Competition between superconductivity and charge density waves

We derive an effective field theory for the competition between superconductivity (SC) and charge density waves (CDWs) by employing the SO(3) pseudospin representation of the SC and CDW order parameters. One important feature in the effective nonlinear $\sigma$ model is the emergence of Berry phase even at half filling, originating from the competition between SC and CDWs, i.e., the pseudospin symmetry. A well known conflict between the previous studies of Oshikawa\cite{Oshikawa} and D. H. Lee et al.\cite{DHLee} is resolved by the appearance of Berry phase. The Berry phase contribution allows a deconfined quantum critical point of fractionalized charge excitations with $e$ instead of $2e$ in the SC-CDW quantum transition at half filling. Furthermore, we investigate the stability of the deconfined quantum criticality against quenched randomness by performing a renormalization group analysis of an effective vortex action. We argue that although randomness results in a weak disorder fixed point differing from the original deconfined quantum critical point, deconfinement of the fractionalized charge excitations still survives at the disorder fixed point owing to a nonzero fixed point value of a vortex charge.Comment: adding a renormalization group analysis with a random fugacity term as an effect of randomness on a deconfined quantum critical poin

Optically mediated nonlinear quantum optomechanics

We consider theoretically the optomechanical interaction of several mechanical modes with a single quantized cavity field mode for linear and quadratic coupling. We focus specifically on situations where the optical dissipation is the dominant source of damping, in which case the optical field can be adiabatically eliminated, resulting in effective multimode interactions between the mechanical modes. In the case of linear coupling, the coherent contribution to the interaction can be exploited e.g. in quantum state swapping protocols, while the incoherent part leads to significant modifications of cold damping or amplification from the single-mode situation. Quadratic coupling can result in a wealth of possible effective interactions including the analogs of second-harmonic generation and four-wave mixing in nonlinear optics, with specific forms depending sensitively on the sign of the coupling. The cavity-mediated mechanical interaction of two modes is investigated in two limiting cases, the resolved sideband and the Doppler regime. As an illustrative application of the formal analysis we discuss in some detail a two-mode system where a Bose-Einstein condensate is optomechanically linearly coupled to the moving end mirror of a Fabry-P\'erot cavity.Comment: 11 pages, 8 figure

Cauchy problem for the Boltzmann-BGK model near a global Maxwellian

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the initial perturbation is sufficiently small in a high order energy norm. We also establish an asymptotic decay estimate and uniform $L^2$-stability for nonlinear perturbations.Comment: 26 page

Bandwidth-control vs. doping-control Mott transition in the Hubbard model

We reinvestigate the bandwidth-control and doping-control Mott transitions (BCMT and DCMT) from a spin liquid Mott insulator to a Fermi liquid metal based on the slave-rotor representation of the Hubbard model,\cite{Florens} where the Mott transitions are described by softening of bosonic collective excitations. We find that the nature of the insulating phase away from half filling is different from that of half filling in the respect that a charge density wave coexists with a topological order (spin liquid) away from half filling because the condensation of vortices generically breaks translational symmetry in the presence of "dual magnetic fields" resulting from hole doping while the topological order remains stable owing to gapless excitations near the Fermi surface. Performing a renormalization group analysis, we discuss the role of dissipative gauge fluctuations due to the Fermi surface in both the BCMT and the DCMT

Optical spectroscopic investigation on the coupling of electronic and magnetic structure in multiferroic hexagonal RMnO3 (R = Gd, Tb, Dy, and Ho) thin films

We investigated the effects of temperature and magnetic field on the electronic structure of hexagonal RMnO3 (R = Gd, Tb, Dy, and Ho) thin films using optical spectroscopy. As the magnetic ordering of the system was disturbed, a systematic change in the electronic structure was commonly identified in this series. The optical absorption peak near 1.7 eV showed an unexpectedly large shift of more than 150 meV from 300 K to 15 K, accompanied by an anomaly of the shift at the Neel temperature. The magnetic field dependent measurement clearly revealed a sizable shift of the corresponding peak when a high magnetic field was applied. Our findings indicated strong coupling between the magnetic ordering and the electronic structure in the multiferroic hexagonal RMnO3 compounds.Comment: 16 pages including 4 figure

Deconfinement in the presence of a Fermi surface

U(1) gauge theory of non-relativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions ($QED_3$) by Hermele et al. [Phys. Rev. B {\bf 70}, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ (the coupling strength between non-relativistic fermions and U(1) gauge fields) reveals that the conductivity $\sigma$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in $QED_3$. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the non-relativistic fermions at the charged fixed point. As a result a critical field theory of non-relativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point