Many-body Hilbert space scarring on a superconducting processor

Application of a renormalization algorithm in Hilbert space to the study of many-body quantum systems

We implement an algorithm which is aimed to reduce the number of basis states spanning the Hilbert space of quantum many-body systems. We test the efficiency of the procedure by working out and analyzing the spectral properties of strongly correlated and frustrated quantum spin systems. The role and importance of symmetries are investigated. PACS numbers: 03.65.-w, 02.70.-c, 68.65.-k, 71.15Nc

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

Hilbert space renormalization for the many-electron problem.

Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces a...

Completely Positive Projections on a Hilbert Space

The purpose of this paper is to prove that a completely positive projection on a Hilbert space associated with a standard form of a von Neumann algebra induces the existence of a conditional expectation of the von Neumann algebra with respect to a normal state, and we consider the application to a standard form of an injective von Neumann algebra.

Quantum physics on a general Hilbert space