Marcel Goihl, Christian Krumnow, Marek Gluza, Jens Eisert, Nicolas Tarantino
SciPost Phys. 6, 072 (2019) ·
published 21 June 2019

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Spin chains with symmetryprotected edge zero modes can be seen as
prototypical systems for exploring topological signatures in quantum systems.
These are useful for robustly encoding quantum information. However in an
experimental realization of such a system, spurious interactions may cause the
edge zero modes to delocalize. To stabilize against this influence beyond
simply increasing the bulk gap, it has been proposed to harness suitable
notions of disorder. Equipped with numerical tools for constructing locally
conserved operators that we introduce, we comprehensively explore the interplay
of local interactions and disorder on localized edge modes in the XZX cluster
Hamiltonian. This puts us in a position to challenge the narrative that
disorder necessarily stabilizes topological order. Contrary to heuristic
reasoning, we find that disorder has no effect on the edge modes in the
Anderson localized regime. Moreover, disorder helps localize only a subset of
edge modes in the manybody interacting regime. We identify one edge mode
operator that behaves as if subjected to a noninteracting perturbation, i.e.,
shows no disorder dependence. This implies that in finite systems, edge mode
operators effectively delocalize at distinct interaction strengths. In essence,
our findings suggest that the ability to identify and control the best
localized edge mode trumps any gains from introducing disorder.
Shira Chapman, Jens Eisert, Lucas Hackl, Michal P. Heller, Ro Jefferson, Hugo Marrochio, Robert C. Myers
SciPost Phys. 6, 034 (2019) ·
published 15 March 2019

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Motivated by holographic complexity proposals as novel probes of black hole
spacetimes, we explore circuit complexity for thermofield double (TFD) states
in free scalar quantum field theories using the Nielsen approach. For TFD
states at t = 0, we show that the complexity of formation is proportional to
the thermodynamic entropy, in qualitative agreement with holographic complexity
proposals. For TFD states at t > 0, we demonstrate that the complexity evolves
in time and saturates after a time of the order of the inverse temperature. The
latter feature, which is in contrast with the results of holographic proposals,
is due to the Gaussian nature of the TFD state of the free bosonic QFT. A novel
technical aspect of our work is framing complexity calculations in the language
of covariance matrices and the associated symplectic transformations, which
provide a natural language for dealing with Gaussian states. Furthermore, for
free QFTs in 1+1 dimension, we compare the dynamics of circuit complexity with
the time dependence of the entanglement entropy for simple bipartitions of
TFDs. We relate our results for the entanglement entropy to previous studies on
nonequilibrium entanglement evolution following quenches. We also present a
new analytic derivation of a logarithmic contribution due to the zero momentum
mode in the limit of vanishing mass for a subsystem containing a single degree
of freedom on each side of the TFD and argue why a similar logarithmic growth
should be present for larger subsystems.