Classical spin systems exhibit a variety of interesting phase transitions wherein there are sudden and dramatic changes in their macroscopic behavior as the temperature varies. In this talk, I will introduce quantum spin systems and study the relationship between entanglement and temperature. In particular, I will show that above a constant temperature, that depends only on the degree and locality of the interactions, there is literally zero entanglement. While the proof involves some unusual manipulations, I will attempt to explain it through analogies with classical approximate counting and sampling. This is based on joint work with Ainesh Bakshi, Allen Liu and Ewin Tang.
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