Ganpathy Murthy

CP N-1 models at a lifshitz point

We consider CP{sup N-1} models in d+1 dimensions around Lifshitz fixed points with dynamical critical exponent z, in the large-N expansion. It is shown that these models are asymptotically free and dynamically generate a mass for the CP{sup N-1} fields for all d=z. We demonstrate that, for z=d=2, the initially nondynamical gauge field acquires kinetic terms in a way similar to usual CP{sup N-1} models in 1+1 dimensions. Lorentz invariance emerges generically in the low-energy electrodynamics, with a nontrivial dielectric constant given by the inverse mass gap and a magnetic permeability which has a logarithmic dependence on scale. At a special multicritical point, the low-energy electrodynamics also has z=2, and an essentially singular dependence of the effective action on B={epsilon}{sub ij}{partial_derivative}{sub i}A{sub j}.

Hamiltonian theory of the composite-fermion Wigner crystal

Experimental results indicating the existence of the high-magnetic-field Wigner crystal have been available for a number of years. While variational wave functions have demonstrated the instability of the Laughlin liquid to a Wigner crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum-Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the transport gaps of the Wigner crystal states. We find that the Wigner crystal states near

Composite fermion hofstadter problem: partially polarized density wave states in the nu = 2/5 fractional quantum hall effect

\ensuremath{\nu}=1/5

Coherence network in the quantum Hall bilayer.

are quantitatively well described as crystals of composite fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.

Critical behavior in graphene with Coulomb interactions.

It is well known that the nu = 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with a charge/spin density wave order for composite fermions is proposed to exist at intermediate values of the Zeeman coupling for nu = 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R. Shankar and the author is used to demonstrate the stability of this state to single-particle excitations and to compute gaps. A very recent experiment shows direct evidence for this state.

Interactions and disorder in quantum dots: instabilities and phase transitions.

Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an imperfect two-dimensional superfluidity, in which there is nearly dissipationless transport at nonvanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a coherence network induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropriate to describe the system as a vortex liquid. We demonstrate that the dynamics of the nodes of the network leads to a power law temperature dependence of the tunneling resistance, whereas thermally activated hops of vortices across the links control the counterflow resistance.

Compact z=2 Electrodynamics in 2+1 dimensions: Confinement with gapless modes

We demonstrate that, in the presence of Coulomb interactions, electrons in graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows that the origin of this behavior lies in particle-hole scattering, for which the Coulomb interaction induces anomalously close approaches. With increasing interaction strength the relevant power law changes from real to complex, leading to an unusual instability characterized by a complex-valued susceptibility in the thermodynamic limit. Measurable quantities, as well as the connection to classical two-dimensional systems, are discussed.

Quantum dots with disorder and interactions: a solvable large-g limit.

Using a fermionic renormalization group approach, we analyze a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by random matrix theory, we find that interactions can induce phase transitions (or crossovers for finite systems) to regimes where fluctuations and collective effects dominate at low energies. Implications for experiments and numerical work on quantum dots are discussed.

Excitonic Effects in Two-Dimensional Massless Dirac Fermions

We consider 2+1-dimensional compact U(1) gauge theory at the Lifshitz point with a dynamical critical exponent z=2. As in the usual z=1 theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms of a nonrelativistic sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wilson loops still obey area laws, implying that minimal charges are confined, but the action of spacelike Wilson loops of linear size L goes instead as L(3).

Absence of U (1) spin liquids in two dimensions

We analyze the problem of interacting electrons on a ballistic quantum dot with chaotic boundary conditions, where the effective interactions at low energies are characterized by Landau parameters. When the dimensionless conductance g of the dot is large, the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as g --> infinity (as in a large-N theory), leading to a phase transition in each Landau interaction channel. In the weak-coupling phase constant charging and exchange interactions dominate the low-energy physics, while the strong-coupling phase displays a spontaneous distortion of the Fermi surface, smeared out by disorder.