Probing Topology of Gaussian Mixed States by the Full Counting Statistics
arxiv(2024)
摘要
Topological band theory has been studied for free fermions for decades, and
one of the most profound physical results is the bulk-boundary correspondence.
Recently a trend in topological physics is extending topological classification
to mixed state. Here, we focus on Gaussian mixed states where the modular
Hamiltonians of the density matrix are quadratic free fermion models and can be
classified by topological invariants. The bulk-boundary correspondence is then
manifested as stable gapless modes of the modular Hamiltonian and degenerate
spectrum of the density matrix. In this letter, we show that these gapless
modes can be detected by the full counting statistics, mathematically described
by a function introduced as F(θ). We show that a divergent derivative at
θ = π probes the gapless modes in the modular Hamiltonian. We can
introduce a topological indicator whose quantization to unity senses
topologically nontrivial mixed states. We present the physical intuition of
these results and also demonstrate these results with concrete models in both
one- and two-dimensions. Our results pave the way for revealing the physical
significance of topology in mixed states.
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