Engineering topics

Sondhi, S L

Publications and source records attributed to Sondhi, S L.

3 records

DOE OSTI2011

Debye-Hueckel theory for spin ice at low temperature

At low temperatures, spin ice is populated by a finite density of magnetic monopoles--pointlike topological defects with a mutual magnetic Coulomb interaction. We discuss the properties of the resulting magnetic Coulomb liquid in the framework of Debye-Hueckel theory, for which we provide a detailed context-specific account. We discuss both thermodynamical and dynamical signatures and compare Debye-Hueckel theory to experiment as well as numerics, including data for specific heat and AC susceptibility. We also evaluate the entropic Coulomb interaction that is present in addition to the magnetic one and show that it is quantitatively unimportant in the current compounds. Finally, we address the role of bound monopole anti-monopole pairs and derive an expression for the monopole mobility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Renormalization group and the superconducting susceptibility of a Fermi liquid

A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2010

Product, generic, and random generic quantum satisfiability

We report a cluster of results on k-QSAT, the problem of quantum satisfiability for k-qubit projectors which generalizes classical satisfiability with k-bit clauses to the quantum setting. First we define the NP-complete problem of product satisfiability and give a geometrical criterion for deciding when a QSAT interaction graph is product satisfiable with positive probability. We show that the same criterion suffices to establish quantum satisfiability for all projectors. Second, we apply these results to the random graph ensemble with generic projectors and obtain improved lower bounds on the location of the SAT-unSAT transition. Third, we present numerical results on random, generic satisfiability which provide estimates for the location of the transition for k=3 and k=4 and mild evidence for the existence of a phase which is satisfiable by entangled states alone.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗