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Using microscopic price models based on Hawkes processes, it has been shownthat under some no-arbitrage condition, the high degree of endogeneity ofmarkets together with the phenomenon of metaorders splitting generate roughHeston-type volatility at the macroscopic scale. One additional importantfeature of financial dynamics, at the heart of several influential works ineconophysics, is the so-called feedback or Zumbach effect. This essentiallymeans that past trends in returns convey significant information on futurevolatility. A natural way to reproduce this property in microstructure modelingis to use quadratic versions of Hawkes processes. We show that after suitablerescaling, the long term limits of these processes are refined versions ofrough Heston models where the volatility coefficient is enhanced compared tothe square root characterizing Heston-type dynamics. Furthermore the Zumbacheffect remains explicit in these limiting rough volatility models.

From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect