We present a comprehensive analysis of the two-dimensional uniform electron gas (2D-UEG, or more commonly 2DEG) at finite temperature, spanning a broad range of densities/coupling strengths ( 0.01 ≤ r s ≤ 20 ) and temperatures/degeneracy parameters ( 0.01 ≤ Θ = k B T / E F ≤ 10 ) . Within the self-consistent dielectric formalism, we construct 2D versions of the Singwi-Tosi-Land-Sjölander (STLS) and hypernetted-chain (HNC) approximation–based schemes. We benchmark the accuracy of the STLS and the HNC schemes against new state-of-the-art path-integral Monte Carlo data. We also report structural and thermodynamic properties across the full ( r s , Θ ) phase diagram domain studied, identify regimes in which these schemes remain quantitatively reliable, and provide an accurate parametrization of the exchange-correlation free energy of the finite-temperature 2DEG.
In Damerow and Kehrein [] proposed the conjecture that, for quantum quenches within the same phase, the overlap between the initial ground state and postquench eigenstates is maximal for the postquench ground state. We show that this statement is not valid in general. An explicit local, translationally invariant, gapped free-fermion counterexample exists even though the pre- and postquench Hamiltonians are connected by a symmetry-preserving gapped path and the thermodynamic-limit spectrum is continuous. The example therefore indicates that phase equivalence must be supplemented by an additional dynamical or geometric condition, beyond the absence of an equilibrium phase boundary.
We derive the first-principles Ehrenfest molecular dynamics describing nonadiabatic processes with the inclusion of the nuclear-velocity-dependent phases (also known as electron-translation factors) on the atomic orbital basis. These phases, appearing when nuclei are treated dynamically, affect effective Hamiltonians constructed from localized orbitals. In this work, we focus on the effects on the first-principles pseudopotential Hamiltonian for both the norm-conserving and ultrasoft cases, derived within the projector augmented wave method framework. Peierls-like phases depending on the nuclear velocities appear in the nonlocal part of the potential, while additional nuclear velocity and acceleration-dependent corrections appear in the ultrasoft pseudopotential case. The use of the velocity-including atomic orbital basis enables a Galilean-invariant description of the nonadiabatic Ehrenfest molecular dynamics, removing spurious nonadiabatic couplings that arise from neglecting the nuclear velocity phases in the atomic orbitals.
