arXiv subjects

Mark Jarrell

Publications and source records attributed to Mark Jarrell.

At least 19 recordsLinked to original sources

arXiv2019

Interatomic Potential in a Simple Dense Neural Network Representation

Simulations at the atomic scale provide a direct and effective way to understand the mechanical properties of materials. In the regime of classical mechanics, simulations for the thermodynamic properties of metals and alloys can be done by either solving the equations of motion or performing Monte Carlo sampling. The key component for an accurate simulation of such physical systems to produce faithful physical quantities is the use of an appropriate potential or a force field. In this paper, we explore the use of methods from the realm of machine learning to overcome and bypass difficulties encountered when fitting potentials for atomic systems. Particularly, we will show that classical potentials can be represented by a dense neural network with good accuracy.

physics.comp-ph↗

arXiv2019

Locally self-consistent embedding approach for disordered electronic systems

We present a new embedding scheme for the locally self-consistent method to study disordered electron systems. We test this method in a tight-binding basis and apply it to the single band Anderson model. The local interaction zone is used to efficiently compute the local Green's function of a supercell embeded into a local typical medium. We find a quick convergence as the size of the local interaction zone which reduces the computational costs as expected. This method captures the Anderson localization transition and accurately predicts the critical disorder strength. The present work opens the path towards the development of a typical medium embedding scheme for the $O(N)$ multiple scattering methods.

cond-mat.dis-nn↗

arXiv2018

Systematic Quantum Cluster Typical Medium Method For the Study of Localization in Strongly Disordered Electronic Systems

Great progress has been made in the last several years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean field theory and the coherent potential approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization, and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Here we provide an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multi-band Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the density functional theory.

cond-mat.dis-nn↗

arXiv2018

Emergent Strange Nodal Metallicity from Orbital-Selective Mott Physics

While a specific kind of strange metal is increasingly found to be the "normal" states in a wide variety of unconventional superconductors, its microscopic origin is presently a hotly debated enigma. Using dynamical mean-field theory (DMFT) based on hybridization expansion of continuous-time quantum Monte-Carlo (CTQMC) solver for an extended two-band Hubbard model (2BHM), we investigate the conditions underlying the emergence of such a metal. Specifically, we tie strange metallicity to an orbital-selective Mottness in 2BHM or momentum-selective Mott phase (OSMP) in 2D Hubbard models inspired by a cluster-to-orbital mapping. We find $(i)$ disparate spin and charge responses, $(ii)$ fractional power-law behavior and $\omega/T$-scaling in the charge and spin fluctuation responses, and $(iii)$ very good accord with optical conductivity and nuclear magnetic relaxation rates in the slightly underdoped normal states of cuprates and Fe-arsenides. We analyze the local problem using bosonization to show that such anomalous responses arise from a lattice orthogonality catastrophe specifically in the OSMP. Our work establishes the intimate link between strange metallicity and selective Mottness in quantum matter.

cond-mat.str-el↗

arXiv2017

Emergence of non-Fermi liquid dynamics through non-local correlations in an interacting disordered system

We provide strong evidence of a quantum critical point (QCP) associated with the destruction of Kondo screening in the Anderson-Hubbard model for interacting electrons with quenched disorder. A unique crossover energy scale, $\omega^*$ separating the Fermi liquid and non-Fermi liquid (nFL) scattering dynamics on the metallic side of the quantum critical fan is identified. The scale vanishes at the disorder driven QCP. We interpret our results by measuring the distribution of Kondo scales and find that the QCP occurs when this distribution acquires a finite intercept, indicating a Kondo destruction scenario, albeit distinct from the local QCP picture. The nFL behavior is shown to stem from an interplay of strong electron-electron interactions and the systematic inclusion of short-range dynamical fluctuations induced by the underlying random potential. The results have been obtained through a computational framework based on the typical medium dynamical cluster approximation.

cond-mat.str-el↗

arXiv2017

Multifractal Study of Quasiparticle Localization in Disordered Superconductors

The thermal metal to thermal insulator transition due to random disorder is studied in the context of the symmetries of the Bogoliubov de Gennes Hamiltonian. We focus on a three dimensional system with gapless s-wave pairing that possesses time reversal and spin rotational symmetry. The quasiparticle excitations (bogolons) undergo a metal insulator transition as the disorder increases. We determine the critical disorder strength and correlation exponent first by the transfer matrix method (TMM). We then apply a multifractal finite sized scaling (MFSS) of the bogolon wavefunction obtained from large scale diagonalization of the Hamiltonian and obtain the critical disorder strength and exponent, in agreement with those found by TMM.

cond-mat.dis-nn↗

arXiv2017

Periodic Anderson model with Holstein phonons for the description of the Cerium volume collapse

Recent experiments have suggested that the electron-phonon coupling may play an important role in the $\gamma \rightarrow \alpha$ volume collapse transition in Cerium. A minimal model for the description of such transition is the periodic Anderson model. In order to better understand the effect of the electron-phonon interaction on the volume collapse transition, we study the periodic Anderson model with coupling between Holstein phonons and electrons in the conduction band. We find that the electron-phonon coupling enhances the volume collapse, which is consistent with experiments in Cerium. While we start with the Kondo Volume Collapse scenario in mind, our results capture some interesting features of the Mott scenario, such as a gap in the conduction electron spectra which grows with the effective electron-phonon coupling.

cond-mat.str-el↗

arXiv2016

Quantum critical local spin dynamics near the Mott metal-insulator transition in infinite dimensions

Finding microscopic models for metallic states that exhibit quantum critical properties such as $\omega/T$ scaling is a major theoretical challenge. We calculate the local dynamical spin susceptibility $\chi(T,\omega)$ for a Hubbard model at half filling using Dynamical Mean-Field Theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite temperature critical point. The signature of the latter is $\omega/T$ scaling where $T$ is the temperature. Our results are consistent with previous results showing scaling of the dc electrical conductivity and are relevant to experiments on organic charge transfer salts.

cond-mat.str-el↗

arXiv2016

A local theory for Mott-Anderson localization

The paramagnetic metallic phase of the Anderson-Hubbard model (AHM) is investigated using a non-perturbative local moment approach within the framework of dynamical mean field theory with a typical medium. Our focus is on the breakdown of the metallic phase near the metal-insulators transition as seen in the single-particle spectra, scattering rates and the associated distribution of Kondo scales. We demonstrate the emergence of a universal, underlying low energy scale, $T_K^{peak}$. This lies close to the peak of the distribution of Kondo scales obtained within the metallic phase of the paramagnetic AHM. Spectral dynamics for energies, $\omega\lesssim T_K^{peak}$ display Fermi liquid universality crossing over to an incoherent universal dynamics for $\omega\gg T_K^{peak}$ in the scaling regime. Such universal dynamics indicate that within a local theory the low to moderately low energy physics is governed by an effective, {\it disorder renormalised} Kondo screening.

cond-mat.str-el↗

arXiv2015

Sign learning kink-based (SiLK) quantum Monte Carlo for molecular systems

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H$_{2}$O, N$_2$, and F$_2$ molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.

physics.comp-ph↗

arXiv2015

A first principles investigation of cubic BaRuO$_3$: A Hund's metal

A first-principles investigation of cubic-BaRuO$_3$, by combining density functional theory with dynamical mean-field theory and a hybridization expansion continuous time quantum Monte-Carlo solver, has been carried out. Non-magnetic calculations with appropriately chosen on-site Coulomb repulsion, $U$ and Hund's exchange, $J$, for single-particle dynamics and static susceptibility show that cubic-BaRuO$_3$ is in a spin-frozen state at temperatures above the ferromagnetic transition point. A strong red shift with increasing $J$ of the peak in the real frequency dynamical susceptibility indicates a dramatic suppression of the Fermi liquid coherence scale as compared to the bare parameters in cubic-BaRuO$_3$. The self-energy also shows clear deviation from Fermi liquid behaviour that manifests in the single-particle spectrum. Such a clean separation of energy scales in this system provides scope for an incoherent spin-frozen (SF) phase, that extends over a wide temperature range, to manifest in non-Fermi liquid behaviour and to be the precursor for the magnetically ordered ground state.

cond-mat.str-el↗

arXiv2015

Quantum critical dynamics of a magnetic impurity in a semiconducting host

We have investigated the finite temperature dynamics of the singlet to doublet continuous quantum phase transition in the gapped Anderson impurity model using hybridization expansion continuous time quantum Monte-Carlo. Using the self-energy and the longitudinal static susceptibility, we obtain a phase diagram in the temperature-gap plane. The separatrix between the low temperature local moment phase and the high temperature generalized Fermi liquid phase of this phase diagram is shown to be the lower bound of the critical scaling region of the zero gap quantum critical point of interacting type. We have computed the nuclear magnetic spin-lattice relaxation rate, the Knight shift and the Korringa ratio, which show strong deviations for any non-zero gap from the corresponding quantities in the gapless Kondo screened impurity case.

cond-mat.str-el↗

arXiv2015

Study of multiband disordered systems using the typical medium dynamical cluster approximation

We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include inter-band and intra-band hopping and an intra-band disorder potential. Our results are consistent with the ones obtained by the transfer matrix and the kernel polynomial methods. We apply the method to K$_x$Fe$_{2-y}$Se$_2$ with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator. Our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.

cond-mat.dis-nn↗

arXiv2015

Cooling Atomic Gases With Disorder

Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a non-disordered state which exhibits these incompletely understood phases. We show, using quantum Monte Carlo simulations, that we can approach the Ne\'el temperature of the three-dimensional Hubbard model for experimentally achievable parameters. Recent experimental estimates suggest the randomness required lies in a regime where atom transport and equilibration are still robust.

cond-mat.quant-gas↗

arXiv2015

A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

Perturbative schemes utilizing a spectral moment expansion are well known and extensively used for investigating the physics of model Hamiltonians and real material systems. The advantages they offer, in terms of being computationally inexpensive, with real frequency output at zero and finite temperatures, compensate for their deficiencies and offer a quick, qualitative analysis of the system behavior. In this work, we have developed a method, that can be classified as a multi-orbital iterative perturbation theory (MO-IPT) to study N-fold degenerate and non degenerate Anderson impurity models. As applications of the solver, we have combined the method with dynamical mean field theory to explore lattice models like the single orbital Hubbard model, covalent band insulator and the multi-orbital Hubbard model for density-density type interactions in different parameter regimes. The Hund's coupling effects in case of multiple orbitals is also studied. The limitations and quality of results are gauged through extensive comparison with data from the numerically exact continuous time quantum Monte Carlo method (hybridization expansion CTQMC). In general we observe that the agreement with CTQMC results gets better as we move away from particle-hole symmetry. We have integrated MO-IPT with density functional theory based electronic structure methods to study real material systems. As a test case, we have studied the classic, strongly correlated electronic material, SrVO$_3$. A comparison of density of states and photo emission spectrum (PES) with results obtained from different impurity solvers and experiments yields good agreement.

cond-mat.str-el↗

arXiv2014

What is the valence of Mn in Ga$_{1-x}$Mn$_x$N?

We investigate the current debate on the Mn valence in Ga$_{1-x}$Mn$_x$N, a diluted magnetic semiconductor (DMSs) with a potentially high Curie temperature. From a first-principles Wannier-function analysis, we unambiguously find the Mn valence to be close to $2+$ ($d^5$), but in a mixed spin configuration with average magnetic moments of 4$\mu_B$. By integrating out high-energy degrees of freedom differently, we further derive for the first time from first-principles two low-energy pictures that reflect the intrinsic dual nature of the doped holes in the DMS: 1) an effective $d^4$ picture ideal for local physics, and 2) an effective $d^5$ picture suitable for extended properties. In the latter, our results further reveal a few novel physical effects, and pave the way for future realistic studies of magnetism. Our study not only resolves one of the outstanding key controversies of the field, but also exemplifies the general need for multiple effective descriptions to account for the rich low-energy physics in many-body systems in general.

cond-mat.mtrl-sci↗

arXiv2014

Ferromagnetic phase in the polarized two-species bosonic Hubbard Model

We recently studied a doped two-dimensional bosonic Hubbard model with two hard-core species, with different masses, using quantum Monte Carlo simulations [Phys. Rev. B 88, 161101(R) (2013)]. Upon doping away from half-filling, we find several distinct phases, including a phase-separated ferromagnet with Mott behavior for the heavy species and both Mott insulating and superfluid behaviors for the light species. Introducing polarization, an imbalance in the population between species, we find a fully phase-separated ferromagnet. This phase exists for a broad range of temperatures and polarizations. By using finite size scaling of the susceptibility, we find a critical exponent which is consistent with the two-dimensional Ising universality class. Significantly, since the global entropy of this phase is higher than that of the ferromagnetic phase with single species, its experimental observation in cold atoms may be feasible.

cond-mat.quant-gas↗

arXiv2014

Three Dimensional Edwards-Anderson Spin Glass Model in an External Field

We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field. We employ an indicator composed of a ratio of susceptibilities at finite wavenumbers, which was recently proposed to avoid the difficulties of a zero momentum quantity, for capturing the spin glass phase transition. Unfortunately, this new indicator is fairly noisy, so a large pool of samples at low temperature and small external field are needed to generate results with sufficiently small statistical error for analysis. We thus implement the Monte Carlo method using graphics processing units to drastically speedup the simulation. We confirm previous findings that conventional indicators for the spin glass transition, including the Binder ratio and the correlation length do not show any indication of a transition for rather low temperatures. However, the ratio of spin glass susceptibilities do show crossing behavior, albeit a systematic analysis is beyond the reach of the present data. This calls for a more thorough study of the three-dimension Edwards-Anderson model in an external field.

cond-mat.stat-mech↗