Robert Konik

Purely transmitting defect field theories

Abstract We define an infinite class of integrable theories with a defect which are formulated as chiral defect perturbations of a conformal field theory. Such theories are massless in the bulk and are purely transmitting through the defect. The integrability of these theories requires the introduction of defect degrees of freedom. Such degrees of freedom lead to a novel set of Yang-Baxter equations. The defect degrees of freedom are identified through folding the chiral defect theories onto massless boundary field theories. The examples of the sine-Gordon theory and Ising model are worked out in some detail.

Constructing the generalized Gibbs ensemble after a quantum quench

Using a numerical renormalization group based on exploiting an underlying exactly solvable nonrelativistic theory, we study the out-of-equilibrium dynamics of a 1D Bose gas (as described by the Lieb-Liniger model) released from a parabolic trap. Our method allows us to track the postquench dynamics of the gas all the way to infinite time. We also exhibit a general construction, applicable to all integrable models, of the thermodynamic ensemble that has been suggested to govern this dynamics, the generalized Gibbs ensemble. We compare the predictions of equilibration from this ensemble against the long time dynamics observed using our method.

Carbon nanotube-based heterostructures for solar energy applications

One means of combining the unique physical and chemical properties of both carbon nanotubes and complementary material motifs (such as metal sulfide quantum dots (QDs), metal oxide nanostructures, and polymers) can be achieved by generating carbon nanotube (CNT)-based heterostructures. These materials can be subsequently utilized as novel and interesting constituent building blocks for the assembly of functional light energy harvesting devices and because of their architectural and functional flexibility, can potentially open up novel means of using and taking advantage of existing renewable energy sources. In this review, we present the reliable and reproducible synthesis of several unique model CNT-based heterostructured systems as well as include an accompanying discussion about the charge transfer and energy flow properties of these materials for their potential incorporation into a range of practical solar energy conversion devices.

Numerical Renormalization Group for Continuum One-Dimensional Systems

We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Wilsons numerical renormalization group with Zamolodchikovs truncated conformal spectrum approach. The key to the method is that such theories provide a set of completely understood eigenstates for which matrix elements can be exactly computed. In this procedure the RG flow of physical observables can be studied both numerically and analytically. To demonstrate the approach, we study the spectrum of a pair of coupled quantum Ising chains and correlation functions in a single quantum Ising chain in the presence of a magnetic field.

Applications of Massive Integrable Quantum Field Theories to Problems in Condensed Matter Physics

We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the determination of dynamical response functions for these problems. These quantities are computed by means of form factor expansions of quantum correlation functions in integrable quantum field theories. This approach is reviewed here in some detail.

Boundary sine-Gordon interactions at the free fermion point

Abstract We study bosonization of the sine-Gordon theory in the presence of boundary interactions at the free fermion point. In this way we obtain the boundary S-matrix as a function of physical parameters in the boundary sine-Gordon Lagrangian. The boundary S-matrix can be matched onto the solution of Ghoshal and Zamolodchikov, thereby relating the formal parameters in the latter solution to the physical parameters in the lagrangian.

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess nontrivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low-dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasiconserved quantities, thus providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasiconserved quantities can be probed experimentally.

Quench dynamics in randomly generated extended quantum models

We analyze the thermalization properties and the validity of the eigenstate thermalization hypothesis in a generic class of quantum Hamiltonians where the quench parameter explicitly breaks a Z2 symmetry. Natural realizations of such systems are given by random matrices expressed in a block form where the terms responsible for the quench dynamics are the off-diagonal blocks. Our analysis examines both dense and sparse random matrix realizations of the Hamiltonians and the observables. Sparse random matrices may be associated with local quantum Hamiltonians and they show a different spread of the observables on the energy eigenstates with respect to the dense ones. In particular, the numerical data seem to support the existence of rare states, i.e., states where the observables take expectation values that are different compared to the typical ones sampled by the microcanonical distribution. In the case of sparse random matrices, we also extract the finite-size behavior of two different time scales associated with the thermalization process.

ON ISING CORRELATION FUNCTIONS WITH BOUNDARY MAGNETIC FIELD

Exact expressions of the boundary state and the form factors of the Ising model are used to derive differential equations for the one-point functions of the energy and magnetization operators of the model in the presence of a boundary magnetic field. We also obtain explicit formulas for the massless limit of the one-point and two-point functions of the energy operator.

Doped Spin Liquid: Luttinger Sum Rule and Low Temperature Order

We analyze a model of two-leg Hubbard ladders weakly coupled by interladder tunneling. At half filling a semimetallic state with small Fermi pockets is induced beyond a threshold tunneling strength. The sign changes in the single electron Greens function relevant for the Luttinger sum rule now take place at surfaces with both zeros and infinities with important consequences for the interpretation of angle-resolved photoemission spectroscopy experiments. Residual interactions between electron and holelike quasiparticles cause a transition to long range order at low temperatures. The theory can be extended to small doping leading to superconducting order.