How to write reduced density matrix of a single site - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-09-17T17:04:08Z https://physics.stackexchange.com/feeds/question/434279 https://creativecommons.org/licenses/by-sa/4.0/rdf https://physics.stackexchange.com/q/434279 0 How to write reduced density matrix of a single site Luqman Saleem https://physics.stackexchange.com/users/140141 2018-10-13T13:35:12Z 2018-10-13T17:04:27Z <p>To clear my concepts about density matrices, I am trying to solve the following system as an example.</p> <p>The density matrix is defined as <span class="math-container">$$\rho=|\psi\rangle \langle \psi |$$</span> where <span class="math-container">$|\psi\rangle$</span> is ground state of the system. Let we have a chain of fermions with hopping strength between two nearest neighbor sites <span class="math-container">$t$</span> i.e. <span class="math-container">$$--\bullet--\bullet--\bullet--\bullet--\bullet--$$</span> The Hamiltonian can be written as <span class="math-container">$$H=t\sum_n c_n^\dagger c_{n+1} + h.c.$$</span></p> <p>I want to write reduce density matrix for <strong>single site (<span class="math-container">$\rho_1$</span>)</strong> and <strong>two sites (<span class="math-container">$\rho_2$</span>)</strong>.</p> <p>I do not understand how can I write reduced matrices for both cases.</p>