Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConformal Profiles in the Hilhorst--van Leeuwen Model
56
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the critical energy and magnetization profiles for the Ising quantum chain with a marginal extended surface perturbation of the form A/y, y being the distance from the surface (Hilhorst-van Leeuwen model). For weak local couplings, A<A_c, the model displays a continuous surface transition with A-dependent exponents, whereas, for A>A_c, there is surface order at the bulk critical point. If conformal invariance is assumed to hold with such marginal perturbations, it predicts conformal profiles with the same scaling form as for the unperturbed quantum chain, with marginal surface exponents replacing the unperturbed ones. The results of direct analytical and numerical calculations of the profiles confirm the validity of the conformal expressions in the regimes of second- and first-order surface transitions.
rate research
Read More
Off-diagonal profiles of local densities (e.g. order parameter or energy density) are calculated at the bulk critical point, by conformal methods, for different types of boundary conditions (free, fixed and mixed). Such profiles, which are defined by a non-vanishing matrix element of the appropriate operator between the ground state and the corresponding lowest excited state of the strip Hamiltonian, enter into the expression of two-point correlation functions on a strip. They are of interest in the finite-size scaling study of bulk and surface critical behaviour since they allow the elimination of regular contributions. The conformal profiles, which are obtained through a conformal transformation of the correlation functions from the half-plane to the strip, are in agreement with the results of a direct calculation, for the energy density of the two-dimensional Ising model.
We investigate the low temperature asymptotics and the finite size spectrum of a class of Temperley-Lieb models. As reference system we use the spin-1/2 Heisenberg chain with anisotropy parameter $Delta$ and twisted boundary conditions. Special emphasis is placed on the study of logarithmic corrections appearing in the case of $Delta=1/2$ in the bulk susceptibility data and in the low-energy spectrum yielding the conformal dimensions. For the $sl(2|1)$ invariant 3-state representation of the Temperley-Lieb algebra with $Delta=1/2$ we give the complete set of scaling dimensions which show huge degeneracies.
The de Haas - van Alphen effect in two-dimensional (2D) metals is investigated at different conditions and with different shapes of Landau levels (LLs). The analytical calculations can be done when many LLs are occupied. We consider the cases of fixed particle number ($N=const$), fixed chemical potential ($mu =const$) and the intermediate situation of finite electron reservoir. The last case takes place in organic metals due to quasi-one-dimensional sheets of Fermi surface. We obtained the envelopes of magnetization oscillations in all these cases in the limit of low temperature and Dingle temperature, where the oscillations can not be approximated by few first terms in the harmonic expansion. The results are compared and shown to be substantially different for different shapes of LLs. The simple relation between the shape of LLs and the wave form of magnetization oscillations is found. It allows to obtain the density of states distribution at arbitrary magnetic field and spin-splitting using the measurement of the magnetization curve. The analytical formula for the magnetization at $mu =const$ and the Lorentzian shape of LLs at arbitrary temperature, Dingle temperature and spin splitting is obtained and used to examine the possibility of the diamagnetic phase transition in 2D metals.
We investigate the behavior of the return amplitude ${cal F}(t)= |langlePsi(0)|Psi(t)rangle|$ following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension $d-1$ and linear size $O(L)$, from a state $|Psi(0)rangle$ of extensive energy with short-range correlations. After an initial gaussian decay ${cal F}(t)$ reaches a plateau value related to the density of available states at the initial energy. However for $d=3,4$ this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least $O(sigma^{1/(d-1)} L)$, where $sigmagg1$ is the dimensionless Stefan-Boltzmann constant. On the other hand for a free field theory on manifolds with high symmetry there are typically revivals at times $tsimmbox{integer}times L$. In particular, on a sphere $S_{d-1}$ of circumference $2pi L$, there is an action of the modular group on ${cal F}(t)$ implying structure near all rational values of $t/L$, similarly to what happens for rational CFTs in $d=2$.
We enumerate the cases in 2d conformal field theory where the logarithm of the reduced density matrix (the entanglement or modular hamiltonian) may be written as an integral over the energy-momentum tensor times a local weight. These include known examples and new ones corresponding to the time-dependent scenarios of a global and local quench. In these latter cases the entanglement hamiltonian depends on the momentum density as well as the energy density. In all cases the entanglement spectrum is that of the appropriate boundary CFT. We emphasize the role of boundary conditions at the entangling surface and the appearance of boundary entropies as universal O(1) terms in the entanglement entropy.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
