Certified algorithms for equilibrium states of local quantum Hamiltonians.

ABSTRACT: Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to result in undecidable problems. Using a finite-size scaling of algorithms devised for finite systems often fails due to the lack of certified convergence bounds for this limit. In this work, we design certified algorithms for computing expectation values of observables in the equilibrium states of local quantum Hamiltonians, both at zero and positive temperature. Importantly, our algorithms output rigorous lower and upper bounds on these values. This allows us to show that expectation values of local observables can be approximated in finite time, contrasti

SUBMITTER: Fawzi H 

PROVIDER: S-EPMC11349919 | biostudies-literature | 2024 Aug

REPOSITORIES: biostudies-literature