Schlittler, T, ; Mosseri, R, ; Barthel, T, *Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps*,
Phys. Rev. B, vol. 96
(November, 2017),
pp. 195142-195142 [doi] .
**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 a local 1+1d field theory, it is shown here 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, we show that 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 R\'{e}nyi entanglement entropies in the TDS. At finite temperatures, they obey the area law. For quantum critical systems, the entanglement is found to grow only logarithmically with inverse temperature, S~log(beta). The field-theoretical results are confirmed by quasi-exact numerical simulations of quantum magnets and interacting bosons.*