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QCR 20190515

QCR 20190515

QCR 20190515

QCR 20190515

QCR 20190515

QCR 20190515

We discuss the quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfil an algebra of current with a Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. Transport of a quantum-mechanical system along a closed loop of parameter space may yield a geometric phase. We discuss models for which nonintegrable phase factors are obtained from the adiabatic parallel transport. After second quantization, one obtains, in addition, a Schwinger term. Depending on the type of transformation, a subtle relationship between these two obstructions can occur. We indicate finally how we may transport density matrices along closed loops in parameter space., QC 20190515

QCR 20190515

QCR 20190515

QCR 20190515

QCR 20190514

QCR 20190514

QCR 20190514

QCR 20190514

We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a non-trivial real regular contribution that depends on details of the impurities., arXiv:1807.10239 [cond-mat.stat-mech]. QC 20181120

We present a 2+1 dimensional quantum gauge theory model with correlated fermions that is exactly solvable by bosonization. This model gives an effective description of partially gapped fermions on a square lattice that have density-density interactions and are coupled to photons. We show that the photons in this model are massive due to gauge-invariant normal-ordering, similarly as in the Schwinger model. Moreover, the exact excitation spectrum of the model has two gapped and one gapless mode. We also compute the magnetic field induced by an external current and show that there is a Meissner effect. We find that the transverse photons have significant effects on the low-energy properties of the model even if the fermion-photon coupling is small., QS 2011 QS 20120326

QS 2011 QS 20120326

QS 20120327

We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation., QS 201605

The deformed Calogero-Sutherland (CS) model is a quantum integrable systemwith arbitrary numbers of two types of particles and reducing to the standard CSmodel in special cases. We show that a known collective field description of theCS model, which is based on conformal field theory (CFT), is actually a collectivefield description of the deformed CS model. This provides a natural application ofthe deformed CS model in Wen’s effective field theory of the fractional quantumHall effect (FQHE), with the two kinds of particles corresponding to electrons andquasi-hole excitations. In particular, we use known mathematical results aboutsuper Jack polynomials to obtain simple explicit formulas for the orthonormal CFTbasis proposed by van Elburg and Schoutens in the context of the FQHE., QC 20161004

We consider the non-stationary Heun equation, also known as quantum PainlevéVI, which has appeared in dierent works on quantum integrable models and conformaleld theory. We use a generalized kernel function identity to transform the problemto solve this equation into a dierential-dierence equation which, as we show, canbe solved by ecient recursive algorithms. We thus obtain series representations ofsolutions which provide elliptic generalizations of the Jacobi polynomials. These seriesreproduces, in a limiting case, a perturbative solution of the Heun equation due toTakemura, but our method is dierent in that we expand in non-conventional basisfunctions that allow us to obtain explicit formulas to all orders, QC 20161004