arXiv subjects

Rajiv R. P. Singh

Publications and source records attributed to Rajiv R. P. Singh.

At least 37 records · Page 2Linked to original sources

arXiv2018

Principal Component Analysis for Fermionic Critical Points

We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine $T_c$. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

cond-mat.str-el↗

arXiv2018

Griffiths-McCoy Singularities in the Dilute Transverse-Field Ising Model: A Numerical Linked Cluster Expansion Study

We use Numerical Linked Cluster Expansions (NLCE) to study the site diluted transverse-field Ising model on the square-lattice at $T=0$. NLCE with a self-consistent mean-field on the boundary of the clusters is used to obtain the ground state magnetization, susceptibility, and structure factor as a function of transverse field $h$ and exchange constant $J$. Adding site-dilution to the model turns NLCE into a series expansion in the dilution parameter $p$. Studying the divergence of the structure factor allows us to establish the phase-diagram in the $h/J$ and $p$ plane. By studying the magnetization of the system in a longitudinal field, we investigate the Griffiths-McCoy (GM) singularities. We find that the magnetization develops non-linearities in the Griffiths phase with exponents that vary continuously with $h$. Additionally, the probability distribution of the local susceptibility develops long tails in the Griffith's phase, which is studied in terms of its moments.

cond-mat.stat-mech↗

arXiv2018

Exotic pairing symmetry of interacting Dirac fermions on a $π$ flux lattice

The pairing symmetry of interacting Dirac fermions on the $π$-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked cluster expansion methods. The extended $s^*$- (i.e. extended $s$-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an exotic $ds^*$-wave phase consisting of alternating stripes of $s^*$- and d-wave phases. A complementary mean-field analysis shows that while the $s^*$- and d-wave symmetries individually have nodes in the energy spectrum, the $ds^*$ channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral d-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.

cond-mat.str-el↗

arXiv2017

Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures

We compute the real-space spin correlations and frquency and wave-vector resolved dynamic structure factors $S(\vec q,ω)$ for the nearest-neighbor Kagome-Lattice Heisenberg Antiferromagnet (KLHM) at finite temperatures using Numerical Linked Cluster Expansion (NLCE) method. A triangle-based NLCE is used to calculate frequency moments of the dynamic structure factors in the thermodynamic limit, which show excellent convergence for $T> J/4$. A Gaussian approximation and the fluctuation-dissipation relation are used to to reconstruct the frequency dependence. We find that some features of the low temperature KLHM structure-factors begin to set in at temperatures of order $J$. Our results are in very good agreement with powder diffraction measurements reported earlier on the Herbertsmithite materials ZnCu$_3$(OH)$_6$Cl$_2$. However, the calculated properties differ from the low temperature ($T\approx J/100$) experimental measurements in one important regard. In line with the experimental observations, the spectral weight has a diffuse nature, which is predominantly spread along the extended Brillouin-Zone boundary. However, the maximum intensity is found in our calculations to be at the $K$ point of the extended Brillouin Zone in contrast to the low temperature experiments, where it is at the $M$ point. We suggest that experiments should be done at various temperatures to look for such a crossover of the maximum from the $K$ point to the $M$ point. In the absence of such a crossover, the Herbertsmithite materials must differ from KLHM in a significant manner.

cond-mat.str-el↗

arXiv2017

High temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high temperature series expansion study

We develop high temperature series expansions for the thermodynamic properties of the honeycomb-lattice Kitaev-Heisenberg model. Numerical results for uniform susceptibility, heat capacity and entropy as a function of temperature for different values of the Kitaev coupling $K$ and Heisenberg exachange coupling $J$ (with $|J|\le |K|$) are presented. These expansions show good convergence down to a temperature of a fraction of $K$ and in some cases down to $T=K/10$. In the Kitaev exchange dominated regime, the inverse susceptibility has a nearly linear temperature dependence over a wide temperature range. However, we show that already at temperatures $10$-times the Curie-Weiss temperature, the effective Curie-Weiss constant estimated from the data can be off by a factor of 2. We find that the magnitude of the heat capacity maximum at the short-range order peak, is substantially smaller for small $J/K$ than for $J$ of order or larger than $K$. We suggest that this itself represents a simple marker for the relative importance of the Kitaev terms in these systems. Somewhat surprisingly, both heat capacity and susceptibility data on Na$_2$IrO$_3$ are consistent with a dominant {\it antiferromagnetic} Kitaev exchange constant of about $300-400$ $K$.

cond-mat.str-el↗

arXiv2017

Interplay of Magnetic Order, Pairing and Phase Separation in a One Dimensional Spin Fermion Model

We consider a lattice model of itinerant electrons coupled to an array of localized classical Heisenberg spins. The nature of the ground state ordered magnetic phases that result from the indirect spin-spin coupling mediated by the electrons is determined as a function of density and the spin-fermion coupling $J$. At a fixed chemical potential, spiral phases exist only up to values of $J$ which are less than roughly half the electronic bandwidth. At a fixed electron density and near half filling, the system phase separates into a half-filled antiferromagnetic phase and a spiral phase. The ferromagnetic phases are shown to be fully polarized, while the spiral phases have equal admixture of up and down spins. Phase separation survives in the presence of weak pairing field $Δ$ but disappears when $Δ$ exceeds a critical value $Δ_c$. If pairing fields are large enough, an additional spiral state arises at strong coupling $J$. The relevance of this study, especially the phase separation, to artificially engineered systems of adjacent itinerant electrons and localized spins is discussed. In particular, we propose a method which might allow for the braiding of Majorana fermions by changing the density and moving their location as they are pulled along by a phase separation boundary.

cond-mat.str-el↗

arXiv2017

Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models - the square and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-one Ising (BSI) model, and the 2D XY model, and examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow exploration of different phases and symmetry-breaking, but can distinguish phase transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which is particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the `charge' correlations (vorticity) in the BSI model (XY model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the `antoencoder method', and demonstrate that it too can be trained to capture phase transitions and critical points.

cond-mat.stat-mech↗

arXiv2017

Cubic trihedral corner entanglement for a free scalar

We calculate the universal contribution to the $α$-Renyi entropy from a cubic trihedral corner in the boundary of the entangling region in 3+1 dimensions for a massless free scalar. The universal number, $v_α$, is manifest as the coefficient of a scaling term that is logarithmic in the size of the entangling region. Our numerical calculations find that this universal coefficient has both larger magnitude and the opposite sign to that induced by a smooth spherical entangling boundary in 3+1 dimensions, for which there is a well-known subleading logarithmic scaling. Despite these differences, up to the uncertainty of our finite-size lattice calculations, the functional dependence of the trihedral coefficient $v_α$ on the Rényi index $α$ is indistinguishable from that for a sphere, which is known analytically for a massless free scalar. We comment on the possible source of this $α$-dependence arising from the general structure of (3+1)-dimensional conformal field theories, and suggest calculations past the free scalar which could further illuminate the general structure of the trihedral divergence in the Rényi entropy.

cond-mat.str-el↗

arXiv2016

Nuclear relaxation rates in the Herbertsmithite Kagome antiferromagnets ZnCu3(OH)6Cl2

Local spectral functions and Nuclear Magnetic Relaxation (NMR) rates, 1/T1, for the spin-half Heisenberg antiferromagnet on the Kagome Lattice are calculated using Moriyas Gaussian approximation, as well as through an extrapolation of multiple frequency moments. The temperature dependence of the calculated rates is compared with the oxygen 1/T1 NMR data in Herbertsmithite. We find that the Gaussian approximation for 1/T1 shows behavior qualitatively similar to experiments with a sharp drop in rates at low temperatures, consistent with a spin-gapped behavior. However, this approximation significantly underestimates the magnitude of 1/T1 even at room temperature. Rates obtained from extrapolation of multiple frequency moments give very good agreement with the room temperature NMR data with J = 195 +/- 20 K and hyperfine couplings determined independently from other measurements. The use of multiple frequency moments also leads to additional low frequency weight in the local structure factors. The convergence of our calculations with higher frequency moments breaks down at low temperatures suggesting the existence of longer range dynamic correlations in the system despite the very short-range static correlations.

cond-mat.str-el↗

arXiv2016

Spiral versus modulated collinear phases in the quantum ANNNH model

Motivated by the discovery of spiral and modulated collinear phases in several magnetic materials, we investigate the magnetic properties of Heisenberg spin S=1/2 antiferromagnets in 2 and 3 dimensions, with frustration arising from 2nd-neighbor couplings in one axial direction (the ANNNH model). Our results clearly demonstrate the presence of an incommensurate spiral phase at T=0 in 2 dimensions, extending to finite temperatures in 3 dimensions. The crossover between Néel and spiral order occurs at a value of the frustration parameter considerably above the classical value 0.25, a sign of substantial quantum fluctuations. We also investigate a possible modulated collinear phase with a wavelength of 4 lattice spacings, and find that it has substantially higher energy and hence is not realized in the model.

cond-mat.str-el↗

arXiv2016

Spin Generation Via Bulk Spin Current in Three Dimensional Topological Insulators

To date, spin generation in three-dimensional topological insulators is primarily modeled as a single-surface phenomenon, attributed to the momentum-spin locking on each individual surface. In this article we propose a mechanism of spin generation where the role of the insulating yet topologically non-trivial bulk becomes explicit: an external electric field creates a transverse pure spin current through the bulk of a three-dimensional topological insulator, which transports spins between the top and bottom surfaces. Under sufficiently high surface disorder, the spin relaxation time can be extended via the Dyakonov-Perel mechanism. Consequently both the spin generation efficiency and surface conductivity are largely enhanced. Numerical simulation confirms that this spin generation mechanism originates from the unique topological connection of the top and bottom surfaces and is absent in other two dimensional systems such as graphene, even though they possess a similar Dirac cone-type dispersion.

cond-mat.mtrl-sci↗

arXiv2015

Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study

We study the competition between $\sqrt{3} \times \sqrt{3}$ (RT3) and $q=0$ (Q0) magnetic orders in spin-one and spin-$3/2$ Kagome-lattice XXZ antiferromagnets with varying XY anisotropy parameter $Δ$, using series expansion methods. The Hamiltonian is split into two parts: an $H_0$ which favors the classical order in the desired pattern and an $H_1$, which is treated in perturbation theory by a series expansion. We find that the ground state energy series for the RT3 and Q0 phases are identical up to sixth order in the expansion, but ultimately a selection occurs, which depends on spin and the anisotropy $Δ$. Results for ground state energy and the magnetization are presented. These results are compared with recent spin-wave theory and coupled-cluster calculations. The series results for the phase diagram are close to the predictions of spin-wave theory. For the spin-one model at the Heisenberg point ($Δ=1$), our results are consistent with a vanishing order parameter, that is an absence of a magnetically ordered phase. We also develop series expansions for the ground state energy of the spin-one Heisenberg model in the trimerized phase. We find that the ground state energy in this phase is lower than those of magnetically ordered ones, supporting the existence of a spontaneously trimerized phase in this model.

cond-mat.str-el↗

arXiv2015

Early breakdown of area-law entanglement at many-body delocalization transition

We introduce the numerical linked cluster (NLC) expansion as a controlled numerical tool for the study of the many-body localization (MBL) transition in a disordered system with continuous non-perturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and find that our conclusion is the same at all examined energies.

cond-mat.str-el↗

arXiv2015

Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death

We show that the bipartite logarithmic entanglement negativity (EN) of quantum spin models obeys an area law at all nonzero temperatures. We develop numerical linked cluster (NLC) expansions for the `area-law' logarithmic entanglement negativity as a function of temperature and other parameters. For one-dimensional models the results of NLC are compared with exact diagonalization on finite systems and are found to agree very well. The NLC results are also obtained for two dimensional XXZ and transverse-field Ising models. In all cases, we find a sudden onset (or sudden death) of negativity at a finite temperature above which the negativity is zero. We use perturbation theory to develop a physical picture for this sudden onset (or sudden death). The onset of EN or its magnitude are insensitive to classical finite-temperature phase transitions, supporting the argument for absence of any role of quantum mechanics at such transitions. On approach to a quantum critical point at $T=0$, negativity shows critical scaling in size and temperature.

cond-mat.stat-mech↗

arXiv2015

Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points

At a quantum critical point, bipartite entanglement entropies have universal quantities which are subleading to the ubiquitous area law. For Renyi entropies, these terms are known to be similar to the von Neumann entropy, while being much more amenable to numerical and even experimental measurement. We show here that when calculating universal properties of Renyi entropies, it is important to account for unusual corrections to scaling that arise from relevant local operators present at the conical singularity in the multi-sheeted Riemann surface. These corrections grow in importance with increasing Renyi index. We present studies of Renyi correlation functions in the 1+1 transverse-field Ising model (TFIM) using conformal field theory, mapping to free fermions, and series expansions, and the logarithmic entropy singularity at a corner in 2+1 for both free bosonic field theory and the TFIM, using numerical linked cluster expansions. In all numerical studies, accurate results are only obtained when unusual corrections to scaling are taken into account. In the worst case, an analysis ignoring these corrections can get qualitatively incorrect answers, such as predicting a decrease in critical exponents with the Renyi index, when they are actually increasing. We discuss a two-step extrapolation procedure that can be used to account for the unusual corrections to scaling.

cond-mat.stat-mech↗

arXiv2015

The many faces of quantum kagome materials: Interplay of further-neighbour exchange and Dzyaloshinskii-Moriya interaction

The field of frustrated magnetism has been enriched significantly by the discovery of various kagome lattice compounds. These materials exhibit a great variety of macroscopic behaviours ranging from magnetic orders to quantum spin liquids. Using large-scale exact diagonalization, we construct the phase diagram of the $S=1/2$ $J_1$-$J_2$ kagome Heisenberg model with $z$-axis Dzyaloshinskii-Moriya interaction $D_z$. We show that this model can systematically account for many of the experimentally observed phases. Small $J_2$ and $D_z$ can stabilize respectively a gapped and a gapless spin liquid. When $J_2$ or $D_z$ is substantial, the ground state develops a $\mathbf{Q}=0$, $120^\textrm{o}$ antiferromagnetic order. The critical strengths for inducing magnetic transition are $D^c_z \sim 0.1\, J_1$ at $J_2=0$, and $J^c_2\sim 0.4\, J_1$ at $D_z=0$. The previously reported values of $D_z$ and $J_2$ for herbertsmithite [ZnCu$_3$(OH)$_6$Cl$_2$] place the compound in close proximity to a quantum critical point.

cond-mat.str-el↗

arXiv2015

Finite-temperature superconducting correlations of the Hubbard model

We utilize numerical linked-cluster expansions (NLCEs) and the determinantal quantum Monte Carlo algorithm to study pairing correlations in the square lattice Hubbard model. To benchmark the NLCE, we first locate the finite-temperature phase transition of the attractive model to a superconducting state away from half filling. We then explore the superconducting properties of the repulsive model for the d-wave and extended s-wave pairing symmetries. The pairing structure factor shows a strong tendency to d-wave pairing and peaks at an interaction strength comparable to the bandwidth. The extended s-wave structure factor and correlation length are larger at higher temperatures but clearly saturate as temperature is lowered, whereas the d-wave counterparts, which start off lower at high temperatures, continue to rise near half filling. This rise is even more dramatic in the d-wave susceptibility. The convergence of NLCEs breaks down as the susceptibilities and correlation lengths become large, so we are unable to determine the onset of long-range order. However, our results extend the conclusion, previously restricted to only magnetic and charge correlations, that NLCEs offer unique window into pairing in the Hubbard model at strong coupling.

cond-mat.str-el↗

arXiv2014

Simulated Cytoskeletal Collapse via Tau Degradation

We present a coarse-grained two dimensional mechanical model for the microtubule-tau bundles in neuronal axons in which we remove taus, as can happen in various neurodegenerative conditions such as Alzheimer's disease, tauopathies, and chronic traumatic encephalopathy. Our simplified model includes (i) taus modeled as entropic springs between microtubules, (ii) removal of taus from the bundles due to phosphorylation, and (iii) a possible depletion force between microtubules due to these dissociated phosphorylated taus. We equilibrate upon tau removal using steepest descent relaxation. In the absence of the depletion force, the transverse rigidity to radial compression of the bundle falls to zero at about 60% tau occupancy, in agreement with standard percolation theory results. However, with the attractive depletion force, spring removal leads to a first order collapse of the bundles over a wide range of tau occupancies for physiologically realizable conditions. While our simplest calculations assume a constant concentration of microtubule intercalants to mediate the depletion force, including a dependence that is linear in the detached taus yields the same collapse. Applying percolation theory to removal of taus at microtubule tips, which are likely to be the protective sites against dynamic instability, we argue that the microtubule instability can only obtain at low tau occupancy, from 0.06-0.30 depending upon the tau coordination at the microtubule tips. Hence, the collapse we discover is likely to be more robust over a wide range of tau occupancies than the dynamic instability. We suggest in vitro tests of our predicted collapse.

q-bio.NC↗