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In physics, the Pauli–Lubanski pseudovector is an operator defined from the momentum and angular momentum, used in the quantum-relativistic description of angular momentum. It is named after Wolfgang Pauli and Józef Lubański. [1] It describes the spin states of moving particles. [2]
The dimension of the on-site basis is 2, because the state of each spin can be described as a superposition of spin-up and spin-down, denoted | and | . The full system has dimension 2 N {\displaystyle 2^{N}} , and the Hamiltonian represented as a matrix has size 2 N × 2 N {\displaystyle 2^{N}\times 2^{N}} .
In what follows we will show how to map a 1D spin chain of spin-1/2 particles to fermions. Take spin-1/2 Pauli operators acting on a site of a 1D chain, +,,.Taking the anticommutator of + and , we find {+,} =, as would be expected from fermionic creation and annihilation operators.
The conventional definition of the spin quantum number is s = n / 2 , where n can be any non-negative integer. Hence the allowed values of s are 0, 1 / 2 , 1, 3 / 2 , 2, etc. The value of s for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the spin ...
Thus, the spin raising and lowering operators + = + and =, so that [+,] =, correspond (in the sense detailed below) to the bosonic annihilation and creation operators, respectively. The precise relations between the operators must be chosen to ensure the correct commutation relations for the spin operators, such that they act on a finite ...
The expected value of a spin measurement on a photon is then | ^ | = | | | |. An operator S has been associated with an observable quantity, the spin angular momentum. The eigenvalues of the operator are the allowed observable values.
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
Snake DMRG program: open source DMRG, tDMRG and finite temperature DMRG program written in C++ ; CheMPS2: open source (GPL) spin-adapted DMRG code for ab initio quantum chemistry written in C++ ; Block: open source DMRG framework for quantum chemistry and model Hamiltonians. Supports SU(2) and general non-Abelian symmetries. Written in C++.