103 research outputs found

### N\'eel and disordered phases of coupled Heisenberg chains with $S=1/2$ to S=4

We use the two-step density-matrix renormalization group method to study the
effects of frustration in Heisenberg models for $S=1/2$ to S=4 in a
two-dimensional anisotropic lattice. We find that as in $S=1/2$ studied
previously, the system is made of nearly disconnected chains at the maximally
frustrated point, $J_d/J_{\perp}=0.5$, i.e., the transverse spin-spin
correlations decay exponentially. This leads to the following consequences: (i)
all half-integer spins systems are gapless, behaving like a sliding Luttinger
liquid as in $S=1/2$; (ii) for integer spins, there is an intermediate
disordered phase with a spin gap, with the width of the disordered state is
roughly proportional to the 1D Haldane gap.Comment: 13 pages, 22 figure

### Critical Exponents in a Quantum Phase Transition of an Anisotropic 2D Antiferromagnet

I use the two-step density-matrix renormalization group method to extract the
critical exponents $\beta$ and $\nu$ in the transition from a N\'eel
$Q=(\pi,\pi)$ phase to a magnetically disordered phase with a spin gap. I find
that the exponent $\beta$ computed from the magnetic side of the transition is
consistent with that of the classical Heisenberg model, but not the exponent
$z\nu$ computed from the disordered side. I also show the contrast between
integer and half-integer spin cases.Comment: 4 pages, 2 figure

### Absence of a Slater Transition in The Two-Dimensional Hubbard Model

We present well-controlled results on the metal to insulator transition (MIT)
within the paramagnetic solution of the dynamical cluster approximation (DCA)
in the two-dimensional Hubbard model at half-filling. In the strong coupling
regime, a local picture describes the properties of the model; there is a large
charge gap $\Delta \approx U$. In the weak-coupling regime, we find a symbiosis
of short-range antiferromagnetic correlations and moment formation cause a gap
to open at finite temperature as in one dimension. Hence, this excludes the
mechanism of the MIT proposed by Slater long ago.Comment: 4 pages, 5 figure

### A Matrix Kato-Bloch Perturbation Method for Hamiltonian Systems

A generalized version of the Kato-Bloch perturbation expansion is presented.
It consists of replacing simple numbers appearing in the perturbative series by
matrices. This leads to the fact that the dependence of the eigenvalues of the
perturbed system on the strength of the perturbation is not necessarily
polynomial. The efficiency of the matrix expansion is illustrated in three
cases: the Mathieu equation, the anharmonic oscillator and weakly coupled
Heisenberg chains. It is shown that the matrix expansion converges for a
suitably chosen subspace and, for weakly coupled Heisenberg chains, it can lead
to an ordered state starting from a disordered single chain. This test is
usually failed by conventional perturbative approaches.Comment: 4 pages, 2 figure

### Disordered phase of a two-dimensional Heisenberg Model with S=1

We study an anisotropic version of the $J_1-J_2$ model with S=1. We find a
second order transition from a N\'eel $Q=(\pi,\pi)$ phase to a disordered phase
with a spin gap.Comment: 4 pages, 5 figure

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