Ground-state Energy Distribution Research Articles

Ground-state energy distribution of disordered many-body quantum systems.

Extreme-value distributions are studied in the context of a broad range of problems, from the equilibrium properties of low-temperature disordered systems to the occurrence of natural disasters. Our focus here is on the ground-state energy distribution of disordered many-body quantum systems. We derive an analytical expression that, upon tuning a parameter, reproduces with high accuracy the ground-state energy distribution of the systems that we consider. For some models, it agrees with the Tracy-Widom distribution obtained from Gaussian random matrices. They include transverse Ising models, the Sachdev-Ye model, and a randomized version of the PXP model. For other systems, such as Bose-Hubbard models with random couplings and the disordered spin-1/2 Heisenberg chain used to investigate many-body localization, the shapes are at odds with the Tracy-Widom distribution. Our analytical expression captures all of these distributions, thus playing a role to the lowest energy level similar to that played by the Brody distribution to the bulk of the spectrum.

Extensive assessment of the charge-trapping kinetics in InGaAs MOS gate-stacks for the demonstration of improved BTI reliability

Gate-stack reliability has been a major roadblock in the realization of InGaAs-channel based logic technology. Excessive charge trapping in the gate-oxide causes time-dependent drift in transistor threshold voltage (Vth). The extent to which Vth drifts under certain stress conditions depends on (i) the defect ground-state energy distributions in the oxide bandgap, and (ii) the specific activation energy distributions for charge capture/emission process. In this work, semi-empirical modelling of ground-state defect energy distributions is revisited to determine the Total Operating Voltage Range of InGaAs-based MOSFETs for a DC-BTI lifetime of 10 years under DC operating conditions. Non-radiative Multiphonon (NMP) theory is subsequently used to describe the microscopic physics of charge (de-)trapping kinetics in terms of activation energy barriers for charge capture (EAc) and emission (EAe) into/from gate-stack defects. These activation energy barriers are visualized using Capture/Emission Time (CET) maps, which are efficient and powerful tools to predict the BTI degradation under different AC operating conditions as well. We demonstrate that the enhanced BTI reliability of a gate-stack with a novel ASM interfacial layer (ASM-IL), as compared to the bilayer gate-stack of Al2O3/HfO2, results from the favorable reconfiguration of the defect energy distribution in the oxide bandgap, as well as their activation energies for capture and emission process.

Atomistic analysis of the electronic structure of m‐plane InGaN/GaN quantum wells: Carrier localization effects in ground and excited states due to random alloy fluctuations

AbstractWe present a detailed atomistic analysis of the electronic properties of m‐plane InGaN/GaN quantum wells. The tight‐binding model used treats realistically sized systems atomistically and accounts for compositional and structural inhomogeneities. Local variation in strain and built‐in potential arising from random alloy fluctuations are explicitly included in the model. Many energy states of the supercells considered are calculated in order to determine the impact of the alloy fluctuations on the electronic structure of the system under investigation. We find that while the electrons are relatively insensitive to the local indium environment, the hole states are highly sensitive to it and are subject to very strong localization effects. These effects persist several states into the valence band. This strong localization of the hole states leads to a very broad distribution of ground state energies in different random configurations. Furthermore, we see that the localization leads to poor overlap between different hole states resulting in a reduced probability of transfer of carriers between different states. This feature should play an important role for transport properties in m‐plane InGaN/GaN QWs.

Typical and large-deviation properties of minimum-energy paths on disordered hierarchical lattices

We perform numerical simulations to study the optimal path problem on disordered hierarchical graphs with effective dimension d=2.32. Therein, edge energies are drawn from a disorder distribution that allows for positive and negative energies. This induces a behavior which is fundamentally different from the case where all energies are positive, only. Upon changing the subtleties of the distribution, the scaling of the minimum energy path length exhibits a transition from self-affine to self-similar. We analyze the precise scaling of the path length and the associated ground-state energy fluctuations in the vincinity of the disorder critical point, using a decimation procedure for huge graphs. Further, using an importance sampling procedure in the disorder we compute the negative-energy tails of the ground-state energy distribution up to 12 standard deviations away from its mean. We find that the asymptotic behavior of the negative-energy tail is in agreement with a Tracy-Widom distribution. Further, the characteristic scaling of the tail can be related to the ground-state energy flucutations, similar as for the directed polymer in a random medium.

Simulations of ground state fluctuations in mean-field Ising spin glasses

The scaling of fluctuations in the distribution of ground state energies or costs with the system sizeN for Ising spin glasses is considered using an extensive set of simulations with the extremaloptimization heuristic across a range of different models on sparse and dense graphs. Thesemodels exhibit very diverse behaviors, and an asymptotic extrapolation is oftencomplicated by higher-order corrections in size. The clearest picture, in fact, emerges fromthe study of graph bipartitioning, a combinatorial optimization problem closely related tospin glasses. Asides from two-spin interactions with discrete bonds, we also considerproblems with Gaussian bonds and three-spin interactions, which behave quite differently.

Probing the tails of the ground-state energy distribution for the directed polymer in a random medium of dimensiond=1,2,3via a Monte Carlo procedure in the disorder

In order to probe with high precision the tails of the ground-state energy distribution of disordered spin systems, Körner, Katzgraber, and Hartmann have recently proposed an importance-sampling Monte Carlo Markov chain in the disorder. In this paper, we combine their Monte Carlo procedure in the disorder with exact transfer matrix calculations in each sample to measure the negative tail of ground-state energy distribution Pd(E0) for the directed polymer in a random medium of dimension d=1,2,3. In d=1, we check the validity of the algorithm by a direct comparison with the exact result, namely, the Tracy-Widom distribution. In dimensions d=2 and d=3, we measure the negative tail up to ten standard deviations, which correspond to probabilities of order Pd(E0) approximately 10(-22). Our results are in agreement with Zhang's argument, stating that the negative tail exponent eta(d) of the asymptotic behavior lnPd(E0) approximately -|E0|eta(d) as E0-->-infinity is directly related to the fluctuation exponent theta(d) [which governs the fluctuations DeltaE0(L) approximately Ltheta(d) of the ground-state energy E0 for polymers of length L] via the simple formula eta(d)=1/[1-theta(d)]. Throughout the paper, we comment on the similarities and differences with spin glasses.

Numerical study of the directed polymer in a 1 + 3 dimensional random medium

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length $L$, the high temperature phase is characterized by a diffusive behavior for the end-point displacement $R^2 \sim L$ and by free-energy fluctuations of order $\Delta F(L) \sim O(1)$. The low-temperature phase is characterized by an anomalous wandering exponent $R^2/L \sim L^{\omega}$ and by free-energy fluctuations of order $\Delta F(L) \sim L^{\omega}$ where $\omega \sim 0.18$. In this paper, we first study the scaling behavior of various properties to localize the critical temperature $T_c$. Our results concerning $R^2/L$ and $\Delta F(L)$ point towards $0.76 < T_c \leq T_2=0.79$, so our conclusion is that $T_c$ is equal or very close to the upper bound $T_2$ derived by Derrida and coworkers ($T_2$ corresponds to the temperature above which the ratio $\bar{Z_L^2}/(\bar{Z_L})^2$ remains finite as $L \to \infty$). We then present histograms for the free-energy, energy and entropy over disorder samples. For $T \gg T_c$, the free-energy distribution is found to be Gaussian. For $T \ll T_c$, the free-energy distribution coincides with the ground state energy distribution, in agreement with the zero-temperature fixed point picture. Moreover the entropy fluctuations are of order $\Delta S \sim L^{1/2}$ and follow a Gaussian distribution, in agreement with the droplet predictions, where the free-energy term $\Delta F \sim L^{\omega}$ is a near cancellation of energy and entropy contributions of order $L^{1/2}$.

Probing tails of energy distributions using importance-sampling in the disorder with aguiding function

We propose a simple and general procedure based on a recently introduced approach thatuses an importance-sampling Monte Carlo algorithm in the disorder to probe to highprecision the tails of ground-state energy distributions of disordered systems. Our approachrequires an estimate of the ground-state energy distribution as a guiding function whichcan be obtained from simple-sampling simulations. In order to illustrate the algorithm, wecompute the ground-state energy distribution of the Sherrington–Kirkpatrickmean-field Ising spin glass to 18 orders of magnitude. We find that if the ground-stateenergy distribution in the thermodynamic limit is described by a modified Gumbeldistribution, as previously predicted, then the value of the slope parameterm is clearly largerthan 6 and ofthe order of 11.

Control of decoherence in the generation of photon pairs from atomic ensembles

We report an investigation to establish the physical mechanisms responsible for decoherence in the generation of photon pairs from atomic ensembles, via the protocol of Duan et al. for long-distance quantum communication [Nature (London) 414, 413 (2001)] and present the experimental techniques necessary to properly control the process. We develop a theory to model in detail the decoherence process in experiments with magneto-optical traps. The inhomogeneous broadening of the ground state by the trap magnetic field is identified as the principal mechanism for decoherence. The theory includes the Zeeman structure of the atomic hyperfine levels used in the experiment, and the polarization of both excitation fields and detected photons. In conjunction with our theoretical analysis, we report a series of measurements to characterize and control the coherence time in our experimental setup. We use copropagating stimulated Raman spectroscopy to access directly the ground-state energy distribution of the ensemble. These spectroscopic measurements allow us to switch off the trap magnetic field in a controlled way, optimizing the repetition rate for single-photon measurements. With the magnetic field off, we then measure nonclassical correlations for pairs of photons generated by the ensemble as a function of the storage time of the single collective atomic excitation. We report coherence times longer than $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, corresponding to an increase of two orders of magnitude compared to previous results in cold ensembles. The coherence time is now two orders of magnitude longer than the duration of the excitation pulses. The comparison between these experimental results and the theory shows good agreement. Finally, we employ our theory to devise ways to improve the experiment by optical pumping to specific initial states.

Universality-class dependence of energy distributions in spin glasses

We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price algorithms. By tuning the exponent of the power-law interactions we are able to scan several universality classes. Our results suggest that mean-field models have a non-Gaussian limiting distribution of the ground-state energies, whereas non-mean-field models have a Gaussian limiting distribution. We compare the results of the disordered one-dimensional Ising chain to results for a disordered two-leg ladder, for which large system sizes can be studied, and find a qualitative agreement between the disordered one-dimensional Ising chain in the short-range universality class and the disordered two-leg ladder. We show that the mean and the standard deviation of the ground-state energy distributions scale with a power of the system size. In the mean-field universality class the skewness does not follow a power-law behavior and converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick model seem to be acceptably well fitted by a modified Gumbel distribution. Finally, we discuss the distribution of the internal energy of the Sherrington-Kirkpatrick model at finite temperatures and show that it behaves similar to the ground-state energy of the system if the temperature is smaller than the critical temperature.

Overcoming System-Size Limitations in Spin Glasses

In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional Hamiltonians in that a large range of system sizes can be studied. In addition, the universality class of the model can be changed by tuning the power law exponent, thus allowing us to scan from the mean-field to long-range and short-range universality classes. We illustrate the advantages of this model by studying the nature of the spin glass state where our results hint towards a replica symmetry breaking scenario. We also compute ground-state energy distributions and show that mean-field and non-mean-field models are intrinsically different.

Two repulsive lines on disordered lattices

We investigate the ground-state properties of two lines with “on-site” repulsion on disordered Cayley tree and (Berker) hierarchical lattices, in connection with the question of multiple “pure states” for the corresponding one-line problem. Exact recursion relations for the distribution of ground-state energies and of the overlaps are derived. Based on a numerical study of the recursion relations, we establish that the total interaction energy on average is asymptotically proportional to the width δ of the ground-state energy fluctuation of a single line for both weak and strong (i.e., hard-core) repulsion. When the lengtht of the lines is finite, there is a finite probability of ordert −a for (nearly) degenerate, nonoverlapping one-line ground-state configurations, in which case the interaction energy vanishes. We show thata=ω (δ∼t ω) on hierarchical lattices. Monte Carlo transfer matrix calculation on a (1+1)-dimensional model yields the same scaling for the interaction energy but ana different from ω=1/3. Finitelength scalings of the distribution of the interaction energy and of the overlap are also discussed.

Laser and thermal bleaching of colour centres in sodium borate glasses

The maximum of the additional absorption band in γ- or UV-irradiated sodium borate glasses shifts to higher energy when the low-energy side of the band is bleached by a helium-neon laser, λ = 632.8 nm. Simultaneously the half-width of the additional absorption band decreases. This phenomenon is associated with the fact that because of structural disorder of glasses there is a distribution of ground-state energies of trapped electrons forming the light-sensitive absorption band. The distribution interval of the activation energy for trapped electrons is estimated using the decomposition of the initial thermal bleaching curves into components. For UV irradiated glasses it is approximately 0.24 eV, and for γ-irradiated glasses only 0.12 eV. These values correlate with the relative shift maximum of the absorption band at laser bleaching. [Russian Text Ignored]

Laser bleaching of trapped electron optical bands in γ-irradiated alkaline ice

The maximum of the optical absorption band of trapped electrons in glassy alkaline ice (10 mol/dm −3 NaOH) at 77 K shifts to higher energy when the low-energy side of the band is optically bleached. This suggests that there is a distribution of ground-state energies for the trapped electrons and, consequently, a distribution of vacancy sizes in which the electrons are trapped. The fine structure of the broad absorption band has been probed by comparing laser bleaching at 633 nm with broad-band monochromator bleaching at 633 nm. Although the laser linewidth is 750 times smaller than that of the monochromator light, the trapped-electron band shifts were equivalent, and it was not possible to bleach a narrow portion out of the broad band corresponding to a single narrow component or resolved single-energy trap depth. It appears that the width of the component optical band corresponding to a particular ground-state energy is broad rather than narrow. Laser bleaching in the low-energy tail of trapped electrons in KCl crystals caused uniform and symmetric bleaching consistent with a single trap depth.