The Matsubara-Fradkin Thermodynamical Quantization of Podolsky Electrodynamics

In this work we apply the Matsubara-Fradkin formalism and the Nakanishi's auxiliary field method to the quantization of the Podolsky electrodynamics in thermodynamic equilibrium. This approach allows us to write consistently the path integral representation for the partition function of gauge theories in a simple manner. Furthermore, we find the Dyson-Schwinger-Fradkin equations and the Ward-Fradkin-Takahashi identities for the Podolsky theory. We also write the most general form for the polarization tensor in thermodynamic equilibrium.Comment: Submitted to Physical Review

Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids

The properties of the isotropic incompressible $\nu=5/2$ fractional quantum Hall (FQH) state are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform $p_x+ip_y$ pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at $\nu=5/2$. This finding motivates us to consider an inhomogeneous paired state - a $p_x+ip_y$ pair-density-wave (PDW) - whose melting could be the origin of the observed liquid-crystalline phases. This state can viewed as an array of domain and anti-domain walls of the $p_x+i p_y$ order parameter. We show that the nodes of the PDW order parameter, the location of the domain walls (and anti-domain walls) where the order parameter changes sign, support a pair of symmetry-protected counter-propagating Majorana modes. The coupling behavior of the domain wall Majorana modes crucially depends on the interplay of the Fermi energy $E_{F}$ and the PDW pairing energy $E_{\textrm{pdw}}$. The analysis of this interplay yields a rich set of topological states. The pair-density-wave order state in paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases - as well as transitions thereof - tuned by the strength of the paired liquid crystalline order.Comment: 27 pages, 11 figures; Published versio

Heat transport through quantum Hall edge states: Tunneling versus capacitive coupling to reservoirs

We study the heat transport along an edge state of a two-dimensional electron gas in the quantum Hall regime, in contact to two reservoirs at different temperatures. We consider two exactly solvable models for the edge state coupled to the reservoirs. The first one corresponds to filling $\nu=1$ and tunneling coupling to the reservoirs. The second one corresponds to integer or fractional filling of the sequence $\nu=1/m$ (with $m$ odd), and capacitive coupling to the reservoirs. In both cases we solve the problem by means of non-equilibrium Green function formalism. We show that heat propagates chirally along the edge in the two setups. We identify two temperature regimes, defined by $\Delta$, the mean level spacing of the edge. At low temperatures, $T< \Delta$, finite size effects play an important role in heat transport, for both types of contacts. The nature of the contacts manifest themselves in different power laws for the thermal conductance as a function of the temperature. For capacitive couplings a highly non-universal behavior takes place, through a prefactor that depends on the length of the edge as well as on the coupling strengths and the filling fraction. For larger temperatures, $T>\Delta$, finite-size effects become irrelevant, but the heat transport strongly depends on the strength of the edge-reservoir interactions, in both cases. The thermal conductance for tunneling coupling grows linearly with $T$, whereas for the capacitive case it saturates to a value that depends on the coupling strengths and the filling factors of the edge and the contacts.Comment: 15 pages, 5 figure

External leg amputation in conformal invariant three-point function

Amputation of external legs is carried out explicitly for the conformal invariant three-point function involving two spinors and one vector field. Our results are consistent with the general result that amputing an external leg in a conformal invariant Green function replaces a field by its conformal partner in the Green function. A new star-triangle relation, involving two spinors and one vector field, is derived and used for the calculation.Comment: 16 pages; last paragraph added in Sec. 10, presentation improved, to appear in Eur. Phys. J.

Fractional statistics and duality: strong tunneling behavior of edge states of quantum Hall liquids in the Jain sequence

While the values for the fractional charge and fractional statistics coincide for fractional Hall (FQH) states in the Laughlin sequence, they do not for more general FQH states, such as those in the Jain sequence. This mismatch leads to additional phase factors in the weak coupling expansion for tunneling between edge states which alter the nature of the strong tunneling limit. We show here how to construct a weak-strong coupling duality for generalized FQH states with simple unreconstructed edges. The correct dualization of quasiparticles into integer charged fermions is a consistency requirement for a theory of FQH edge states with a simple edge. We show that this duality also applies for weakly reconstructed edges.Comment: 4+epsilon page

The imbalanced antiferromagnet in an optical lattice

We study the rich properties of the imbalanced antiferromagnet in an optical lattice. We present its phase diagram, discuss spin waves and explore the emergence of topological excitations in two dimensions, known as merons, which are responsible for a Kosterlitz-Thouless transition that has never unambiguously been observed.Comment: 4 pages, 5 figures, RevTe

Photon and electron spectra in hot and dense QED

Photon and electron spectra in hot and dense QED are found in the high temperature limit for all |\q| using the Feynman gauge and the one-loop self-energy. All spectra are split by the medium and their branches develop the gap (the dynamical mass) at zero momentum. The photon spectrum has two branches (longitudinal and transverse) with the common mass; but electron spectrum is split on four branches which are well-separated for any |\q| including their |\q|=0 limits (their effective masses). These masses and the photon thermal mass are calculated explicitly and the different limits of spectrum branches are established in detail. The gauge invariance of the high-temperature spectra is briefly discussed.Comment: 9 pages, latex, no figure

Polaron action for multimode dispersive phonon systems

Path-integral approach to the tight-binding polaron is extended to multiple optical phonon modes of arbitrary dispersion and polarization. The non-linear lattice effects are neglected. Only one electron band is considered. The electron-phonon interaction is of the density-displacement type, but can be of arbitrary spatial range and shape. Feynman's analytical integration of ion trajectories is performed by transforming the electron-ion forces to the basis in which the phonon dynamical matrix is diagonal. The resulting polaron action is derived for the periodic and shifted boundary conditions in imaginary time. The former can be used for calculating polaron thermodynamics while the latter for the polaron mass and spectrum. The developed formalism is the analytical basis for numerical analysis of such models by path-integral Monte Carlo methods.Comment: 9 page