Energy as an entanglement witness for quantum many-body systems

We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

Mechanistic aspects of proton chain transfer: A computational study for the green fluorescent protein chromophore

We explore several models for the ground-state proton chain transfer pathway between the green fluorescent protein chromophore and its surrounding protein matrix, with a view to elucidating mechanistic aspects of this process. We have computed quantum chemically the minimum energy pathways (MEPs) in the ground electronic state for one-, two-, and three-proton models of the chain transfer. There are no stable intermediates for our models, indicating that the proton chain transfer is likely to be a single, concerted kinetic step. However, despite the concerted nature of the overall energy profile, a more detailed analysis of the MEPs reveals clear evidence of sequential movement of protons in the chain. The ground-state proton chain transfer does not appear to be driven by the movement of the phenolic proton off the chromophore onto the neutral water bridge. Rather, this proton is the last of the three protons in the chain to move. We find that the first proton movement is from the bridging Ser205 moiety to the accepting Glu222 group. This is followed by the second proton moving from the bridging water to the Ser205for our model this is where the barrier occurs. The phenolic proton on the chromophore is hence the last in the chain to move, transferring to a bridging “water” that already has substantial negative charge.