195 research outputs found
Anomalous bulk behaviour in the free parafermion spin chain
We demonstrate using direct numerical diagonalization and extrapolation
methods that boundary conditions have a profound effect on the bulk properties
of a simple model for for which the model hamiltonian is
non-hermitian. For the model reduces to the well known quantum Ising
model in a transverse field. For open boundary conditions the model is
known to be solved exactly in terms of free parafermions. Once the ends of the
open chain are connected by considering the model on a ring, the bulk
properties, including the ground-state energy per site, are seen to differ
dramatically with increasing . Other properties, such as the leading
finite-size corrections to the ground-state energy, the mass gap exponent and
the specific heat exponent, are also seen to be dependent on the boundary
conditions. We speculate that this anomalous bulk behaviour is a topological
effect.Comment: 8 pages, 8 figures, minor change
The Bethe ansatz after 75 years
Hans Bethe introduced his now-famous ansatz to obtain the energy eigenstates of the one-dimensional version of Werner Heisenberg’s model of interacting, localized spins in a solid. Although it is among Bethe’s most cited works and has a wide range of applications, it is rarely included in the graduate physics curriculum except at the advanced level. The 75th anniversary of the Bethe ansatz is appropriately marked by reflecting on the impact of Bethe’s result on modern physics, ranging from its profound influence on the field of exactly solved models in statistical mechanics to insights into the subtle nature of quantum many-body effects observed in cold quantum gases
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