation with the critical exponents.

We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter K and the deviation from the resonance condition is obtained. For weak dissipation and 1/2

Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2k_F$-wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.

We present a theory of the elasticity and fluctuations of the Smectic A and C phases in uniaxial, anisotropic disordered environments, e.g., stretched aerogel. We find that, bizarrely, the low-temperature, lower-symmetry Smectic $C$ phase is less translationally ordered than the high-temperature, higher-symmetry Smectic $A$ phase, with short-ranged "$m=1$ Bragg glass" and algebraic "XY Bragg glass" order, respectively. The $AC$ phase transition belongs to a new universality class, whose fixed points and exponents we find in a $d=5-\epsilon$ expansion. We give very detailed predictions for the very rich light scattering behavior of both phases, and the critical point.

We study the smectic AC transition in anisotropic and uniaxial disordered environments, e.g., aerogel with an external field. We find very strange behavior of translational correlations: the low-temperature, lower-symmetry Smectic C phase is itless translationally ordered than the it high-temperature, higher-symmetry Smectic A phase, with short-ranged and algebraic translational correlations, respectively. Specifically, the A and C phase belong to the quasi-long-ranged translationally ordered " XY Bragg glass '' and short-ranged translationally ordered " m=1 Bragg glass '' phase, respectively. The AC phase transition itself belongs to a new universality class, whose fixed points and exponents we find in a d=5-epsilon expansion.