Theoretical Physics – Quantum Condensed Matter. I am interested in systems of many quantum particles, where strong interactions lead to new states of matter. These new states can potentially be realized in experimental systems ranging from strongly correlated materials to dilute atomic gases confined to optical lattices.
Fractionalization: Conventional theories of electronic matter assume that the electron is a well defined excitation. However, materials like the high temperature cuprate superconductors, frustrated magnets and heavy fermion systems where interactions between electrons are particularly important, show many phenomena that are strikingly unconventional. This led to the radical proposal that the electron breaks apart, or fractionalizes, in such systems. This idea could potentially explain many of these anomalies, although unambiguous experimental evidence for this is still lacking. Fractionalization is found to go hand in hand with emergent gauge fields. One of the attractive features of deconfined states is that they can naturally lead to dimensional confinement – excitations can be confined to planes or chains of a three dimensional systems - which could explain phenomena seen in different materials
Unconventional Quantum Phase Transitions: Recently, it has become clear that quantum phase transitions can also exhibit fractionalization, although the phases on either side of the transition are perfectly conventional. Remarkably, this allows for a (generically) continuous transition between states of very different symmetry, e.g. a superfluid, and a crystal. Such transitions are forbidden according to Landau’s theory of classical phase transitions, and appear here due to the presence of quantum interference effects. I will be pursuing this exciting new development, which may be the key to understanding certain puzzling quantum phase transitions seen in heavy fermion systems.
Fluctuating Superconductivity: When superconductivity is destroyed by thermal or quantum fluctuations – its presence may still be felt in different ways, for example in anomalies in the electrical or thermal conduction properties of the system, or in more subtle signatures such as the Nernst effect. We have worked on establishing the universal signatures in thermal resistivity and thermopower, as well as current noise near quantum phase transitions out of a superconductor. Thermally fluctuating superconductors have also been studied, in particular a theory based on fluctuating vortex degrees of freedom is found to agree well with Nernst experiments on the cupartes.
Quantum Magnetism: Frustrated quantum magnets offer perhaps the simplest setting where novel many body effects could occur. We have worked on a number of problems in this area, from characterizing the different spin liquid states possible on frustrated lattices such as the triangular, Kagome and the newly discovered hyper-Kagome lattice, to studying models to explain experimental data in specific materials. Another interesting class of problems occurs in metallic helimagnets such as MnSi, where fluctuating magnetic spirals give rise to unusual metallic behavior that poses a major theoretical challenge.
Cold Atomic Gases: I am currently interested in spinor condensates: Bose-Einstein condensates of particles with spin. We have found novel magnetic phases, stabilized (paradoxically) by quantum or thermal fluctuations; and new kinds of phase transitions. An important set of issues here is how one may probe these exciting new systems – I have worked on noise measurements as a probe of Luttinger liquid physics in cold atom systems, and dynamics across the BCS-BEC crossover, to probe Cooper pair formation.
A. Turner, R. Barnett, E. Demler and Ashvin Vishwanath. “Nematic Order by Disorder in Spin-2 BECs”. Phys. Rev. Lett. 98, 190404 (2007).
B. Binz, A. Vishwanath, and V. Aji. “Theory of the helical spin crytal: a candidate for the partially ordered state of MnSi ” Phys. Rev. Lett. 96, 207202 (2006).
Fa Wang and A. Vishwanath “Spin Liquid States on the Triangular and Kagome Lattices: A PSG Analysis of Schwinger Boson States” Phys Rev. B. 74, 174423 (2006)
Daniel Podolsky, Srinivas Raghu, Ashvin Vishwanath. “Nernst effect and diamagnetism in phase fluctuating superconductors” cond-mat/0612096. Submitted to Phys. Rev. Lett.
T. Senthil, Ashvin Vishwanath, Leon Balents, Subir Sachdev, M. P. A. Fisher “Deconfined Quantum Critical Points” Science 303, 1490 (2004).
O. I. Motrunich and Ashvin Vishwanath, “Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression” Phys. Rev. B 70, 075104 (2004).
Ashvin Vishwanath, “Quantized Thermal Hall Effect in the Mixed State of d-Wave Superconductors”. Phys. Rev. Lett. 87, 217004 (2001).