Reminder: Thomas Barthel is talking today at 2pm, in room 6C-442.
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Speaker: Thomas Barthel (Duke University)
Date/time: Thursday Nov 30th, 2 PM
Location: 6C-442
*Title: *Typical 1d quantum systems at finite temperatures can be
simulated efficiently
on classical computers
*Abstract:*
It is by now well-known that ground states of gapped one-dimensional (1d)
quantum-many body systems with short-range interactions can be studied
efficiently using classical computers and matrix product state techniques.
A corresponding result for finite temperatures was missing.
For 1d systems that can be described by an appropriate 1+1d field theory, I
show that the cost for the classical simulation at finite temperatures
grows in fact only polynomially with the inverse temperature and is
system-size independent -- even for quantum critical systems. In
particular, the thermofield double state (TDS), a purification of the
equilibrium density operator, can be obtained efficiently in matrix-product
form. The argument is based on the scaling behavior of Rényi entanglement
entropies in the TDS. At finite temperatures, they obey the area law. For
quantum critical, conformally invariant systems, the Rényi entropies are
found to grow only logarithmically with inverse temperature. For gapped
systems, they converge to a constant. The field-theoretical results are
confirmed by quasi-exact numerical simulations for integrable and
non-integrable spin systems, and interacting bosons.
Ref: T. Barthel, arXiv:1708.09349 (2017)
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