Hilbert space renormalization for the many-electron problem

Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the 'physical indices' or the coupling rules in the HS-MPS. Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to a family of size-extensive wave function ansaetze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.Comment: 23 pages, 14 figures, The following article has been submitted to The Journal of Chemical Physic

Incubators vs Zombies: Fault-Tolerant, Short, Thin and Lanky Spanners for Doubling Metrics

Recently Elkin and Solomon gave a construction of spanners for doubling metrics that has constant maximum degree, hop-diameter O(log n) and lightness O(log n) (i.e., weight O(log n)w(MST). This resolves a long standing conjecture proposed by Arya et al. in a seminal STOC 1995 paper. However, Elkin and Solomon's spanner construction is extremely complicated; we offer a simple alternative construction that is very intuitive and is based on the standard technique of net tree with cross edges. Indeed, our approach can be readily applied to our previous construction of k-fault tolerant spanners (ICALP 2012) to achieve k-fault tolerance, maximum degree O(k^2), hop-diameter O(log n) and lightness O(k^3 log n)

Optical gain of interdiffused InGaAs-As and AlGaAs-GaAs quantum wells

We have analyzed theoretically the effects of interdiffusion on the gain, differential gain, linewidth enhancement factor, and the injection current density of In0.2Ga0.8As-GaAs and Al0.3Ga0.7As-GaAs quantum-well (QW) lasers. We have calculated the electron and hole subband structures including the effects of valence band mixing and strains. The optical gain is then calculated using the density matrix approach. Our results show that the gain spectrum can be blue-shifted without an enormous increase in the injected current density. Imposing an upper limit (416 A·cm-2) on the injection current density for a typical laser structure, we find that the InGaAs-GaAs and AlGaAs-GaAs QW lasers can be blue-shifted by 24 and 54 mn, respectively. Our theoretical results compare well with the tuning ranges of 53 and 66 meV found for AlGaAs-GaAs QWs in some experiments. This indicates that the interdiffusion technique is useful for the tuning of laser operation wavelength for multiwavelength applications.published_or_final_versio

Electro-absorption and refraction at 1.5 μm in InGaAs/AlGaAssuperlattice growth on GaAs substrate

High indium concentration In0.65Ga0.35As/Al 0.33Ga0.67As superlattices on GaAs substrates are useful for modulators and optical communication applications. This is due to the lowest loss 1.55 μm optimum wavelength for operation of fiber optic systems. The optical parameters such as absorption coefficient and change in refractive index with applied electric field are investigated.published_or_final_versio

Modeling of optical gain properties of multiple cations InGaAs-InAlAs quantum-well intermixing

Multiple cations intermixing in an In0.53Ga0.47 As-In0.52Al0.48As quantum-well (QW) structure with 60-Å well width is being studied based on the expanded form of Fick's second law. Interdiffusion of the indium sublattice can result in a maximum compressive strain of 0.64% when annealing time reaches 3 h at 812°C. For a small interdiffusion, i.e., 1-1.5 h, the subband separation between the lowest heavy and light hole states is at its greatest. This has a major contribution to the modified band structure and averaged density of states which can result in an enhanced optical gain up to 40%. This initial stage of intermixing provides the best lasing performance. For large interdiffusion, i.e., up to 6 h, a large blue shift of the peak gain from 0.842 eV (λ=1.47 μm) to 1.016 eV (λ=1.22 μm) is obtained, thus giving a high tunability of the lasing wavelength.published_or_final_versio