2,136 research outputs found
Equilibrium and dynamical properties of the ANNNI chain at the multiphase point
We study the equilibrium and dynamical properties of the ANNNI (axial
next-nearest-neighbor Ising) chain at the multiphase point. An interesting
property of the system is the macroscopic degeneracy of the ground state
leading to finite zero-temperature entropy. In our equilibrium study we
consider the effect of softening the spins. We show that the degeneracy of the
ground state is lifted and there is a qualitative change in the low temperature
behaviour of the system with a well defined low temperature peak of the
specific heat that carries the thermodynamic ``weight'' of the ground state
entropy. In our study of the dynamical properties, the stochastic Kawasaki
dynamics is considered. The Fokker-Planck operator for the process corresponds
to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with
constraints on allowed states. This leads to a number of differences in its
properties which are obtained through exact numerical diagonalization,
simulations and by obtaining various analytic bounds.Comment: 9 pages, RevTex, 6 figures (To appear in Phys. Rev. E
Single-shot simulations of dynamics of quantum dark solitons
Eigenstates of Bose particles with repulsive contact interactions in
one-dimensional space with periodic boundary conditions can be found with the
help of the Bethe ansatz. The type~II excitation spectrum identified by E. H.
Lieb, reproduces the dispersion relation of dark solitons in the mean-field
approach. The corresponding eigenstates possess translational symmetry which
can be broken in measurements of positions of particles. We analyze emergence
of single and double solitons in the course of the measurements and investigate
dynamics of the system. In the weak interaction limit, the system follows the
mean-field prediction for a short period of time. Long time evolution reveals
many-body effects that are related to an increasing uncertainty of soliton
positions. In the strong interaction regime particles behave like impenetrable
bosons. Then, the probability densities in the configuration space become
identical to the probabilities of non-interacting fermions but the
wave-functions themselves remember the original Bose statistics. Especially,
the phase flips that are key signatures of the solitons in the weak interaction
limit, can be observed in the time evolution of the strongly interacting
bosons.Comment: 11 pages, 9 figure
Numerical approach to low-doping regime of the t-J model
We develop an efficient numerical method for the description of a single-hole
motion in the antiferromagnetic background. The method is free of finite-size
effects and allows calculation of physical properties at an arbitrary
wavevector. Methodical increase of the functional space leads to results that
are valid in the thermodynamic limit. We found good agreement with cumulant
expansion, exact- diagonalization approaches on finite lattices as well as
self-consistent Born approximations. The method allows a straightforward
addition of other inelastic degrees of freedom, such as lattice effects. Our
results confirm the existence of a finite quasiparticle weight near the band
minimum for a single hole and the existence of string-like peaks in the
single-hole spectral function.Comment: 6 pages, 6 figures, accepted for publication in PR
Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model
A quantum Monte Carlo algorithm is constructed starting from the standard
perturbation expansion in the interaction representation. The resulting
configuration space is strongly related to that of the Stochastic Series
Expansion (SSE) method, which is based on a direct power series expansion of
exp(-beta*H). Sampling procedures previously developed for the SSE method can
therefore be used also in the interaction representation formulation. The new
method is first tested on the S=1/2 Heisenberg chain. Then, as an application
to a model of great current interest, a Heisenberg chain including phonon
degrees of freedom is studied. Einstein phonons are coupled to the spins via a
linear modulation of the nearest-neighbor exchange. The simulation algorithm is
implemented in the phonon occupation number basis, without Hilbert space
truncations, and is exact. Results are presented for the magnetic properties of
the system in a wide temperature regime, including the T-->0 limit where the
chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics
are also discussed. The results suggest that the effects of dynamic phonons in
spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to
obtain a correct quantitative description of their magnetic properties, both
above and below the dimerization temperature.Comment: 23 pages, Revtex, 11 PostScript figure
Direct simulations of small multi-fermion systems
I explore computer simulations of the dynamics of small multi-fermion lattice
systems. The method is more general, but I concentrate on Hubbard type models
where the fermions hop between a small number of connected sites. I use the
natural mapping of fermion occupation numbers onto computer bits. Signs from
fermion interchange are reduced to bit counting. The technique inherently
requires computer resources growing exponentially with the system volume; so,
it restricted to modestly small systems. Large volume results would require
combining these techniques with further approximations, perhaps in a recursive
renormalization group manner.Comment: 17 pages, 9 figures, revtex
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