331 research outputs found

### Two-component abelian sandpile models

In one-component abelian sandpile models, the toppling probabilities are
independent quantities. This is not the case in multi-component models. The
condition of associativity of the underlying abelian algebras impose nonlinear
relations among the toppling probabilities. These relations are derived for the
case of two-component quadratic abelian algebras. We show that abelian sandpile
models with two conservation laws have only trivial avalanches.Comment: Final version. To appear in Phys.Rev.

### Integrable dissipative exclusion process: Correlation functions and physical properties

We study a one-parameter generalization of the symmetric simple exclusion
process on a one dimensional lattice. In addition to the usual dynamics (where
particles can hop with equal rates to the left or to the right with an
exclusion constraint), annihilation and creation of pairs can occur. The system
is driven out of equilibrium by two reservoirs at the boundaries. In this
setting the model is still integrable: it is related to the open XXZ spin chain
through a gauge transformation. This allows us to compute the full spectrum of
the Markov matrix using Bethe equations. Then, we derive the spectral gap in
the thermodynamical limit. We also show that the stationary state can be
expressed in a matrix product form permitting to compute the multi-points
correlation functions as well as the mean value of the lattice current and of
the creation-annihilation current. Finally the variance of the lattice current
is exactly computed for a finite size system. In the thermodynamical limit, it
matches perfectly the value obtained from the associated macroscopic
fluctuation theory. It provides a confirmation of the macroscopic fluctuation
theory for dissipative system from a microscopic point of view.Comment: 31 pages, 7 figures ; introduction expanded, typos corrected and
title change

### Finite Chains with Quantum Affine Symmetries

We consider an extension of the (t-U) Hubbard model taking into account new
interactions between the numbers of up and down electrons. We confine ourselves
to a one-dimensional open chain with L sites (4^L states) and derive the
effective Hamiltonian in the strong repulsion (large U) regime. This
Hamiltonian acts on 3^L states. We show that the spectrum of the latter
Hamiltonian (not the degeneracies) coincides with the spectrum of the
anisotropic Heisenberg chain (XXZ model) in the presence of a Z field (2^L
states). The wave functions of the 3^L-state system are obtained explicitly
from those of the 2^L-state system, and the degeneracies can be understood in
terms of irreducible representations of U_q(\hat{sl(2)}).Comment: 31pp, Latex, CERN-TH.6935/93. To app. in Int. Jour. Mod. Phys. A.
(The title of the paper is changed. This is the ONLY change. Previous title
was: Hubbard-Like Models in the Infinite Repulsion Limit and
Finite-Dimensional Representations of the Affine Algebra U_q(\hat{sl(2)}).

### A New Family of Integrable Extended Multi-band Hubbard Hamiltonians

We consider exactly solvable 1d multi-band fermionic Hamiltonians, which have
affine quantum group symmetry for all values of the deformation. The simplest
Hamiltonian is a multi-band t-J model with vanishing spin-spin interaction,
which is the affinization of an underlying XXZ model. We also find a multi-band
generalization of standard t-J model Hamiltonian.Comment: 8 pages, LaTeX file, no figure

### Directed abelian algebras and their applications to stochastic models

To each directed acyclic graph (this includes some D-dimensional lattices)
one can associate some abelian algebras that we call directed abelian algebras
(DAA). On each site of the graph one attaches a generator of the algebra. These
algebras depend on several parameters and are semisimple. Using any DAA one can
define a family of Hamiltonians which give the continuous time evolution of a
stochastic process. The calculation of the spectra and ground state
wavefunctions (stationary states probability distributions) is an easy
algebraic exercise. If one considers D-dimensional lattices and choose
Hamiltonians linear in the generators, in the finite-size scaling the
Hamiltonian spectrum is gapless with a critical dynamic exponent $z = D$. One
possible application of the DAA is to sandpile models. In the paper we present
this application considering one and two dimensional lattices. In the one
dimensional case, when the DAA conserves the number of particles, the
avalanches belong to the random walker universality class (critical exponent
$\sigma_{\tau} = 3/2$). We study the local densityof particles inside large
avalanches showing a depletion of particles at the source of the avalanche and
an enrichment at its end. In two dimensions we did extensive Monte-Carlo
simulations and found $\sigma_{\tau} = 1.782 \pm 0.005$.Comment: 14 pages, 9 figure

### Non-contractible loops in the dense O(n) loop model on the cylinder

A lattice model of critical dense polymers $O(0)$ is considered for the
finite cylinder geometry. Due to the presence of non-contractible loops with a
fixed fugacity $\xi$, the model is a generalization of the critical dense
polymers solved by Pearce, Rasmussen and Villani. We found the free energy for
any height $N$ and circumference $L$ of the cylinder. The density $\rho$ of
non-contractible loops is found for $N \rightarrow \infty$ and large $L$. The
results are compared with those obtained for the anisotropic quantum chain with
twisted boundary conditions. Using the latter method we obtained $\rho$ for any
$O(n)$ model and an arbitrary fugacity.Comment: arXiv admin note: text overlap with arXiv:0810.223

### Tsirelson's bound and supersymmetric entangled states

A superqubit, belonging to a $(2|1)$-dimensional super-Hilbert space,
constitutes the minimal supersymmetric extension of the conventional qubit. In
order to see whether superqubits are more nonlocal than ordinary qubits, we
construct a class of two-superqubit entangled states as a nonlocal resource in
the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the
result depends on how we extract real probabilities and we examine three
choices of map: (1) DeWitt (2) Trigonometric (3) Modified Rogers. In cases (1)
and (2) the winning probability reaches the Tsirelson bound
$p_{win}=\cos^2{\pi/8}\simeq0.8536$ of standard quantum mechanics. Case (3)
crosses Tsirelson's bound with $p_{win}\simeq0.9265$. Although all states used
in the game involve probabilities lying between 0 and 1, case (3) permits other
changes of basis inducing negative transition probabilities.Comment: Updated to match published version. Minor modifications. References
adde

- …