arXiv subjects

Arnab Banerjee

Publications and source records attributed to Arnab Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2023

Experimental Evidence for Non-spherical Magnetic Form Factor in Ru$^{3+}$

The Mott insulator $α$-RuCl$_3$ has generated great interest in the community due to its possible field-induced Kitaev quantum spin liquid state. Despite enormous effort spent trying to obtain the form of the low energy Hamiltonian, there is currently no agreed upon set of parameters which is able to explain all of the data. A key piece of missing information lies in the determination of the magnetic form factor of Ru$^{3+}$, particularly for a true quantitative treatment of inelastic neutron scattering data. Here we present the experimentally derived magnetic form factor of Ru$^{3+}$ in the low spin 4$d^5$ state using polarized neutron diffraction within the paramagnetic regime on high quality single crystals of $α$-RuCl$_3$. We observe strong evidence of an anisotropic form factor, expected of the spin-orbit coupled $j_{\textrm{eff}} = \frac{1}{2}$ ground state. We model the static magnetization density in increasing complexity from simple isotropic cases, to a multipolar expansion, and finally \emph{ab initio} calculations of the generalized $j_{\textrm{eff}} = \frac{1}{2}$ ground state. Comparison of both single ion models and inclusion of Cl$^-$ anions support the presence of hybridization of Ru$^{3+}$ with the surrounding Cl$^{-}$ ligands.

cond-mat.str-el↗

arXiv2023

Gibbs state sampling via cluster expansions

Gibbs states (i.e., thermal states) can be used for several applications such as quantum simulation, quantum machine learning, quantum optimization, and the study of open quantum systems. Moreover, semi-definite programming, combinatorial optimization problems, and training quantum Boltzmann machines can all be addressed by sampling from well-prepared Gibbs states. With that, however, comes the fact that preparing and sampling from Gibbs states on a quantum computer are notoriously difficult tasks. Such tasks can require large overhead in resources and/or calibration even in the simplest of cases, as well as the fact that the implementation might be limited to only a specific set of systems. We propose a method based on sampling from a quasi-distribution consisting of tensor products of mixed states on local clusters, i.e., expanding the full Gibbs state into a sum of products of local "Gibbs-cumulant" type states easier to implement and sample from on quantum hardware. We begin with presenting results for 4-spin linear chains with XY spin interactions, for which we obtain the $ZZ$ dynamical spin-spin correlation functions. We also present the results of measuring the specific heat of the 8-spin chain Gibbs state $ρ_8$.

quant-ph↗

arXiv2023

High-fidelity dimer excitations using quantum hardware

Many-body entangled quantum spin systems exhibit emergent phenomena such as topological quantum spin liquids with distinct excitation spectra accessed in inelastic neutron scattering (INS) experiments. Here we simulate the dynamics of a quantum spin dimer, the basic quantum unit of emergent many-body spin systems. While canonical Trotterization methods require deep circuits precluding long time-scale simulations, we demonstrate 'direct' Resource-Efficient Fast-forwarding (REFF) measurements with short-depth circuits that can be used to capture longer time dynamics on quantum hardware. The temporal evolution of the 2-spin correlation coefficients enabled the calculation of the dynamical structure factor $S(\mathbf{Q},ω)$ - the key component of the neutron scattering cross-section. We simulate the triplet gap and the triplet splitting of the quantum dimer with sufficient fidelity to compare to experimental neutron data. Our results on current circuit hardware pave an important avenue to benchmark, or even predict, the outputs of the costly INS experiments.

quant-ph↗

arXiv2022

Characterizing the memory capacity of transmon qubit reservoirs

Quantum Reservoir Computing (QRC) exploits the dynamics of quantum ensemble systems for machine learning. Numerical experiments show that quantum systems consisting of 5-7 qubits possess computational capabilities comparable to conventional recurrent neural networks of 100 to 500 nodes. Unlike traditional neural networks, we do not understand the guiding principles of reservoir design for high-performance information processing. Understanding the memory capacity of quantum reservoirs continues to be an open question. In this study, we focus on the task of characterizing the memory capacity of quantum reservoirs built using transmon devices provided by IBM. Our hybrid reservoir achieved a Normalized Mean Square Error (NMSE) of 6x10^{-4} which is comparable to recent benchmarks. The Memory Capacity characterization of a n-qubit reservoir showed a systematic variation with the complexity of the topology and exhibited a peak for the configuration with n-1 self-loops. Such a peak provides a basis for selecting the optimal design for forecasting tasks.

q-fin.RM↗

arXiv2022

Extraction of the interaction parameters for $α-$RuCl$_3$ from neutron data using machine learning

Single crystal inelastic neutron scattering data contain rich information about the structure and dynamics of a material. Yet the challenge of matching sophisticated theoretical models with large data volumes is compounded by computational complexity and the ill-posed nature of the inverse scattering problem. Here we utilize a novel machine-learning-assisted framework featuring multiple neural network architectures to address this via high-dimensional modeling and numerical methods. A comprehensive data set of diffraction and inelastic neutron scattering measured on the Kitaev material $α-$RuCl$_3$ is processed to extract its Hamiltonian. Semiclassical Landau-Lifshitz dynamics and Monte-Carlo simulations were employed to explore the parameter space of an extended Kitaev-Heisenberg Hamiltonian. A machine-learning-assisted iterative algorithm was developed to map the uncertainty manifold to match experimental data; a non-linear autoencoder used to undertake information compression; and Radial Basis networks utilized as fast surrogates for diffraction and dynamics simulations to predict potential spin Hamiltonians with uncertainty. Exact diagonalization calculations were employed to assess the impact of quantum fluctuations on the selected parameters around the best prediction.

cond-mat.str-el↗

arXiv2022

The Role of the Third Dimension in Searching Majorana Fermions in $α$-RuCl$_3$ via Phonons

Understanding phonons in $α$-RuCl$_3$ is critical to analyze the controversy around the observation of the half-integer thermal quantum Hall effect. While many studies have focused on the magnetic excitations in $α$-RuCl$_3$, its vibrational excitation spectrum has remained relatively unexplored. We investigate the phonon structure of $α$-RuCl$_3$ via inelastic neutron scattering experiments and density functional theory calculations. Our results show excellent agreement between experiment and first principles calculations. After validating our theoretical model, we extrapolate the low energy phonon properties. We find that the phonons in $α$-RuCl$_3$ that either propagate or vibrate in the out-of-plane direction have significantly reduced velocities, and therefore have the potential to dominate the observability of the elusive half integer plateaus in the thermal Hall conductance. In addition, we use low-energy interlayer phonons to resolve the low temperature stacking structure of our large crystal of $α$-RuCl$_3$, which we find to be consistent with that of the $R\bar{3}$ space group, in agreement with neutron diffraction.

cond-mat.str-el↗

arXiv2022

Finite-Size Scaling on a Digital Quantum Simulator using Quantum Restricted Boltzmann Machine

The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occuring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g. in the Quantum Rabi Model (QRM). Since, these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space. This approach has previously been used to calculate the critical parameters for stability and symmetry breaking of electronic structure configurations of atomic and molecular systems. We calculate the critical point for the quantum phase transition of the QRM using this approach. We also provide a protocol to implement this method on a digital quantum simulator using the Quantum Restricted Boltzmann Machine algorithm. Our work opens up a new direction in the study of quantum phase transitions on quantum devices.

quant-ph↗

arXiv2022

The planar thermal Hall conductivity in the Kitaev magnet α-RuCl3

We report detailed measurements of the Onsager-like planar thermal Hall conductivity $κ_{xy}$ in $α$-RuCl$_3$, a spin-liquid candidate of topical interest. With the thermal current ${\bf J}_{\rm Q}$ and magnetic field $\bf B\parallel a$ (zigzag axis), the observed $κ_{xy}/T$ varies strongly with temperature $T$ (1-10 K). The results are well-described by bosonic edge excitations which evolve to topological magnons at large $B$. Fits to $κ_{xy}/T$ yield a Chern number $\sim 1$ and a band energy $ω_1\sim$1 meV, in agreement with sharp modes seen in electron spin-resonance experiments. The bosonic character is incompatible with half-quantization of $κ_{xy}/T$.

cond-mat.str-el↗

arXiv2021

Metadamping in inertially amplified metamaterials: Trade-off between spatial attenuation and temporal attenuation

Metadamping is the phenomenon of either enhanced or diminished intrinsic dissipation in a material stemming from the material's internal structural dynamics. It has been previously shown that a locally resonant elastic metamaterial may be designed to exhibit higher or lower dissipation compared to a statically equivalent phononic crystal with the same amount of prescribed damping. Here we reveal that even further dissipation, or alternatively further reduction of loss, may be reached in an inertially amplified metamaterial that is also statically equivalent and has the same amount of prescribed damping. This is demonstrated by a passive configuration whereby an attenuation peak is generated by the motion of a mass supported by an inclined lever arm. We further show that by coupling this inertially amplified attenuation peak with that of a local resonance attenuation peak, a trade-off between the intensity of spatial attenuation versus temporal attenuation is realized for a range of the inclination angles. Design for performance along this trade-off is therefore possible by adjustment of the lever angle. These findings open the way for highly expanding the Ashby space for stiffness-damping capacity or stiffness-spatial attenuation capacity through design of the internal structure of materials.

physics.app-ph↗

arXiv2021

Magnetic properties and signatures of moment ordering in triangular lattice antiferromagnet KCeO$_2$

The magnetic ground state and the crystalline electric field level scheme of the triangular lattice antiferromagnet KCeO$_2$ are investigated. Below $T_N =$ 300 mK, KCeO$_2$ develops signatures of magnetic order in specific heat measurements and low energy inelastic neutron scattering data. Trivalent Ce$^{3+}$ ions in the $D_{3d}$ local environment of this compound exhibit large splittings among the lowest three $4f^1$ Kramers doublets defining for the free ion the $J = 5/2$ sextet and a ground state doublet with dipole character, consistent with recent theoretical predictions in M. S. Eldeeb et al. Phys. Rev. Materials 4, 124001 (2020). An unexplained, additional local mode appears, and potential origins of this anomalous mode are discussed.

cond-mat.str-el↗

arXiv2021

Oscillations of the thermal conductivity observed in the spin-liquid state of $α$-RuCl$_3$

In the class of materials called spin liquids, a magnetically ordered state cannot be attained even at milliKelvin temperatures because of conflicting constraints on each spin (for e.g. from geometric or exchange frustration). The resulting quantum spin-liquid (QSL) state is currently of intense interest because it exhibits novel excitations as well as wave-function entanglement. The layered insulator $α$-RuCl$_3$ orders as a zigzag antiferromagnet below $\sim$7 K in zero magnetic field. The zigzag order is destroyed when a magnetic field $\bf H$ is applied parallel to the zigzag axis a. Within the field interval (7.3, 11) Tesla, there is growing evidence that a QSL state exists. Here we report the observation of oscillations in its thermal conductivity below 4 K. The oscillation amplitude is very large within the interval (7.3, 11) T and strongly suppressed on either side. Paradoxically, the oscillations are periodic in 1/\emph{H}, analogous to quantum oscillations in metals, even though $α$-RuCl$_3$ is an excellent insulator with a gap of 1.9 eV. By tilting $\bf H$ out of the plane, we find that the oscillation period is determined by the in-plane component $H_a$. As the temperature is raised above 0.5 K, the oscillation amplitude decreases exponentially. The decrease anticorrelates with the emergence above $\sim$2 K of an anomalous planar thermal Hall conductivity measured with $\bf H\parallel a$. To exclude extrinsic artifacts, we carried out several tests. The implications of the oscillations are discussed.

cond-mat.str-el↗

arXiv2021

Field-induced intermediate ordered phase and anisotropic interlayer interactions in $α$-RuCl$_3$

In $α$-RuCl$_3$, an external magnetic field applied within the honeycomb plane can induce a transition from a magnetically ordered state to a disordered state that is potentially related to the Kitaev quantum spin liquid. In zero field, single crystals with minimal stacking faults display a low-temperature state with in-plane zigzag antiferromagnetic order and a three-layer periodicity in the direction perpendicular to the honeycomb planes. Here, we present angle-dependent magnetization, ac susceptibility, and thermal transport data that demonstrate the presence of an additional intermediate-field ordered state at fields below the transition to the disordered phase. Neutron diffraction results show that the magnetic structure in this phase is characterized by a six-layer periodicity in the direction perpendicular to the honeycomb planes. Theoretically, the intermediate ordered phase can be accounted for by including spin-anisotropic couplings between the layers in a three-dimensional spin model. Together, this demonstrates the importance of interlayer exchange interactions in $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2020

Frustrated Heisenberg $J_1-J_2$ model within the stretched diamond lattice of LiYbO2

We investigate the magnetic properties of LiYbO$_2$, containing a three-dimensionally frustrated, diamond-like lattice via neutron scattering, magnetization, and heat capacity measurements. The stretched diamond network of Yb$^{3+}$ ions in LiYbO$_2$ enters a long-range incommensurate, helical state with an ordering wave vector ${\bf{k}} = (0.384, \pm 0.384, 0)$ that "locks-in" to a commensurate ${\bf{k}} = (1/3, \pm 1/3, 0)$ phase under the application of a magnetic field. The spiral magnetic ground state of LiYbO$_2$ can be understood in the framework of a Heisenberg $J_1-J_2$ Hamiltonian on a stretched diamond lattice, where the propagation vector of the spiral is uniquely determined by the ratio of $J_2/|J_1|$. The pure Heisenberg model, however, fails to account for the relative phasing between the Yb moments on the two sites of the bipartite lattice, and this detail as well as the presence of an intermediate, partially disordered, magnetic state below 1 K suggests interactions beyond the classical Heisenberg description of this material.

cond-mat.str-el↗

arXiv2020

Antiferromagnetism and crystalline-electric field excitations in tetragonal NaCeO2

We investigate the crystal structure, magnetic properties, and crystalline-electric field of tetragonal, $I4_1/amd$, NaCeO$_2$. In this compound, Ce$^{3+}$ ions form a tetragonally elongated diamond lattice coupled by antiferromagnetic interactions ($Θ_{CW} = -7.69$ K) that magnetically order below $T_N = 3.18$ K. The Ce$^{3+}$ $J = 5/2$ crystalline-electric field-split multiplet is studied via inelastic neutron scattering to parameterize a $J_{eff} = 1/2$ ground state doublet comprised of states possessing mixed $|m_z \rangle$ character. Neutron powder diffraction data reveal the onset of $A$-type antiferromagnetism with $μ=0.57(2)$ $μ_B$ moments aligned along the $c$-axis. The magnetic structure is consistent with the expectations of a frustrated Heisenberg $J_1$-$J_2$ model on the elongated diamond lattice with effective exchange values $J_1 > 4 J_2$ and $J_1 > 0$.

cond-mat.str-el↗

arXiv2020

Strongly two-dimensional exchange interactions in the in-plane metallic antiferromagnet Fe$_2$As probed by inelastic neutron scattering

To understand spin interactions in materials of the Cu$_2$Sb structure type, inelastic neutron scattering of Fe$_2$As single crystals was examined at different temperatures and incident neutron energies. The experimental phonon spectra match well with the simulated phonon spectra obtained from density functional theory (DFT) calculations. The measured magnon spectra were compared to the simulated magnon spectra obtained via linear spin wave theory with the exchange coupling constants calculated using the spin polarized, relativistic Korringa-Kohn-Rostoker method in Zhang et al. (2013). The simulated magnon spectra broadly agree with the experimental data although, the energy values are underestimated along the $K$ direction. Exchange coupling constants between Fe atoms were refined by fits to the experimental magnon spectra, revealing stronger nearest neighbor Fe1-Fe1 exchange coupling than previously reported. The strength of this exchange coupling is almost an order of magnitude higher than other exchange interactions despite the three-dimensional nature of the phonon interactions. The lack of scattering intensity at energies above 60 meV makes unconstrained determination of the full set of exchange interactions difficult, which may be a fundamental challenge in metallic antiferromagnets.

cond-mat.mtrl-sci↗

arXiv2020

Quantum Annealing Algorithm for Expected Shortfall based Dynamic Asset Allocation

The 2008 mortgage crisis is an example of an extreme event. Extreme value theory tries to estimate such tail risks. Modern finance practitioners prefer Expected Shortfall based risk metrics (which capture tail risk) over traditional approaches like volatility or even Value-at-Risk. This paper provides a quantum annealing algorithm in QUBO form for a dynamic asset allocation problem using expected shortfall constraint. It was motivated by the need to refine the current quantum algorithms for Markowitz type problems which are academically interesting but not useful for practitioners. The algorithm is dynamic and the risk target emerges naturally from the market volatility. Moreover, it avoids complicated statistics like generalized pareto distribution. It translates the problem into qubit form suitable for implementation by a quantum annealer like D-Wave. Such QUBO algorithms are expected to be solved faster using quantum annealing systems than any classical algorithm using classical computer (but yet to be demonstrated at scale).

q-fin.RM↗

arXiv2020

Spin excitations in the frustrated triangular lattice antiferromagnet NaYbO$_2$

Here we present a neutron scattering-based study of magnetic excitations and magnetic order in NaYbO$_2$ under the application of an external magnetic field. The crystal electric field-split $J = 7/2$ multiplet structure is determined, revealing a mixed $|m_z>$ ground state doublet and is consistent with a recent report Ding et al. [1]. Our measurements further suggest signatures of exchange effects in the crystal field spectrum, manifested by a small splitting in energy of the transition into the first excited doublet. The field-dependence of the low-energy magnetic excitations across the transition from the quantum disordered ground state into the fluctuation-driven ordered regime is analyzed. Signs of a first-order phase transition into a noncollinear ordered state are revealed at the upper-field phase boundary of the ordered regime, and higher order magnon scattering, suggestive of strong magnon-magnon interactions, is resolved within the previously reported $up-up-down$ phase. Our results reveal a complex phase diagram of field-induced order and spin excitations within NaYbO$_2$ and demonstrate the dominant role of quantum fluctuations cross a broad range of fields within its interlayer frustrated triangular lattice.

cond-mat.str-el↗

arXiv2020

Skin Diseases Detection using LBP and WLD- An Ensembling Approach

In all developing and developed countries in the world, skin diseases are becoming a very frequent health problem for the humans of all age groups. Skin problems affect mental health, develop addiction to alcohol and drugs and sometimes causes social isolation. Considering the importance, we propose an automatic technique to detect three popular skin diseases- Leprosy, Tinea versicolor and Vitiligofrom the images of skin lesions. The proposed technique involves Weber local descriptor and Local binary pattern to represent texture pattern of the affected skin regions. This ensemble technique achieved 91.38% accuracy using multi-level support vector machine classifier, where features are extracted from different regions that are based on center of gravity. We have also applied some popular deep learn-ing networks such as MobileNet, ResNet_152, GoogLeNet,DenseNet_121, and ResNet_101. We get 89% accuracy using ResNet_101. The ensemble approach clearly outperform all of the used deep learning networks. This imaging tool will be useful for early skin disease screening.

cs.CV↗