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 Wilson's numerical renormalization group with Zamolodchikov's 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.

We consider the Fermi gas in a non-equilibrium state obtained by applying an arbitrary timedependent potential to the Fermi gas in the ground state. We present a general method that gives the quantum statistics of any single-particle quantity, such as the charge, total energy or momentum, in this non-equilibrium state. We show that the quantum statistics may be found from the solution of a matrix Riemann-Hilbert problem. We use the method to study how the finite measuring time modifies the distribution of the charge transferred through a biased quantum point contact.

Motivated by recent experiments, we study the interaction corrections to the damping of magnetooscillations in a two-dimensional electron gas (2DEG). We identify leading contributions to the interaction-induced damping which are induced by corrections to the effective mass and quantum scattering time. The damping factor is calculated for Coulomb and short-range interaction in the whole range of temperatures, from the ballistic to the diffusive regime. It is shown that the dominant effect is that of the renormalization of the effective electron mass due to the interplay of the interaction and impurity scattering. The results are relevant to the analysis of experiments on magnetooscillations (in particular, for extracting the value of the effective mass) and are expected to be useful for understanding the physics of a high-mobility 2DEG near the apparent metal-insulator transition.

We study the spectrum of two dimensional coupled arrays of continuum one-dimensional systems by wedding a density matrix renormalization group procedure to a renormalization group improved truncated spectrum approach. To illustrate the approach we study the spectrum of large arrays of coupled quantum Ising chains. We demonstrate explicitly that the method can treat the various regimes of chains, in particular the three dimensional Ising ordering transition the chains undergo as a function of interchain coupling.PACS numbers: 05.10.Cc, 75.10.JmThe density matrix renormalization group (DMRG) [1] is one of the primary theoretical tools for the quantitative description of low dimensional lattice models. For a wide range of one dimensional (1D) lattice models, DMRG can characterize the model's spectrum and correlation functions [2]. While there have been notable recent advancements [3,4], its use on 2D lattice models is more circumscribed [5].There exist several strategies to apply DMRG to 2D models. In the first, the 2D lattice is reduced to a 1D lattice with long range interactions [6]. A second approach sees short chains treated as individual lattice sites, allowing the 1D DMRG algorithm to be applied to a model with short ranged interactions directly [7]. In a more sophisticated variant of this methodology, the DMRG is applied in a two stage process [3]. The 2D system is first divided into a set of coupled 1D chains and the DMRG is used to determine a low energy reduction thereof. For the second stage, the reduced chains, coupled together and treated as individual lattice sites in a 1D lattice, are analyzed again using DMRG. In a final approach, the 1D matrix product states underlying the DMRG algorithm [8] are replaced by a higher dimensional generalization, projected entangled pair states [9].In this letter we present a distinct approach to applying DMRG to 2D models. This approach trades upon a description of a 2D system as a mixture of continuum and discrete degrees of freedom. In particular, we approach 2D systems as coupled arrays of continuum 1D chains with truncated Hilbert spaces. This methodology offers several distinct advantages. It allows us to treat any 2D strongly correlated model provided it can be conceived as composed of continuum 1D subunits. Furthermore, the approach affords superior finite size scaling. As a function of the length, R, of the composite 1D systems, finite size corrections behave exponentially. This implies that we can access, at the very least, the infinite volume limit in the dimension parallel to the chains. Finally, the truncation of the underlying 1D Hilbert space dramatically lessens the numerical burden of the DMRG algorithm, while providing a natural means to perform a Wilsonian renormalization group (RG) improvement of any resulting answer [10].The specific type of system that we propose to study takes the form,(1)The 1D continuum subunits of the array are governed by H 1D i which we insist must be either gapless (and so governed by a conformal field theory) or gapped...