Geometric approach to inhomogeneous Floquet systems

Abstract

We present a new geometric approach to Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. It is based on an exact correspondence with dynamical systems on the circle that we establish and use to prove existence of (non)heating phases characterized by the (absence) presence of fixed or higher-periodic points of coordinate transformations encoding the time evolution: Heating corresponds to energy and excitations concentrating exponentially fast at unstable such points while nonheating to pseudoperiodic motion. We show that the heating rate (serving as the order parameter for transitions between these two) can have cusps, even within the overall heating phase, and that there is a rich structure of phase diagrams with different heating phases distinguishable through kinks in the entanglement entropy, reminiscent of Lifshitz phase transitions. Our geometric approach generalizes previous results for a subfamily of similar systems that used only the sl(2) algebra to general smooth deformations that require the full infinite-dimensional Virasoro algebra, and we argue that it has wider applicability, even beyond conformal field theory.

Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics

“…The dynamically stable (unstable) regime then corresponds to the timelike (spacelike) regime. Similar conclusions hold in Floquet deformed conformal field theory, where the non-heating (heating) phase corresponds to the timelike (spacelike) regime [39,40]. Among all representations of SU (1,1) group, it is worth mentioning the non-Hermitian one, as shown by the last row of Table I.…”

Floquet conformal field theories with generally deformed Hamiltonians

“…Note added: During the preparation of this work, we noted a related work [63], which also studies Floquet CFTs beyond the SL 2 deformation, while concrete examples are different. We thank the authors for their communications.…”

Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches

“…( 37) are small, subjected to the condition |x| λ T0 . The arbitrary coefficients φ ± highlight the degeneracy of the gravitational zero modes (37) which parametrizes the anomalous isothermal surfaces in the metric space. Note that in the case of a finite system with periodic boundary conditions, imposing the smoothness of the gravitational potential allows to recover a unique gravitational potential φ(x) = φ 0 = const.…”

“…Finally, we focus on a periodic sequence of temperature quenches applied to a relativistic fermions (Fig 1(d)). This thermal procedure induces a Floquet state recently described within Floquet conformal field theory [33][34][35][36][37][38]. While the total energy of this state increases exponentially, it concentrates on a few points [35,36] which effectively behave as black holes [36]: the rate of increase of their energy is strongly corrected by quantum anomaly corrections, and the energy density is negative in their vicinity as in a black hole atmosphere.…”