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We study the transport dynamics of an interacting tilted (Stark) chain. We show that the crossover between diffusive and subdiffusive dynamics is governed by $F\sqrt{L}$, where $F$ is the strength of the field, and $L$ is the wave-length of the excitation. While the subdiffusive dynamics persist for large fields, the corresponding transport coefficient is exponentially suppressed with $F$ so that the finite-time dynamics appear almost frozen. We explain the crossover scale between the diffusive and subdiffusive transport by bounding the dynamics of the dipole moment for arbitrary initial state. We also prove its emergent conservation at infinite temperature. Consequently, the studied chain is one of the simplest experimentally realizable models for which numerical data are consistent with the hydrodynamics of fractons., Comment: 8 pages, 4 figures (including Supplementary Material). Changes in the second version: The typo of the first version in the arrow directions of Fig. 1 panel (b) and Fig. S1 (upper panel) is corrected

The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite magnetization $m\ne0$, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant ${\cal D}_0(\Delta)$ on the spin anisotropy $\Delta$, with a pronounced maximum at $\Delta =1$. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at $\Delta=1$ that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms., Comment: 5+5 pages, 4+5 figures

The recent discovery of magnetic Weyl semimetal Co3Sn2S2 opens up new avenues for research into the interactions between topological orders, magnetism, and electronic correlations. Motivated by the observations of large anomalous Hall effect because of large Berry curvature, we investigate another Berry curvature-induced phenomenon, the anomalous thermal Hall effect in Co3Sn2S2. We study it with and without strain, using a Wannier tight-binding Hamiltonian derived from first principles density functional theory calculations. We first identify this material as a tilted type-I Weyl semimetal based on the band structure calculation. Within the quasi-classical framework of Boltzmann transport theory, a giant anomalous thermal Hall signal appears due to the presence of large Berry curvature. Surprisingly, the thermal Hall current changes and even undergoes a sign-reversal upon varying the chemical potential. Furthermore, applying about 13 GPa stress, an enhancement as large as 33% in the conductivity is observed; however, the tilt vanishes along the path connecting the Weyl nodes. In addition, we have confirmed the validity of the Wiedemann-Franz law in this system for anomalous transports. We propose specific observable signatures that can be directly tested in experiments., Comment: 10 pages, 6 figures

The anomalous spin diffusion of the integrable easy-axis Heisenberg chain originates in the ballistic transport of symmetry sectors with nonzero magnetization. Ballistic transport is replaced by normal dissipative transport in all magnetization sectors upon introducing the integrability-breaking perturbations, including external driving. Such behavior implies that the diffusion constant obtained for the integrable model is relevant for the spread of spin excitations but not for the spin conductivity. We present numerical results for closed systems and driven open systems, indicating that the diffusion constant shows a discontinuous variation as the function of perturbation strength.

We propose a novel technique to constrain parameters in CNN based on symmetric filters. We investigate the impact on SOTA networks when varying the combinations of symmetricity. We demonstrate that our models offer effective generalisation and a structured elimination of redundancy in parameters. We conclude by comparing our method with other pruning techniques., Comment: Copyright 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

We consider effects of spatial dispersion in noncentrosymmetric time-reversal invariant Weyl metals in the presence of a static magnetic field. In particular, we study currents that are linear in both the spatial derivatives of an applied electric field, and the static magnetic field, which are responsible for the phenomenon of gyrotropic birefringence. We show that the chiral anomaly and the chiral magnetic effect make the leading contribution to this class of phenomena in metals. We apply the obtained results to the problem of electromagnetic wave transmission through a thin slab of a Weyl semimetal, and show that the transmission coefficient contains a component that is odd in the applied static magnetic field. As such, it can be easily distinguished from conventional Ohmic magnetotransport effects, which are quadratic in the applied magnetic field. The relative magnitude of the effect can reach a few percent in Weyl materials subject to magnetic fields of 0.1Tesla, while the effect is several orders of magnitude smaller in metals without Berry monopoles. We conclude that the nonreciprocal optical and magnetotransport effects can be a robust probe of band topology in metals., Comment: 5 pages, 2 figures

We develop a symmetry-based low-energy theory for monolayer $\mathrm{WTe}_2$ in its 1T$^{\prime}$ phase, which includes eight bands (four orbitals, two spins). This model reduces to the conventional four-band spin-degenerate Dirac model near the Dirac points of the material. We show that measurements of the spin susceptibility, and of the magnitude and time dependence of the anomalous Hall conductivity induced by injected or equilibrium spin polarization can be used to determine the magnitude and form of the spin-orbit coupling Hamiltonian, as well as the dimensionless tilt of the Dirac bands., Comment: 11 pages, 4 figures, Submission to SciPost

It has recently been realized that the first-order moment of the Berry curvature, namely the Berry curvature dipole (BCD) can give rise to non-linear current in a wide variety of time-reversal invariant and non-centrosymmetric materials. While the BCD in two-dimensional Dirac systems is known to be finite only in the presence of either substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones or higher order warping of the Fermi surface, we argue that the low-energy Dirac quasiparticles arising from the merging of a pair of Dirac points without any tilt or warping of the Fermi surface can lead to a non-zero BCD. Remarkably, in such systems, the BCD is found to be independent of Dirac velocity as opposed to the Dirac dispersion with a tilt or warping effects. We further show that the proposed systems can naturally host helicity-dependent photocurrent due to their linear momentum-dependent Berry curvatures. Finally, we discuss an important byproduct of this work, i.e., nonlinear anomalous Nernst effect as a second-order thermal response., Comment: 5 pages, 4 figues

The manifestation of chiral anomaly in Weyl semimetals typically relies on the observation of longitudinal magnetoconductance (LMC) along with the planar Hall effect, with a specific magnetic field and angle dependence. Here we solve the Boltzmann equation in the semiclassical regime for a prototype of a Weyl semimetal, allowing for both intravalley and intervalley scattering, along with including effects from the orbital magnetic moment (OMM), in a geometry where the electric and magnetic fields are not necessarily parallel to each other. We construct the phase diagram in the relevant parameter space that describes the shift from positive to negative LMC in the presence of OMM and sufficiently strong intervalley scattering, as has been recently pointed out for only parallel electric and magnetic fields. On the other hand, we find that the chiral anomaly contribution to the planar Hall effect always remains positive (unlike the LMC) irrespective of the inclusion or exclusion of OMM, or the strength of the intervalley scattering. Our predictions can be directly tested in experiments, and may be employed as new diagnostic procedures to verify chiral anomaly in Weyl systems., Comment: Some results updated

We theoretically investigate the optical activity of three dimensional Dirac semimetals (DSMs) using circular dichroism (CD). We show that DSMs in the presence of a magnetic field in any one of the mirror-symmetric planes of the materials exhibit a notable dichroic behavior. In particular, for different orientations of the light field with respect to the mirror-symmetric plane, the CD in type-II DSMs can detect the presence of mirror anomaly by showing sharply distinct patterns at the mirror-symmetric angle. Interestingly, CD can also distinguish type-II DSMs having only one Dirac point at a time-reversal invariant momentum from type-I DSMs with a pair of Dirac points on the rotation axis of the crystals., Comment: 8 pages, 5 figures

We propose a way to observe the chiral magnetic effect in non-centrosymmetric Weyl semimetals under the action of strong electric field, via the non-linear part of their I-V characteristic that is odd in the external magnetic field, or odd-in-magnetic field voltages in electrically open circuits. This effect relies on valley-selective heating in such materials, which in general leads to nonequilibrium valley population imbalances. In the presence of an external magnetic field, such a valley-imbalanced Weyl semimetal will in general develop an electric current along the direction of the magnetic field -- the chiral magnetic effect. We also discuss a specific experimental setup to observe the chiral magnetic effect of hot electrons., Comment: 4 pages, 2 figures

We study the dynamic chiral magnetic conductivity (DCMC) and natural optical activity in an inversion-broken tilted Weyl semimetal (WSM). Starting from the Kubo formula, we derive the analytical expressions for the DCMC for two different directions of the incident electromagnetic wave. We show that the angle of rotation of the plane of polarization of the transmitted wave exhibits remarkable anisotropic behavior and is larger along the tilt direction. This striking anisotropy of DCMC which results in anisotropic optical activity and rotary power, can be experimentally observed as a topological magneto-electric effect of inversion-broken tilted WSMs. Finally, using the low energy Hamiltonian, we show that the DCMC follows the universal $\frac{1}{\omega^2}$ decay in the high frequency regime. In the low frequency regime, however, the DCMC shows sharp peaks at the tilt dependent effective chemical potentials of the left-handed and right-handed Weyl points. This can serve as a signature to distinguish between the type-I and type-II Weyl semimetals.

In addition to the well known chiral anomaly, Dirac semimetals have been argued to exhibit mirror anomaly, close analogue to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular step-like anomalous Hall response across the mirror-symmetric plane in the presence of a magnetic field. Although this result seems to be valid in type-II Dirac semimetals (strictly speaking, in the linearized theory), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the linearized theory. In particular, we show that the anomalous Hall response continuously approaches zero as one approaches the mirror symmetric angle in a type-I Dirac semimetal as opposed to the singular Hall response in a type-II Dirac semimetal. Moreover, we show that, under certain condition, the anomalous Hall response may vanish in a linearized type-I Dirac semimetal, even in the presence of time reversal symmetry breaking., Comment: 6 pages, 5 figures

Recent experimental observations of magnetization plateau in metallic tetraboride $\textrm{TmB}_{4}$ have created a lot of interest in these class of materials. Hysteretic longitudinal resistance and anomalous Hall Effect are other remarkable features in the rare-earth tetraborides which represent experimental realizations of Archimedean Shastry-Sutherland (SSL) lattice. Electronic band structures, calculated under GGA and GGA+SO approximations, show that $\textrm{TmB}_{4}$ is a narrow band system with considerable correlation in its f-level. Strong correlation effects in this system are studied under single-site dynamical mean field theory (DMFT) [LDA+DMFT scheme] using multi-orbital generalization of iterated perturbation theory (MO-IPT). Pseudo-gap behaviour in spectral function and non-Fermi liquid behaviour of self-energy shows non-trivial strong correlation effects present in this geometrically frustrated metallic magnets. We also consider the extant, heather-to-neglected, strong atomic spin-orbit coupling (SOC) effects. While there is a significant change in the topology of the Fermi surface in the presence of SOC, the non-Fermi liquid behavior survives. The system can be modelled by an effective two orbital spinless Falicov-Kimball model together with two free band like states., Comment: 13 pages, 17 figures, submitted to Physical Review B

We present efficient realization of Generalized Givens Rotation (GGR) based QR factorization that achieves 3-100x better performance in terms of Gflops/watt over state-of-the-art realizations on multicore, and General Purpose Graphics Processing Units (GPGPUs). GGR is an improvement over classical Givens Rotation (GR) operation that can annihilate multiple elements of rows and columns of an input matrix simultaneously. GGR takes 33% lesser multiplications compared to GR. For custom implementation of GGR, we identify macro operations in GGR and realize them on a Reconfigurable Data-path (RDP) tightly coupled to pipeline of a Processing Element (PE). In PE, GGR attains speed-up of 1.1x over Modified Householder Transform (MHT) presented in the literature. For parallel realization of GGR, we use REDEFINE, a scalable massively parallel Coarse-grained Reconfigurable Architecture, and show that the speed-up attained is commensurate with the hardware resources in REDEFINE. GGR also outperforms General Matrix Multiplication (gemm) by 10% in-terms of Gflops/watt which is counter-intuitive.

In this paper, we present efficient realization of Kalman Filter (KF) that can achieve up to 65% of the theoretical peak performance of underlying architecture platform. KF is realized using Modified Faddeeva Algorithm (MFA) as a basic building block due to its versatility and REDEFINE Coarse Grained Reconfigurable Architecture (CGRA) is used as a platform for experiments since REDEFINE is capable of supporting realization of a set algorithmic compute structures at run-time on a Reconfigurable Data-path (RDP). We perform several hardware and software based optimizations in the realization of KF to achieve 116% improvement in terms of Gflops over the first realization of KF. Overall, with the presented approach for KF, 4-105x performance improvement in terms of Gflops/watt over several academically and commercially available realizations of KF is attained. In REDEFINE, we show that our implementation is scalable and the performance attained is commensurate with the underlying hardware resources, Comment: Accepted in ARC 2018

Strong light-matter interactions in layered transition metal dichalcogenides (TMDs) open up vivid possibilities for novel exciton-based devices. The optical properties of TMDs are dominated mostly by the tightly bound excitons and more complex quasiparticles, the biexcitons. Instead of physically exfoliated monolayers, the solvent-mediated chemical exfoliation of these 2D crystals is a cost-effective, large-scale production method suitable for real device applications. We explore the ultrafast excitonic processes in WS$_{2}$ dispersion using broadband femtosecond pump-probe spectroscopy at room temperature. We detect the biexcitons experimentally and calculate their binding energies, in excellent agreement with earlier theoretical predictions. Using many-body physics, we show that the excitons act like Weiner-Mott excitons and explain the origin of excitons via first-principles calculations. Our detailed time-resolved investigation provides ultrafast radiative and non-radiative lifetimes of excitons and biexcitons in WS$_{2}$. Indeed, our results demonstrate the potential for excitonic quasiparticle-controlled TMDs-based devices operating at room temperature., Comment: 9 pages, 7 figures

Weyl semimetals are intriguing topological states of matter that support various anomalous magneto-transport phenomena. One such phenomenon is a negative longitudinal ($\mathbf{\nabla} T \parallel \mathbf{B}$) magneto-thermal resistivity, which arises due to chiral magnetic effect (CME). In this paper we show that another fascinating effect induced by CME is the planar thermal Hall effect (PTHE), i.e., appearance of an in-plane transverse temperature gradient when the current due to $\mathbf{\nabla} T$ and the magnetic field $\mathbf{B}$ are not aligned with each other. Using semiclassical Boltzmann transport formalism in the relaxation time approximation we compute both longitudinal magneto-thermal conductivity (LMTC) and planar thermal Hall conductivity (PTHC) for a time reversal symmetry breaking WSM. We find that both LMTC and PTHC are quadratic in B in type-I WSM whereas each follows a linear-B dependence in type-II WSM in a configuration where $\mathbf{\nabla} T$ and B are applied along the tilt direction. In addition, we investigate the Wiedemann-Franz law for an inversion symmetry broken WSM (e.g., WTe$_{2}$) and find that this law is violated in these systems due to both chiral anomaly and CME., Comment: 9 pages, 5 figures Version accepted in Phys. Rev. B

Negative longitudinal magnetoresistance, in the presence of an external magnetic field parallel to the direction of an applied current, has recently been experimentally verified in Weyl semimetals and topological insulators in the bulk conduction limit. The appearance of negative longitudinal magnetoresistance in topological semimetals is understood as an effect of chiral anomaly, whereas it is not well-defined in topological insulators. Another intriguing phenomenon, planar Hall effect - appearance of a transverse voltage in the plane of applied co-planar electric and magnetic fields not perfectly aligned to each other, a configuration in which the conventional Hall effect vanishes, has recently been suggested to exist in Weyl semimetals. In this paper we present a quasi-classical theory of planar Hall effect of a three-dimensional topological insulator in the bulk conduction limit. Starting from Boltzmann transport equations we derive the expressions for planar Hall conductivity and longitudinal magnetoconductivity in topological insulators and show the important roles played by the orbital magnetic moment for the appearance of planar Hall effect. Our theoretical results predict specific experimental signatures for topological insulators that can be directly checked in experiments., Comment: 18 pages, 3 figures

In condensed matter physics, the term "chiral anomaly" implies the violation of the separate number conservation laws of Weyl fermions of different chiralities in the presence of parallel electric and magnetic fields. One effect of chiral anomaly in the recently discovered Dirac and Weyl semimetals is a positive longitudinal magnetoconductance (LMC). Here we show that chiral anomaly and non-trivial Berry curvature effects engender another striking effect in WSMs, the planar Hall effect (PHE). Remarkably, PHE manifests itself when the applied current, magnetic field, and the induced transverse "Hall" voltage all lie in the same plane, precisely in a configuration in which the conventional Hall effect vanishes. In this work we treat PHE quasi-classically, and predict specific experimental signatures for type-I and type-II Weyl semimetals that can be directly checked in experiments., Comment: 4+ pages; Version accepted in Phys. Rev. Lett

Contradictory results on the ferroelectric response of type II multiferroic YBaCuFeO$_{5}$, in its incommensurate phase, has of late, opened up a lively debate. There are ambiguous reports on the nature of the spiral magnetic state. Using first-principles DFT calculations for the parent compound within LSDA+U+SO approximation, the multiferroic response and the nature of spiral state is revealed. The helical spiral is found to be more stable below the transition temperature as spins prefer to lie in ab plane. The Dzyaloshinskii-Moriya (DM) interaction and the spin current mechanism were earlier invoked to account for the electric polarisation in this system. However, the DM interaction is found to be absent, spin current mechanism is not valid in the helical spiral state and there is no electric polarisation thereof. These results are in good agreement with the recent single-crystal data. We also investigate the magnetic transitions in YBa$_{1-x}$Sr$_x$CuFeO$_5$ for the entire range $0\le x\le 1$ of doping. The exchange interactions are estimated as a function of doping and a quantum Monte Carlo (QMC) calculation on an effective spin Hamiltonian shows that the paramagnetic to commensurate phase transition temperature increases with doping till $x=0.5$ and decreases beyond. Our observations are consistent with experimental findings., Comment: 8 pages, 7 figures

Understanding the pseudogap phase in hole-doped high temperature cuprate superconductors remains a central challenge in condensed matter physics. From a host of recent experiments there is now compelling evidence of translational symmetry breaking charge density wave (CDW) order in a wide range of doping inside this phase. Two distinct types of incommensurate charge order -- bidirectional at zero or low magnetic fields and unidirectional at high magnetic fields close to the upper critical field $H_{c2}$ -- have been reported so far in approximately the same doping range between $p\simeq 0.08$ and $p\simeq 0.16$. In concurrent developments, recent high field Hall experiments have also revealed two indirect but striking signatures of Fermi surface reconstruction in the pseudogap phase, namely, a sign change of the Hall coefficient to negative values at low temperatures at intermediate range of hole doping and a rapid suppression of the positive Hall number without change in sign near optimal doping $p \sim 0.19$. We show that the assumption of a unidirectional incommensurate CDW (with or without a coexisting weak bidirectional order) at high magnetic fields near optimal doping and a coexistence of both types of orders of approximately equal magnitude at high magnetic fields at intermediate range of doping may help explain the striking behavior of low temperature Hall effect in the entire pseudogap phase., Comment: Phys. Rev. B version. 10 pages, 5 figures

We present efficient realization of Householder Transform (HT) based QR factorization through algorithm-architecture co-design where we achieve performance improvement of 3-90x in-terms of Gflops/watt over state-of-the-art multicore, General Purpose Graphics Processing Units (GPGPUs), Field Programmable Gate Arrays (FPGAs), and ClearSpeed CSX700. Theoretical and experimental analysis of classical HT is performed for opportunities to exhibit higher degree of parallelism where parallelism is quantified as a number of parallel operations per level in the Directed Acyclic Graph (DAG) of the transform. Based on theoretical analysis of classical HT, an opportunity re-arrange computations in the classical HT is identified that results in Modified HT (MHT) where it is shown that MHT exhibits 1.33x times higher parallelism than classical HT. Experiments in off-the-shelf multicore and General Purpose Graphics Processing Units (GPGPUs) for HT and MHT suggest that MHT is capable of achieving slightly better or equal performance compared to classical HT based QR factorization realizations in the optimized software packages for Dense Linear Algebra (DLA). We implement MHT on a customized platform for Dense Linear Algebra (DLA) and show that MHT achieves 1.3x better performance than native implementation of classical HT on the same accelerator. For custom realization of HT and MHT based QR factorization, we also identify macro operations in the DAGs of HT and MHT that are realized on a Reconfigurable Data-path (RDP). We also observe that due to re-arrangement in the computations in MHT, custom realization of MHT is capable of achieving 12% better performance improvement over multicore and GPGPUs than the performance improvement reported by General Matrix Multiplication (GEMM) over highly tuned DLA software packages for multicore and GPGPUs which is counter-intuitive.

Basic Linear Algebra Subprograms (BLAS) and Linear Algebra Package (LAPACK) form basic building blocks for several High Performance Computing (HPC) applications and hence dictate performance of the HPC applications. Performance in such tuned packages is attained through tuning of several algorithmic and architectural parameters such as number of parallel operations in the Directed Acyclic Graph of the BLAS/LAPACK routines, sizes of the memories in the memory hierarchy of the underlying platform, bandwidth of the memory, and structure of the compute resources in the underlying platform. In this paper, we closely investigate the impact of the Floating Point Unit (FPU) micro-architecture for performance tuning of BLAS and LAPACK. We present theoretical analysis for pipeline depth of different floating point operations like multiplier, adder, square root, and divider followed by characterization of BLAS and LAPACK to determine several parameters required in the theoretical framework for deciding optimum pipeline depth of the floating operations. A simple design of a Processing Element (PE) is presented and shown that the PE outperforms the most recent custom realizations of BLAS and LAPACK by 1.1X to 1.5X in Gflops/W, and 1.9X to 2.1X in Gflops/mm^2.

Basic Linear Algebra Subprograms (BLAS) play key role in high performance and scientific computing applications. Experimentally, yesteryear multicore and General Purpose Graphics Processing Units (GPGPUs) are capable of achieving up to 15 to 57% of the theoretical peak performance at 65W to 240W respectively for compute bound operations like Double/Single Precision General Matrix Multiplication (XGEMM). For bandwidth bound operations like Single/Double precision Matrix-vector Multiplication (XGEMV) the performance is merely 5 to 7% of the theoretical peak performance in multicores and GPGPUs respectively. Achieving performance in BLAS requires moving away from conventional wisdom and evolving towards customized accelerator tailored for BLAS through algorithm-architecture co-design. In this paper, we present acceleration of Level-1 (vector operations), Level-2 (matrix-vector operations), and Level-3 (matrix-matrix operations) BLAS through algorithm architecture co-design on a Coarse-grained Reconfigurable Architecture (CGRA). We choose REDEFINE CGRA as a platform for our experiments since REDEFINE can be adapted to support domain of interest through tailor-made Custom Function Units (CFUs). For efficient sequential realization of BLAS, we present design of a Processing Element (PE) and perform micro-architectural enhancements in the PE to achieve up-to 74% of the theoretical peak performance of PE in DGEMM, 40% in DGEMV and 20% in double precision inner product (DDOT). We attach this PE to REDEFINE CGRA as a CFU and show the scalability of our solution. Finally, we show performance improvement of 3-140x in PE over commercially available Intel micro-architectures, ClearSpeed CSX700, FPGA, and Nvidia GPGPUs.

The two-dimensional electron liquid, at the (001) interface between band insulators {L}a{A}l{O}$_3$ and {S}r{T}i{O}$_3$, undergoes Lifshitz transition as the interface is doped with carriers. At a critical carrier density, two new orbitals populate at the Fermi level, with a concomitant change in the Fermi surface topology. Using dynamical mean-field theory, formulated within a realistic three-orbital model, we study the influence of the Lifshitz transition and local electron correlations on the transport properties. We look at the thermal conductivity, optical conductivity, Seebeck coefficient and angle resolved photoemission spectra and find that at a critical density, both the thermal and dc conductivities rise sharply to higher values while the Seebeck coefficient shows a cusp. The inter-orbital electron-electron interaction transfers spectral weight near the $\Gamma$ point towards lower energy, thereby reducing the critical density. In the presence of external magnetic field, the critical density further reduces due to exchange splitting. Beyond a sufficiently large field, multiple cusps appear in the Seebeck coefficient revealing multiple Lifshitz transitions., Comment: 9 pages, 8 figures