Speaker
Piotr Czarnik
Description
The Gibbs operator $e^{−\beta H}$ for a two-dimensional
(2D) lattice system with a Hamiltonian H can be represented
by a three-dimensional tensor network, the third dimension
being the imaginary time (inverse temperature) $\beta$.
Coarse-graining the network along $beta$ results in a 2D
projected entangled-pair operator (PEPO) with a finite bond
dimension D. The coarse-graining is performed by a tree
tensor network of isometries. The isometries are optimized
variationally --- taking into account full tensor environment --
- to maximize the accuracy of the PEPO. The algorithm is
applied to the isotropic quantum compass model on an
infinite square lattice near a symmetry-breaking phase
transition at finite temperature. From the linear susceptibility
in the symmetric phase and the order parameter in the
symmetry-broken phase the critical temperature is estimated
at $T_c=0.0606(4)J$, where J is the isotropic coupling
constant between S=1/2 pseudospins. The algorithm is also
applied to the two-dimensional Hubbard model on an infinite
square lattice. Benchmark results are obtained that are
consistent with the best dynamical mean field theory (DCA -
dynamical cluster approximation) and power series
expansion (NLCE - numerically linked cluster expansion) in
the regime of parameters where these more conventional
methods yield mutually consistent results.
