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First-order quantum phase transitions as condensations in the space of states. (arXiv:1712.05294v1 [quant-ph])
来源于:arXiv
We demonstrate that a large class of first-order quantum phase transitions
can be described as a condensation in the space of states. Given a system
having Hamiltonian $H=K+gV$, where $K$ and $V$ are hopping and potential
operators acting on the space of states $\mathbb{F}$, we may always write
$\mathbb{F}=\mathbb{F}_\mathrm{cond} \oplus \mathbb{F}_\mathrm{norm}$ where
$\mathbb{F}_\mathrm{cond}$ is the subspace which spans the eigenstates of $V$
with minimal eigenvalue and
$\mathbb{F}_\mathrm{norm}=\mathbb{F}_\mathrm{cond}^\perp$. If, in the
thermodynamic limit, $M_\mathrm{cond}/M \to 0$, where $M$ and $M_\mathrm{cond}$
are, respectively, the dimensions of $\mathbb{F}$ and
$\mathbb{F}_\mathrm{cond}$, the above decomposition of $\mathbb{F}$ becomes
effective, in the sense that the ground state energy per particle of the
system, $\epsilon$, coincides with the smaller between $\epsilon_\mathrm{cond}$
and $\epsilon_\mathrm{norm}$, the ground state energies per particle of the
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