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Entanglement and computational complexity for 1D quantum systems at finite T

Thomas Barthel, Duke University, Durham, USA

26.06.2017 at 14:00 

Using the replica trick in 1+1 dimensional quantum field theory, one can show that the cost for the classical simulation of one-dimensional quantum many-body systems at finite temperatures grows only polynomially with the inverse temperature and is system-size independent - even for gapless systems. In particular, I will show that the thermofield
double state (TDS), a widely used purification of the equilibrium density operator, has a faithful matrix product state (MPS) representation. The argument is based on the scaling behavior of Rényi entanglement entropies in the TDS. At finite temperatures, they obey the area law. For gapless conformally invariant systems, the Rényi entropies are found to
grow only logarithmically with inverse temperature.
The field-theoretical results are complemented by exact and quasi-exact numerical computations for integrable as well as non-integrable spin chains, and the Bose-Hubbard model. This allows us to compare actual matrix product truncation dimensions with upper bounds derived from Rényi entropies.

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