Edge Critical Behaviour of the 2-Dimensional Tri-critical Ising Model

Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling constant. A boundary tri-critical point separates phases where the spins on the boundary are ordered or disordered. In the latter range of coupling constant, there is a non-zero critical field where the magnetization is singular. In the former range, as the temperature is lowered, the boundary undergoes a first order transition while the bulk simultaneously undergoes a second order transition.Comment: 6 pages, RevTex, 3 postscript figure

Neel order in doped quasi one-dimensional antiferromagnets

We study the Neel temperature of quasi one-dimensional S=1/2 antiferromagnets containing non-magnetic impurities. We first consider the temperature dependence of the staggered susceptibility of finite chains with open boundary conditions, which shows an interesting difference for even and odd length chains. We then use a mean field theory treatment to incorporate the three dimensional inter-chain couplings. The resulting Neel temperature shows a pronounced drop as a function of doping by up to a factor of 5.Comment: 4 pages in revtex4 format including 2 epsf-embedded figures. The latest version in PDF format is available from http://fy.chalmers.se/~eggert/papers/staggered.pd

Non-Fermi liquid behavior in Kondo models

Despite the fact that the low energy behavior of the basic Kondo model cannot be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres and others to have a simple "local Fermi liquid theory" description. That is, electronic degrees of freedom become effectively non-interacting in the zero energy limit. However, generalized versions of the Kondo model involving more than one channel or impurity may exhibit low energy behavior of a less trivial sort which can, nonetheless, be solved exactly using either Bethe ansatz or conformal field theory and bosonization techniques. Now the low energy limit exhibits interacting many body behavior. For example, processes in which a single electron scatters off the impurity into a multi electron-hole state have a non-vanishing (and sometimes large) amplitude at zero energy. This corresponds to a rare solveable example of non-Fermi liquid behavior. Essential features of these phenomena are reviewed.Comment: A brief review submitted to the special issue of J. Phys. Soc. of Japan, "Kondo effect -- 40 years after the discovery

S(k) for Haldane Gap Antiferromagnets: Large-scale Numerical Results vs. Field Theory and Experiment

The structure function, S(k), for the s=1, Haldane gap antiferromagnetic chain, is measured accurately using the recent density matrix renormalization group method, with chain-length 100. Excellent agreement with the nonlinear $\sigma$ model prediction is obtained, both at $k\approx \pi$ where a single magnon process dominates and at $k\approx 0$ where a two magnon process dominates. We repeat our calculation with crystal field anisotropy chosen to model NENP, obtaining good agreement with both field theory predictions and recent experiments. Correlation lengths, gaps and velocities are determined for both polarizations.Comment: 11 pages, 3 postscript figures included, REVTEX 3.0, UBCTP-93-02

Logarithmic corrections to finite size spectrum of SU(N) symmetric quantum chains

We consider SU(N) symmetric one dimensional quantum chains at finite temperature. For such systems the correlation lengths, ground state energy, and excited state energies are investigated in the framework of conformal field theory. The possibility of different types of excited states are discussed. Logarithmic corrections to the ground state energy and different types of excited states in the presence of a marginal opeartor, are calculated. Known results for SU(2) and SU(4) symmetric systems follow from our general formula.Comment: 5 pages, 1 figure; Typos corrected and minor changes made for clarit

The Haldane Energy Gap of A Doped Linear-Chain Heisenberg Antiferromagnet

Using the valence-bond-solid (VBS) approach and the Schwinger boson mean field approximation, we study the dependence of the Haldane gap of a spin-1 linear chain Heisenberg antiferromagnet on impurity doping with different spins. The impurity spins affect the singlet pairing order parameter $\Delta$ and the constraint factor $\lambda$. As a result, the Haldane gap is reduced by a factor $\sim n_i^{2/3}$, with $n_i$ as the impurity concentration, and eventually collapses at $n_i \sim 1/\xi$ with $\xi$ as the VBS correlation length. This theoretical prediction can be verified by neutron scattering experiments.Comment: REVTEX, 12 pages, no figure

Crossover in the two-impurity Kondo model induced by direct charge tunneling

Quantum critical behavior in the two-impurity Kondo model requires the distinct separation of two scales, T_K >> T*, where T_K is the Kondo temperature and T* is the scale at which the system renormalizes away from the quantum critical point to a stable Fermi liquid fixed point. We provide a derivation of T* based on the renormalization group to lowest order. This result is confirmed by a numerical renormalization group (NRG) analysis which supplements the analytic derivation with additional quantitative precision. The form of the low-energy Fermi liquid fixed point is derived and subsequently confirmed by the NRG. We discuss implications for series double quantum dot systems.Comment: 10 pages, 6 figures; resubmitted Oct. 31, 2011 to include corrections discovered after original submissio

Abelian bosonization approach to quantum impurity problems

Using Abelian Bosonization, we develop a simple and powerful method to calculate the correlation functions of the two channel Kondo model and its variants. The method can also be used to identify all the possible boundary fixed points and their maximum symmetry, to calculate straightforwardly the finite size spectra, to demonstrate the physical picture at the boundary explicitly. Comparisons with Non-Abelian Bosonization method are made. Some fixed points corresponding to 4 pieces of bulk fermions coupled to s=1/2 impurity are listed.Comment: 12 pages, REVTEX, 1 Table, no figures. To appear in Phys. Rev. Letts. July 21, 199

Corrections to scaling in entanglement entropy from boundary perturbations

We investigate the corrections to scaling of the Renyi entropies of a region of size l at the end of a semi-infinite one-dimensional system described by a conformal field theory when the corrections come from irrelevant boundary operators. The corrections from irrelevant bulk operators with scaling dimension x have been studied by Cardy and Calabrese (2010), and they found not only the expected corrections of the form l^(4-2x) but also unusual corrections that could not have been anticipated by finite-size scaling arguments alone. However, for the case of perturbations from irrelevant boundary operators we find that the only corrections that can occur to leading order are of the form l^(2-2x_b) for boundary operators with scaling dimension x_b < 3/2, and l^(-1) when x_b > 3/2. When x_b=3/2 they are of the form l^(-1)log(l). A marginally irrelevant boundary perturbation will give leading corrections going as log(l)^(-3). No unusual corrections occur when perturbing with a boundary operator.Comment: 8 pages. Minor improvements and updated references. Published versio

Impurities in s=1s=1 Heisenberg Antiferromagnets

The $s=1$ Heisenberg Antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with $J'\ne J$ at the center of an even-length open chain is considered. Using the density matrix renormalization group method we find that, for sufficiently strong or weak $J'$, a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbative results, based on $s=1/2$ chain-end excitations, both in the weak and strong coupling limit. In a region around the uniform limit, $J'=J$, no states are found with energy below the Haldane gap. Secondly, a $s=1/2$ impurity at the center of an otherwise even-length open chain is considered. The coupling to the $s=1/2$ impurity is varied. Bound states in the Haldane gap are found {\it only} for sufficiently weak (antiferromagnetic) coupling. For a $s=1/2$ impurity coupled with a strong (antiferromagnetic) bond, {\it no} states are found in the Haldane. Our results are in good qualitative agreement with recent experiments on doped NENP and Y$_2$BaNiO$_5$.Comment: 29 pages, RevTeX 3.0, 12 uuencoded postscript figures include