Estimating eigenvalues for lattice hamiltonian models

Bekzod I. Bahronov, Tulkin Husenovich Rasulov, Mutti-Ur Rehman

Ammar Daskin, Sabre Kais

Mukhiddin Ishkobilovich Muminov, Hagen Neidhardt, Tulkin Husenovich Rasulov

A lattice model of radiative decay (so-called spin-boson model) of a two level atom and at most two photons is considered. The location of the essential spectrum is described. For any coupling constant, the finiteness of the number of eigenvalues below the bottom of its essential spectrum is proved. The results are obtained by considering a more general model H for which the lower bound of its essential spectrum is estimated. Conditions which guarantee the finiteness of the number of eigenvalues of H below the bottom of its essential spectrum are found. It is shown that the discrete spectrum might be infinite if the parameter functions are chosen in a special form.

Abhishek Karna, Hansen S. Wu, Shailesh Chandrasekharan A +1 more

Chris J. Hamer

Hamiltonian eigenvalues are calculated for the (2+1)D Ising model on lattices up to 5*5 sites. Finite-size scaling techniques are used to estimate the critical coupling x c =0.329+or-0.001, and index v=0.635+or-0.005. The prospects are discussed for further applications of these methods in three and four dimensions.

Peter Majcen, Giovanni Cataldi, Pietro Silvi +1 more

We show how to optimally reduce the local Hilbert basis of lattice quantum many-body (QMB) Hamiltonians. The basis truncation exploits the most relevant eigenvalues of the estimated single-site reduced density matrix (RDM). It is accurate and numerically stable across different model phases, even close to quantum phase transitions. We apply this procedure to different models, such as the Sine-Gordon model, the $φ^{4}$ theory, and lattice gauge theories, namely Abelian $\mathrm{U}(1)$ and non-Abelian $\mathrm{SU}(2)$, in one and two spatial dimensions. Our results reduce state-of-the-art estimates of computational resources for classical and quantum simulations.