Equivalent Hamiltonians

TL;DR

This paper characterizes when two Hamiltonians are equivalent, explains how to construct operators relating them, and introduces variational methods to select Hamiltonians with specific desirable properties.

Contribution

It provides a new framework for understanding Hamiltonian equivalence and introduces variational techniques for selecting optimal Hamiltonians from equivalence classes.

Findings

Conditions for Hamiltonian equivalence are characterized.

Methods for constructing operators relating equivalent Hamiltonians are discussed.

Variational methods for selecting Hamiltonians with desired features are introduced.

Abstract

I give a characterization of the conditions for two Hamiltonians to be equivalent, discuss the construction of the operators that relate equivalent Hamiltonians, and introduce variational methods that can select Hamiltonians with desirable features from the space of equivalent Hamiltonians.