arXiv subjects

Chenggang Zhou

Publications and source records attributed to Chenggang Zhou.

15 recordsLinked to original sources

arXiv2011

Electronic stress tensor analysis of hydrogenated palladium clusters

We study the chemical bonds of small palladium clusters Pd_n (n=2-9) saturated by hydrogen atoms using electronic stress tensor. Our calculation includes bond orders which are recently proposed based on the stress tensor. It is shown that our bond orders can classify the different types of chemical bonds in those clusters. In particular, we discuss Pd-H bonds associated with the H atoms with high coordination numbers and the difference of H-H bonds in the different Pd clusters from viewpoint of the electronic stress tensor. The notion of "pseudo-spindle structure" is proposed as the region between two atoms where the largest eigenvalue of the electronic stress tensor is negative and corresponding eigenvectors forming a pattern which connects them.

physics.chem-ph↗

arXiv2008

Optimal Modification Factor and Convergence of the Wang-Landau Algorithm

We propose a strategy to achieve the fastest convergence in the Wang-Landau algorithm with varying modification factors. With this strategy, the convergence of a simulation is at least as good as the conventional Monte Carlo algorithm, i.e. the statistical error vanishes as $1/\sqrt{t}$, where $t$ is a normalized time of the simulation. However, we also prove that the error cannot vanish faster than $1/t$. Our findings are consistent with the $1/t$ Wang-Landau algorithm discovered recently, and we argue that one needs external information in the simulation to beat the conventional Monte Carlo algorithm.

cond-mat.stat-mech↗

arXiv2007

Spectral weight transfer in a disorder-broadened Landau level

In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/ϕ_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $ϕ_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the top and bottom of the broadened LL, while states in the center of the LL (the critical region) remain delocalized. This well-known phenomenology is sufficient to explain most aspects of the Integer Quantum Hall Effect (IQHE) [1]. One unnoticed issue is where the new states appear as the magnetic field is increased. Here we demonstrate that they appear predominantly inside the critical region. This leads to a certain ``spectral ordering'' of the localized states that explains the stripes observed in measurements of the local inverse compressibility [2-3], of two-terminal conductance [4], and of Hall and longitudinal resistances [5] without invoking interactions as done in previous work [6-8].

cond-mat.dis-nn↗

arXiv2007

Monte Carlo simulations of ${\rm Rb_2MnF_4}$, a classical Heisenberg antiferromagnet in two-dimensions with dipolar interaction

We study the phase diagram of a quasi-two dimensional magnetic system ${\rm Rb_2MnF_4}$ with Monte Carlo simulations of a classical Heisenberg spin Hamiltonian which includes the dipolar interactions between ${\rm Mn}^{2+}$ spins. Our simulations reveal an Ising-like antiferromagnetic phase at low magnetic fields and an XY phase at high magnetic fields. The boundary between Ising and XY phases is analyzed with a recently proposed finite size scaling technique and found to be consistent with a bicritical point at T=0. We discuss the computational techniques used to handle the weak dipolar interaction and the difference between our phase diagram and the experimental results.

cond-mat.stat-mech↗

arXiv2006

Hidden zero-temperature bicritical point in the two-dimensional anisotropic Heisenberg model: Monte Carlo simulations and proper finite-size scaling

By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in $2+ε$ dimensions. We found that the long length scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $σ$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at T=0, therefore the uncertainty in the phase diagram of this model is removed.

cond-mat.stat-mech↗

arXiv2005

Monte Carlo simulations of ${\rm Ni Fe_2O_4}$ Nanoparticles

We use Monte Carlo simulations to study ${\rm Ni Fe_2O_4}$ nanoparticles. Finite size and surface effects differentiate them from their bulk counterparts. A continuous version of the Wang-Landau algorithm is used to calculate the joint density of states $g(M_z, E)$ efficiently. From $g(M_z, E)$, we obtain the Bragg-Williams free energy of the particle, and other physical quantities. The hysteresis is observed when the nanoparticles have both surface disorder and surface anisotropy. We found that the finite coercivity is the result of interplay between surface disorder and surface anisotropy. If the surface disorder is absent or the surface anisotropy is relatively weak, the nanoparticles often exhibit superparamagnetism.

cond-mat.stat-mech↗

arXiv2005

Wang-Landau algorithm for continuous models and joint density of states

We present modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states $g(M,E)$ of ferromagnet Heisenberg models. The joint density of states contains more information than the density of states of a single variable--energy, but is also much more time-consuming to calculate. We discuss the strategies to perform this calculation efficiently for models with several thousand degrees of freedom, much larger than other continuous models studied previously with the Wang-Landau algorithm.

cond-mat.stat-mech↗

arXiv2005

Understanding and Improving the Wang-Landau Algorithm

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a stage of initial accumulation, and the statistical error is found to scale as $\sqrt{\ln f}$ with the modification factor $f$. This has implications for strategies for obtaining fast convergence.

cond-mat.stat-mech↗

arXiv2005

Correlated mesoscopic fluctuations in integer quantum Hall transitions

We investigate the origin of the resistance fluctuations of mesoscopic samples, near transitions between Quantum Hall plateaus. These fluctuations have been recently observed experimentally by E. Peled et al. [Phys. Rev. Lett. 90, 246802 (2003); ibid 90, 236802 (2003); Phys. Rev. B 69, R241305 (2004)]. We perform realistic first-principles simulations using a six-terminal geometry and sample sizes similar to those of real devices, to model the actual experiment. We present the theory and implementation of these simulations, which are based on the linear response theory for non-interacting electrons. The Hall and longitudinal resistances extracted from the Landauer formula exhibit all the observed experimental features. We give a unified explanation for the three regimes with distinct types of fluctuations observed experimentally, based on a simple generalization of the Landauer-Buttiker model. The transport is shown to be determined by the interplay between tunneling and chiral currents. We identify the central part of the transition, at intermediate filling factors, as the critical region where the localization length is larger than the sample size.

cond-mat.mes-hall↗

arXiv2004

The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation; the results are exact for non-interacting electrons. Our method fully accounts for the effects of the disorder and the periodic modulation, irrespective of their relative strength, as long as Landau level mixing is negligible. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder. This appears to be the relevant regime to understand recent experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multi-channel scattering problems.

cond-mat.mes-hall↗

arXiv2004

Effects of large disorder on the Hofstadter butterfly

Motivated by the recent experiments on periodically modulated, two dimensional electron systems placed in large transversal magnetic fields, we investigate the interplay between the effects of disorder and periodic potentials in the integer quantum Hall regime. In particular, we study the case where disorder is larger than the periodic modulation, but both are small enough that Landau level mixing is negligible. In this limit, the self-consistent Born approximation is inadequate. We carry extensive numerical calculations to understand the relevant physics in the lowest Landau level, such as the spectrum and nature (localized or extended) of the wave functions. Based on our results, we propose a qualitative explanation of the new features uncovered recently in transport measurements.

cond-mat.mes-hall↗

arXiv2003

First-Principles Study of Integer Quantum Hall Transitions in Mesoscopic Samples

We perform first principles numerical simulations to investigate resistance fluctuations in mesoscopic samples, near the transition between consecutive Quantum Hall plateaus. We use six-terminal geometry and sample sizes similar to those of real devices. The Hall and longitudinal resistances extracted from the generalized Landauer formula reproduce all the experimental features uncovered recently. We then use a simple generalization of the Landauer-Büttiker model, based on the interplay between tunneling and chiral currents -- the co-existing mechanisms for transport -- to explain the three distinct types of fluctuations observed, and identify the central region as the critical region.

cond-mat.mes-hall↗

arXiv2003

Exchange anisotropy, disorder and frustration in diluted, predominantly ferromagnetic, Heisenberg spin systems

Motivated by the recent suggestion of anisotropic effective exchange interactions between Mn spins in Ga$_{1-x}$Mn$_x$As (arising as a result of spin-orbit coupling), we study their effects in diluted Heisenberg spin systems. We perform Monte Carlo simulations on several phenomenological model spin Hamiltonians, and investigate the extent to which frustration induced by anisotropic exchanges can reduce the low temperature magnetization in these models and the interplay of this effect with disorder in the exchange. In a model with low coordination number and purely ferromagnetic (FM) exchanges, we find that the low temperature magnetization is gradually reduced as exchange anisotropy is turned on. However, as the connectivity of the model is increased, the effect of small-to-moderate anisotropy is suppressed, and the magnetization regains its maximum saturation value at low temperatures unless the distribution of exchanges is very wide. To obtain significant suppression of the low temperature magnetization in a model with high connectivity, as is found for long-range interactions, we find it necessary to have both ferromagnetic and antiferromagnetic (AFM) exchanges (e.g. as in the RKKY interaction). This implies that disorder in the sign of the exchange interaction is much more effective in suppressing magnetization at low temperatures than exchange anisotropy.

cond-mat.dis-nn↗

arXiv2002

Spin Waves in Random Spin Chains

We study quantum spin-1/2 Heisenberg ferromagnetic chains with dilute, random antiferromagnetic impurity bonds with modified spin-wave theory. By describing thermal excitations in the language of spin waves, we successfully observe a low-temperature Curie susceptibility due to formation of large spin clusters first predicted by the real-space renormalization-group approach, as well as a crossover to a pure ferromagnetic spin chain behavior at intermediate and high temperatures. We compare our results of the modified spin-wave theory to quantum Monte Carlo simulations.

cond-mat.dis-nn↗

arXiv2001

One Dimensional Chain with Long Range Hopping

The one-dimensional (1D) tight binding model with random nearest neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effects of random long range (power-law) hopping with an ensemble averaged magnitude $\expectation{|t_{ij}|} \propto |i-j|^{-σ}$ in the 1D chain, while maintaining the particle-hole symmetry present in the nearest neighbor model. We find, in agreement with results of position space renormalization group techniques applied to the random XY spin chain with power-law interactions, that there is a change of behavior when the power-law exponent $σ$ becomes smaller than 2.

cond-mat.dis-nn↗