434 research outputs found
Quantum dynamics of thermalizing systems
We introduce a method "DMT" for approximating density operators of 1D systems
that, when combined with a standard framework for time evolution (TEBD), makes
possible simulation of the dynamics of strongly thermalizing systems to
arbitrary times. We demonstrate that the method performs well for both
near-equilibrium initial states (Gibbs states with spatially varying
temperatures) and far-from-equilibrium initial states, including quenches
across phase transitions and pure states
Stability of zero modes in parafermion chains
One-dimensional topological phases can host localized zero-energy modes that
enable high-fidelity storage and manipulation of quantum information. Majorana
fermion chains support a classic example of such a phase, having zero modes
that guarantee two-fold degeneracy in all eigenstates up to exponentially small
finite-size corrections. Chains of `parafermions'---generalized Majorana
fermions---also support localized zero modes, but, curiously, only under much
more restricted circumstances. We shed light on the enigmatic zero mode
stability in parafermion chains by analytically and numerically studying the
spectrum and developing an intuitive physical picture in terms of domain-wall
dynamics. Specifically, we show that even if the system resides in a gapped
topological phase with an exponentially accurate ground-state degeneracy,
higher-energy states can exhibit a splitting that scales as a power law with
system size---categorically ruling out exact localized zero modes. The
transition to power-law behavior is described by critical behavior appearing
exclusively within excited states.Comment: 15 pages, 8 figures; substantial improvements to chiral case,
coauthor added. Published 7 October 201
Parafermionic conformal field theory on the lattice
Finding the precise correspondence between lattice operators and the
continuum fields that describe their long-distance properties is a largely open
problem for strongly interacting critical points. Here we solve this problem
essentially completely in the case of the three-state Potts model, which
exhibits a phase transition described by a strongly interacting 'parafermion'
conformal field theory. Using symmetry arguments, insights from integrability,
and extensive simulations, we construct lattice analogues of nearly all the
relevant and marginal physical fields governing this transition. This
construction includes chiral fields such as the parafermion. Along the way we
also clarify the structure of operator product expansions between order and
disorder fields, which we confirm numerically. Our results both suggest a
systematic methodology for attacking non-free field theories on the lattice and
find broader applications in the pursuit of exotic topologically ordered phases
of matter.Comment: 27 pages, 4 figures; v2 added reference
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