Abstract
Driven quantum systems exhibit a large variety of interesting and sometimes exotic phenomena. Of particular interest are driven conformal field theories (CFTs) which describe quantum many-body systems at criticality. In this paper, we develop both a spacetime and a quantum information geometry perspective on driven 2d CFTs. We show that for a large class of driving protocols the theories admit an alternative but equivalent formulation in terms of a CFT defined on a spacetime with a time-dependent metric. We prove this equivalence both in the operator formulation as well as in the path integral description of the theory. A complementary quantum information geometric perspective for driven 2d CFTs employs the so-called Bogoliubov-Kubo-Mori (BKM) metric, which is the counterpart of the Fisher metric of classical information theory, and which is obtained from a perturbative expansion of relative entropy. We compute the BKM metric for the universal sector of Virasoro excitations of a thermal state, which captures a large class of driving protocols, and find it to be a useful tool to classify and characterize different types of driving. For Möbius driving by the SL(2, ℝ) subgroup, the BKM metric becomes the hyperbolic metric on the disk. We show how the non-trivial dynamics of Floquet driven CFTs is encoded in the BKM geometry via Möbius transformations. This allows us to identify ergodic and non-ergodic regimes in the driving. We also explain how holographic driven CFTs are dual to driven BTZ black holes with evolving horizons. The deformation of the black hole horizon towards and away from the asymptotic boundary provides a holographic understanding of heating and cooling in Floquet CFTs.
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Acknowledgments
We thank Johanna Erdmenger, Marius Gerbershagen, Antti Kupiainen, Diego Liska, R. Loganayagam and Anna-Lena Weigel for useful discussions during the completion of this work. JdB is supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013), ERC Grant agreement ADG 834878. VG acknowledges the postdoctoral program at ICTS for funding support through the Department of Atomic Energy, Government of India, under project no. RTI4001. JK is supported by the Osk. Huttunen foundation and by the Magnus Ehrnrooth foundation. EKV’s research has been conducted within the framework of InstituteQ — the Finnish Quantum Institute.
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de Boer, J., Godet, V., Kastikainen, J. et al. Quantum information geometry of driven CFTs. J. High Energ. Phys. 2023, 87 (2023). https://doi.org/10.1007/JHEP09(2023)087
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DOI: https://doi.org/10.1007/JHEP09(2023)087