Critical Theory of Two-Dimensional Mott Transition: Integrability and Hilbert Space Mapping

We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical point by use of the representation theory of the q-oscillator and Weyl algebras. The transition is further characterized by the ground state modification. The explicit mapping provides a new tool to further probe and test the detailed physical properties of the fermionic lattice model considered here and to enhance our understanding of the Mott transition(s)

Coulomb Blockade in Hierarchical Quantum Hall Droplets

The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both Abelian and non-Abelian statistics, upon adapting known results for the annulus geometry. We analyze the Abelian states with hierarchical filling fractions, \nu=m/(mp \pm 1), and find a non trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, that is due to the extended symmetry of the m-folded edge. Experimental tests of the multiplicity can shed more light on the dynamics of this composite edge.Comment: 8 pages; v2: published version; effects of level multiplicities not well understood, see arXiv:0909.3588 for the correct analysi

Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models

We propose an approach to treat (1+1)--dimensional fermionic systems based on the idea of algebraic bosonization. This amounts to decompose the elementary low-lying excitations around the Fermi surface in terms of basic building blocks which carry a representation of the W_{1+\infty} \times {\overline W_{1+\infty}} algebra, which is the dynamical symmetry of the Fermi quantum incompressible fluid. This symmetry simply expresses the local particle-number current conservation at the Fermi surface. The general approach is illustrated in detail in two examples: the Heisenberg and Calogero-Sutherland models, which allow for a comparison with the exact Bethe Ansatz solution.Comment: 51 pages, plain LaTe

Universal power-law exponents in differential tunneling conductance for planar insulators near Mott criticality at low temperatures

We consider the low-temperature differential tunneling conductance $G$ for interfaces between a planar insulating material in the Mott-class and a metal. For values of the the applied potential difference $V$ that are not very small, there is a experimentally observed universal regime in which $G \sim V^m$, where $m$ is a universal exponent. We consider the theoretical prediction of the values of $m$ by using the method of Effective Field Theory ($EFT$), which is appropriate for discussing universal phenomena. We describe the Mott material by the $EFT$ pertaining the long-distance behavior of a spinless Hubbard-like model with nearest neighbors interactions previously considered. At the Mott transition, the $EFT$ is known to be given by a double Abelian Chern-Simons theory. The simplest realization of this theory at the tunneling interface yields a Conformal Field Theory with central charges $(c,\bar c) =(1,1)$ and Jain filling fraction $\nu = 2/3$ describing a pair of independent counter-propagating chiral bosons (one charged and one neutral). Tunneling from the material into the metal is, therefore, described by this $EFT$ at the Mott critical point. The resulting tunneling conductance behaves as $G \sim V^{(1/\nu -1)}$, yielding the prediction $m=1/2$, which compares well (within a $10 \%$ deviation) with the results for this exponent in two experimental studies considered here

Mott transition and integrable lattice models in two dimensions

We describe the two-dimensional Mott transition in a Hubbard-like model with nearest neighbors interactions based on a recent solution to the Zamolodchikov tetrahedron equation, which extends the notion of integrability to two-dimensional lattice systems. At the Mott transition, we find that the system is in a d-density wave or staggered flux phase that can be described by a double Chern Simons effective theory with symmetry \su2 \otimes \su2. The Mott transition is of topological nature, characterized by the emergence of vortices in antiferromagnetic arrays interacting strongly with the electric charges and an electric-magnetic duality. We also consider the effect of small doping on this theory and show that it leads to a quantum gas-liquid coexistence phase, which belongs to the Ising universality class and which is consistent with several experimental observations.Comment: 6 pages, two column forma

Thermodynamics of a model for RNA folding

We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by G. Vernizzi, H. Orland, A. Zee (in {\it Phys. Rev. Lett.} {\bf 94} (2005) 168103). The model consists of a chain of one-flavor base molecules with a flexible backbone and all possible pairing interactions equally allowed. The spatial pseudoknot structure of the model can be efficiently studied by introducing a $N \times N$ hermitian random matrix model at each chain site, and associating Feynman diagrams of these models to spatial configurations of the molecules. We obtain an exact expression for the topological expansion of the partition function of the system. We calculate exact and asymptotic expressions for the free energy, specific heat, entanglement and chemical potential and study their behavior as a function of temperature. Our results are consistent with the interpretation of $1/N$ as being a measure of the concentration of $\rm{Mg}^{++}$ in solution.Comment: 11 pages, 4 figure

Effective Field Theories for Electrons in Crystalline Structures

We present an effective field theory formulation for a class of condensed matter systems with crystalline structures for which some of the discrete symmetries of the underlying crystal survive the long distance limit, up to mesoscopic scales, and argue that this class includes interesting materials, such as $Si$-doped $GaAs$. The surviving symmetries determine a limited set of possible effective interactions, that we analyze in detail for the case of $Si$-doped $GaAs$ materials. These coincide with the ones proposed in the literature to describe the spin relaxation times for the $Si$-doped $Ga As$ materials, obtained here as a consequence of the choice of effective fields and their symmetries. The resulting low-energy effective theory is described in terms of three (six chiral) one-dimensional Luttinger liquid systems and their corresponding intervalley transitions. We also discuss the Mott transition within the context of the effective theory.Comment: 24 pages, 3 figure