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1

Is there any good definition of many body localization? Let's start with single-body (Anderson) localization. There, in a non-interacting system, a particle (e.g. an electron) becomes localized due to destructive interference with itself. This interference is induced by the presence of disorder. Turning interactions on brings us to the realm of ...

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I'm not completely sure why you think that the bosonic mode fails, but it seems to me that the answer is definitely yes. The system is solvable in both the finite-dimensional and the bosonic case; the problem with the bosonic case is that the solution is ugly, because the hamiltonian is ugly. Take a hamiltonian of the form  H=E_0S+S\sum_k (g_k ...

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DFT is based on two important theorems: (1) Hohenberg & Kohn: the potential and the density are connected by a one-to-one map (2) Kohn & Sham: there is always a non-interacting reference system (map: V_xc: non-interacting <-> interacting problem) having the same density as the interacting one. In a nutshell: the potential and the density of the ...

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As suggested by WSA aka RV, I copy my comments into a (partial) answer. The key point is that the theorem says "for any given $\psi$ there exist two bases $\{i_A\}$ and $\{i_B\}$ such that...". This means that the choice of the bases depends on the vector $\psi$ we are considering. So there is not an $n$ dimensional common basis that span the whole ...

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Denote $|\psi\rangle = \sum\limits_{i = 1}^m \sum\limits_{j = 1}^n h_{ij} |ij\rangle$ as $|\psi\rangle \rightarrow H = (h_{ij})_{m \times n}$. Then we have the following lemma: Lemma: Define matrix $U$ (in the original basis) as a new setting for Alice and $V$ for Bob, then a state $|\psi\rangle$ in the basis of the new settings is $U^* H V^\dagger$. ...

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