arXiv subjects

Robert M. Konik

Publications and source records attributed to Robert M. Konik.

47 records · Page 3Linked to original sources

arXiv2007

A 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 Kenneth Wilson's numerical renormalization group with Al. B. Zamolodchikov's truncated conformal spectrum approach. 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.

cond-mat.str-el↗

arXiv2004

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.

cond-mat.str-el↗

arXiv2004

Fano Resonances in Quantum Dots: A Non-Perturbative Role for Potential-Like Scattering

We consider the physics of transport through quantum dots in the presence of two tunneling paths. The first path sees electrons hopping on and off the dot while the second path is modeled through a potential scattering-like term. To study the effects of potential scattering, we employ a modified version of the Anderson model. Such a model can be exactly solved through the Bethe ansatz, thus allowing a comprehensive and exact analysis of the zero temperature linear response conductance. We find transport properties to be extremely sensitive to the introduction of a potential scattering term. Indeed the presence of such a scattering term, inter alia, induces a series of first order quantum phase transitions. Focusing on the Kondo regime of the quantum dot, the non-perturbative effect of potential-like scattering can be directly tied to both the breaking of particle-hole symmetry and the interlinking of charge and spin degrees of freedom in the Anderson model. The sensitivity to potential scattering is also reflected in a set of complementary exact diagonalization computations. The consequences of this analysis extends to observations in general of Fano resonances in quantum dots as well as to the physics of transport through quantum dots embedded in Aharonov-Bohm rings.

cond-mat.mes-hall↗

arXiv2003

Haldane-Gapped Spin Chains as Luttinger Liquids: Correlation Functions at Finite Field

We study the behavior of Heisenberg, antiferromagnetic, integer-spin chains in the presence of a magnetic field exceeding the attendant spin gap. For temperatures much smaller than the gap, the spin chains exhibit Luttinger liquid behavior. We compute exactly both the corresponding Luttinger parameter and the Fermi velocity as a function of magnetic field. This enables the computation of a number of correlators from which we derive the spin conductance, the expected form of the dynamic structure factor relevant to inelastic neutron scattering experiments, and NMR relaxation rates. We also comment upon the robustness of the magnetically induced gapless phase both to finite temperature and finite couplings between neighbouring chains.

cond-mat.str-el↗

arXiv2002

Non-Perturbative Aspects of Fano Resonances in Quantum Dots: An Exact Treatment

We consider transport through quantum dots with two tunneling paths. Interference between paths gives rise to Fano resonances exhibiting Kondo-like physics. In studying such quantum dots, we employ a generalized Anderson model which we argue to be integrable. The exact solution is non-perturbative in the tunneling strengths of both paths. By exploiting this integrability, we compute the zero temperature linear response conductance of the dot and so obtain reasonable quantitative agreement with the experimental measurements reported in Gores et al. PRB 62, 2188 (2000).

cond-mat.str-el↗

arXiv2002

Quantum fluctuations of charge and phase transitions of a large Coulomb-blockaded quantum dot

We analyze ground-state properties of a large gated quantum dot coupled via a quantum point contact to a reservoir of one-dimensional interacting spinless electrons. We find that the classical step-like dependence of the dot population on the gate voltage is preserved under certain conditions. We point out that the problem is related to the classical one-dimensional Ising model with inverse-square interactions. This Ising universality class further subdivides into (i) the Kondo/Ising class and (ii) the tricritical class. For systems of the Kondo/Ising class, and repulsive electrons, the gate voltage dependence of the dot population is continuous for sufficiently open dots, while taking the form of a modified staircase for dots sufficiently isolated from the reservoir. At the phase transition between the two regimes the magnitude of the dot population jump is universal. For systems in the tricritical class we find in addition an intermediate regime where the dot population jumps from near integer value to a region of stable population centered about a half-integer value. In particular, this tricritical behaviour (together with the two dependencies already seen in the Kondo/Ising class) is realized for non-interacting electrons.

cond-mat↗

arXiv2001

Haldane Gapped Spin Chains: Exact Low Temperature Expansions of Correlation Functions

We study both the static and dynamic properties of gapped, one-dimensional, Heisenberg, anti-ferromagnetic, spin chains at finite temperature through an analysis of the O(3) non-linear sigma model. Exploiting the integrability of this theory, we are able to compute an exact low temperature expansion of the finite temperature correlators. We do so using a truncated `form-factor' expansion and so provide evidence that this technique can be successfully extended to finite temperature. As a direct test, we compute the static zero-field susceptibility and obtain an exact match to the susceptibility derived from the low temperature expansion of the exact free energy. We also study transport properties, computing both the spin conductance and the NMR-relaxation rate, 1/T_1. We find these quantities to show ballistic behaviour. In particular, the computed spin conductance exhibits a non-zero Drude weight at finite temperature and zero applied field. The physics thus described differs from the spin diffusion reported by Takigawa et al. from experiments on the Haldane gap material, AgVP_2S_6.

cond-mat.str-el↗

arXiv2000

Interplay of the Scaling Limit and the Renormalization Group: Implications for Symmetry Restoration

Symmetry restoration is usually understood as a renormalization group induced phenomenon. In this context, the issue of whether one-loop RG equations can be trusted in predicting symmetry restoration has recently been the subject of much debate. Here we advocate a more pragmatic point of view and expand the definition of symmetry restoration to encompass all situations where the physical properties have only a weak dependence upon an anisotropy in the bare couplings. Moreover we concentrate on universal properties, and so take a scaling limit where the physics is well described by a field theory. In this context, we find a large variety of models that exhibit, for all practical purposes, symmetry restoration: even if symmetry is not restored in a strict sense, physical properties are surprisingly insensitive to the remaining anisotropy. Although we have adopted an expanded notion of symmetry restoration, we nonetheless emphasize that the scaling limit also has implications for symmetry restoration as a renormalization group induced phenomenon. In all the models we considered, the scaling limit turns out to only permit bare couplings which are nearly isotropic and small. Then the one-loop beta-function should contain all the physics and higher loop orders can be neglected. We suggest that this feature generalizes to more complex models. We exhibit a large class of theories with current-current perturbations (of which the SO(8) model of interest in two-leg Hubbard ladders/armchair carbon nanotubes is one) where the one-loop beta-functions indicates symmetry restoration and so argue that these results can be trusted within the scaling limit.

cond-mat.str-el↗

arXiv2000

On phase transitions in two-dimensional disordered systems

The low-energy limits of models with disorder are frequently described by sigma models. In two dimensions, most sigma models admit either a Wess-Zumino-Witten or a theta term. When such a term is present the model can have a stable critical point with gapless excitations. We describe how such a critical point appears, in particular in two-dimensional superconductors with disorder. The presence of such terms is required by the underlying (anomalous) symmetries of the original electron model. This indicates that the usual symmetry classes of disordered systems in two dimensions can be further refined. Conversely, our results also indicate that models previously thought to be in different universality classes are in fact the same once the appropriate extra terms are included.

cond-mat.supr-con↗

arXiv1995

Massless Boundary Sine-Gordon at the Free Fermion Point: Correlation and Partition Functions with Applications to Quantum Wires

In this report we compute the boundary states (including the boundary entropy) for the boundary sine-Gordon theory. From the boundary states, we derive both correlation and partition functions. Through the partition function, we show that boundary sine-Gordon maps onto a doubled boundary Ising model. With the current-current correlators, we calculate for finite system size the ac-conductance of tunneling quantum wires with dimensionless free conductance 1/2 (or, alternatively interacting quantum Hall edges at filling fraction 1/2). In the dc limit, the results of C. Kane and M. Fisher, Phys. Rev. B46 (1992) 15233, are reproduced.

hep-th↗

arXiv1995

Short Distance Expansions of Correlation Functions in the Sine-Gordon Theory

We examine the two-point correlation functions of the fields exp(i$αΦ$) in the sine-Gordon theory at all values of the coupling constant $\hatβ$. Using conformal perturbation theory, we write down explicit integral expressions for every order of the short distance expansion. Using a novel technique analagous to dimensional regularisation, we evaluate these integrals for the first few orders finding expressions in terms of generalised hypergeometric functions. From these derived expressions, we examine the limiting forms at the points where the sine-Gordon theory maps onto a doubled Ising and the Gross-Neveu SU(2) models. In this way we recover the known expansions of the spin and disorder fields about criticality in the Ising model and the well known Kosterlitz-Thouless flows in the Gross-Neveu SU(2) model.

hep-th↗