Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems

We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions within the differential equation for the populations that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Here we show how care must be taken to ensure an accurate treatment of the equation of motion for the populations due to the fact that there are identities that require cancellations of terms that naively look like they contribute to the decay rates. In particular, the average time dependence of the Green's functions and self-energies plays a pivotal role in determining these decay rates.Comment: Submitted to Entrop

Field Tuning Beyond the Heat Death of a Charge-Density-Wave Chain

Time-dependent driving of quantum systems has emerged as a powerful tool to engineer exotic phases far from thermal equilibrium; when the drive is periodic this is called Floquet engineering. The presence of many-body interactions can lead to runaway heating, so that generic systems are believed to heat up until they reach a featureless infinite-temperature state. Finding mechanisms to slow down or even avoid this heat death is a major goal -- one such mechanism is to drive toward an even distribution of electrons in momentum space. Here we show how such a mechanism avoids the heat death for a charge-density-wave chain in a strong dc electric field; minibands with nontrivial distribution functions develop as the current is prematurely driven to zero. We also show how the field strength tunes between positive, negative, or close-to-infinite effective temperatures for each miniband. These results suggest that nontrivial metastable distribution functions should be realized in the prethermal regime of quantum systems coupled to slow bosonic modes.Comment: 5 pages, 4 figures (plus supplemental material: 8 pages, 7 figures

Sparse-Hamiltonian approach to the time evolution of molecules on quantum computers

Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the phase-estimation algorithm. In both cases, the complexity of the problem increases for basis sets where either the Hamiltonian is not sparse, or it is sparse, but many orbitals are required to accurately describe the molecule of interest. In this work, we explore the possibility of mapping the molecular problem onto a sparse Hubbard-like Hamiltonian, which allows a Green's-function-based approach to electronic structure via a hybrid quantum-classical algorithm. We illustrate the time-evolution aspect of this methodology with a simple four-site hydrogen ring

Lanczos-based Low-Rank Correction Method for Solving the Dyson Equation in Inhomogenous Dynamical Mean-Field Theory

Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each lattice site from the corresponding local self-energy. We present a new efficient algorithm, the Lanczos-based low-rank algorithm, for the calculation of the inverse of a large sparse matrix which yields this local (imaginary time) Green's function. The Lanczos-based low-rank algorithm is based on a domain decomposition viewpoint, but avoids explicit calculation of Schur complements and relies instead on low-rank matrix approximations derived from the Lanczos algorithm, for solving the Dyson equation. We report at least a 25-fold improvement of performance compared to explicit decomposition (such as sparse LU) of the matrix inverse. We also report that scaling relative to matrix sizes, of the low-rank correction method on the one hand and domain decomposition methods on the other, are comparable.Comment: 13 pages, 1 figure, 24th Annual CSP Workshop, University of Georgia, Athens, GA, submitted to Physics Procedia. New version has some of the References correcte

Employing an operator form of the Rodrigues formula to calculate wavefunctions without differential equations

The factorization method of Schrodinger shows us how to determine the energy eigenstates without needing to determine the wavefunctions in position or momentum space. A strategy to convert the energy eigenstates to wavefunctions is well known for the one-dimensional simple harmonic oscillator by employing the Rodrigues formula for the Hermite polynomials in position or momentum space. In this work, we illustrate how to generalize this approach in a representation-independent fashion to find the wavefunctions of other problems in quantum mechanics that can be solved by the factorization method. We examine three problems in detail: (i) the one-dimensional simple harmonic oscillator; (ii) the three-dimensional isotropic harmonic oscillator; and (iii) the three-dimensional Coulomb problem. This approach can be used in either undergraduate or graduate classes in quantum mechanics.Comment: (10 pages, 1 figure, plus supplemental material

Phase separation due to quantum mechanical correlations

Can phase separation be induced by strong electron correlations? We present a theorem that affirmatively answers this question in the Falicov-Kimball model away from half-filling, for any dimension. In the ground state the itinerant electrons are spatially separated from the classical particles.Comment: 4 pages, 1 figure. Note: text and figure unchanged, title was misspelle