1,462 research outputs found
Supersymmetry and the Hartmann Potential of Theoretical Chemistry
The ring-shaped Hartmann potential was
introduced in quantum chemistry to describe ring-shaped molecules like benzene.
In this article, the supersymmetric features of the Hartmann potential are
discussed. We first review the results of a previous paper in which we
rederived the eigenvalues and radial eigenfunctions of the Hartmann potential
using a formulation of one-dimensional supersymmetric quantum mechanics
(SUSYQM) on the half-line . A reformulation of SUSYQM
in the full line is subsequently developed. It
is found that the second formulation makes a connection between states having
the same quantum number but different values of and
quantum number . This is in contrast to the first formulation, which relates
states with identical values of the quantum number and
but different values of the quantum number .Comment: 24 pages; uses LaTex; to be published at the Theoretica Chimica Acta;
hard copy available from the author upon request (use address:
[email protected]
The degree of commutativity and lamplighter groups
The degree of commutativity of a group measures the probability of
choosing two elements in which commute. There are many results studying
this for finite groups. In [AMV17], this was generalised to infinite groups. In
this note, we compute the degree of commutativity for wreath products of the
form and where is any finite
group.Comment: 9 pages, accepted, International Journal of Algebra and Computation
(IJAC
Density Matrix Renormalization Group Lagrangians
We introduce a Lagrangian formulation of the Density Matrix Renormalization
Group (DMRG). We present Lagrangians which when minimised yield the optimal
DMRG wavefunction in a variational sense, both within the general matrix
product ansatz, as well as within the canonical form of the matrix product that
is constructed within the DMRG sweep algorithm. Some of the results obtained
are similar to elementary expressions in Hartree-Fock theory, and we draw
attention to such analogies. The Lagrangians introduced here will be useful in
developing theories of analytic response and derivatives in the DMRG.Comment: 6 page
Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
We investigate tree tensor network states for quantum chemistry. Tree tensor
network states represent one of the simplest generalizations of matrix product
states and the density matrix renormalization group. While matrix product
states encode a one-dimensional entanglement structure, tree tensor network
states encode a tree entanglement structure, allowing for a more flexible
description of general molecules. We describe an optimal tree tensor network
state algorithm for quantum chemistry. We introduce the concept of
half-renormalization which greatly improves the efficiency of the calculations.
Using our efficient formulation we demonstrate the strengths and weaknesses of
tree tensor network states versus matrix product states. We carry out benchmark
calculations both on tree systems (hydrogen trees and \pi-conjugated
dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and
chromium dimer). In general, tree tensor network states require much fewer
renormalized states to achieve the same accuracy as matrix product states. In
non-tree molecules, whether this translates into a computational savings is
system dependent, due to the higher prefactor and computational scaling
associated with tree algorithms. In tree like molecules, tree network states
are easily superior to matrix product states. As an ilustration, our largest
dendrimer calculation with tree tensor network states correlates 110 electrons
in 110 active orbitals.Comment: 15 pages, 19 figure
First principles coupled cluster theory of the electronic spectrum of the transition metal dichalcogenides
The electronic properties of two-dimensional transition metal dichalcogenides (2D TMDs) have attracted much attention during the last decade. We show how a diagrammatic ab initio coupled cluster singles and doubles (CCSD) treatment paired with a careful thermodynamic limit extrapolation in two dimensions can be used to obtain converged band gaps for monolayer materials in the MoSâ‚‚ family. We find CCSD gaps to lie in the upper range of the spread of GW approximation based on density functional theory (DFT) simulations, and also find slightly higher effective hole masses compared to previous reports. We also investigate the ability of CCSD to describe trion states, finding a reasonable qualitative structure, but poor excitation energies due to the lack of screening of three-particle excitations in the effective Hamiltonian. Our study provides an independent high-level benchmark of the role of many-body effects in 2D TMDs and showcases the potential strengths and weaknesses of diagrammatic coupled cluster approaches for realistic materials
Excited state geometry optimization with the density matrix renormalization group as applied to polyenes
We describe and extend the formalism of state-specific analytic density
matrix renormalization group (DMRG) energy gradients, first used by Liu et al
(J. Chem. Theor.Comput. 9, 4462 (2013)). We introduce a DMRG wavefunction
maximum overlap following technique to facilitate state-specific DMRG excited
state optimization. Using DMRG configuration interaction (DMRG-CI) gradients we
relax the low-lying singlet states of a series of trans-polyenes up to C20H22.
Using the relaxed excited state geometries as well as correlation functions, we
elucidate the exciton, soliton, and bimagnon ("single-fission") character of
the excited states, and find evidence for a planar conical intersection
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
Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization
We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study the interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D weakly asymmetric simple exclusion process. We show that with modest resources, we can capture the features of the susceptibility in large systems that mark the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems
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