Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration

We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type $\operatorname{SL}_n$ and $\operatorname{PGL}_n$. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore we prove for $d$ coprime to $n$, that the number of rank $n$ Higgs bundles of degree $d$ over a fixed curve defined over a finite field, is independent of $d$. This proves a conjecture by Mozgovoy--Schiffman in the coprime case.Comment: Various part of the article have been revise

A new variational, information theory based atoms in molecules method

A new iterative Hirshfeld type AIM method, called Hirshfeld-I-Lambda, is presented. The weight function that defines the AIM is constructed by minimizing the information loss on formation of the molecule, with explicitly requiring that the promolecular densities integrate to the same number of electrons as the AIM densities constructed. The atoms defined by this AIM method are the ones that minimize the information lost upon formation of the molecule out of its isolated atoms. The resulting Hirshfeld-I-Lambda AIM scheme is examined and discussed

CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry

The density matrix renormalization group (DMRG) has become an indispensable numerical tool to find exact eigenstates of finite-size quantum systems with strong correlation. In the fields of condensed matter, nuclear structure and molecular electronic structure, it has significantly extended the system sizes that can be handled compared to full configuration interaction, without losing numerical accuracy. For quantum chemistry (QC), the most efficient implementations of DMRG require the incorporation of particle number, spin and point group symmetries in the underlying matrix product state (MPS) ansatz, as well as the use of so-called complementary operators. The symmetries introduce a sparse block structure in the MPS ansatz and in the intermediary contracted tensors. If a symmetry is non-abelian, the Wigner-Eckart theorem allows to factorize a tensor into a Clebsch-Gordan coefficient and a reduced tensor. In addition, the fermion signs have to be carefully tracked. Because of these challenges, implementing DMRG efficiently for QC is not straightforward. Efficient and freely available implementations are therefore highly desired. In this work we present CheMPS2, our free open-source spin-adapted implementation of DMRG for ab initio QC. Around CheMPS2, we have implemented the augmented Hessian Newton-Raphson complete active space self-consistent field method, with exact Hessian. The bond dissociation curves of the 12 lowest states of the carbon dimer were obtained at the DMRG(28 orbitals, 12 electrons, D$_{\mathsf{SU(2)}}$=2500)/cc-pVDZ level of theory. The contribution of $1s$ core correlation to the $X^1\Sigma_g^+$ bond dissociation curve of the carbon dimer was estimated by comparing energies at the DMRG(36o, 12e, D$_{\mathsf{SU(2)}}$=2500)/cc-pCVDZ and DMRG-SCF(34o, 8e, D$_{\mathsf{SU(2)}}$=2500)/cc-pCVDZ levels of theory.Comment: 16 pages, 13 figure

Asset management as creator of market inefficiency

In this paper, we describe how agency frictions in asset management can generate prime violations of the Efficient Markets Hypothesis, such as momentum, value and an inverted risk-return relationship. Momentum in our theory is associated with procyclical fund flows and price over-reaction, and is more pronounced for overvalued assets. The investors who generate the momentum and who are losing from it are those requiring their asset managers to keep their portfolios close to benchmark indices. Our theory suggests a rethinking of asset management contracts. Contracts should employ measures of long-run risk and return, and benchmark indices that emphasize asset fundamentals. There should also be greater transparency on managers’ choice of strategies

Matrix product states and their uses in quantum chemistry

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Curse of the benchmarks

Obsession with short-term performance against market cap benchmarks preordains the dysfunctionality of asset markets. The problems start when trustees hire fund managers to outperform benchmark indexes subject to limits on annual divergence. For multi-asset portfolios the benchmark is generally the performance of peer group funds, also based on market cap. In the absence of formal instructions, asset managers, as well as off-the-peg mutual funds, are still keen to demonstrate their ability against the competition in the short run. If securities markets were efficiently priced in the sense of reflecting best estimates of fundamental value, there would be no problem in using market cap benchmarks. But the terms under which most professional investment is handled ensure that markets are not efficient. Benchmarking causes, first, the inversion of the relationship between risk and return so that high volatile securities and asset classes offer lower returns than low volatile ones. Second, it fosters the pursuit of momentum strategies which then earn profits at the expense of benchmarked funds. The paper explains how these problems arise using rational models of asset mispricing and proposes an incentive-based solution