We consider a family of quantum spin systems which includes, as special cases, the ferromagnetic X Y model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any model in this family can be efficiently approximated to a given relative error ∊ using a classical randomized algorithm with runtime polynomial in ∊-1, system size, and inverse temperature. As a consequence, we obtain a polynomial time algorithm which approximates the free energy or ground energy to a given additive error. We first show how to approximate the partition function by the perfect matching sum of a finite graph with positive edge weights. Although the perfect matching sum is not known to be efficiently approximable in general, the graphs obtained by our method have a special structure which facilitates efficient approximation via a randomized algorithm due to Jerrum and Sinclair.
Physical Review Letters
- Pub Date:
- September 2017
- Quantum Physics;
- Condensed Matter - Strongly Correlated Electrons;
- Computer Science - Computational Complexity
- Phys. Rev. Lett. 119, 100503 (2017)