The folding algorithmcite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the temporal entanglem
ent. We show that this temporal entanglement is, in many cases, equal to the spatial entanglement of a modified Hamiltonian. This inspires a modification to the folding algorithm, that we call the hybrid algorithm. We find that this leads to improved accuracy for the same numerical effort. We then use these algorithms to study relaxation in a transverse plus parallel field Ising model, finding persistent quasi-periodic oscillations for certain choices of initial conditions.
We study the problem of disorder-free metals near a continuous Ising nematic quantum critical point in $d=3+1$ dimensions. We begin with perturbation theory in the `Yukawa coupling between the electrons and undamped bosons (nematic order parameter fl
uctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the `marginal Fermi liquid phenomenologycite{Varma}. We discuss a large N theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.
A high level polarizable force field is used to study the temperature dependence of hydrophobic hydration of small-sized molecules from computer simulations. Molecular dynamics (MD) simulations of liquid water at various temperatures form the basis o
f free energy perturbation calculations that consider the onset and growth of a repulsive sphere. This repulsive sphere acts as a model construct for the hydrophobic species. In the present study, an extension is pursued for seven independent target temperatures, ranging from close to the freezing point almost up to the boiling point of liquid water under standard conditions. Care is taken to maintain proper physico-chemical model descriptions by cross-checking with experimental water densities at the selected target temperatures. The polarizable force field description of molecular water turns out to be suitable throughout the entire temperature domain considered. Derivatives of the computed free energies of hydrophobic hydration with respect to the temperature give access to the changes in entropy. In practice the entropy differential is determined from the negative of the slope of tangential lines formed at a certain target temperature in the free energy profile. The obtained changes in entropy are negative for small-sized cavities, and hence reconfirm the basic ideas of the Lum Chandler Weeks theory on hydrophobic hydration of small-sized solutes.
