A bstract 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.
A bstract 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.
This paper investigates the dynamical phases of Floquet Conformal Field Theories (CFTs) in space-time dimensions greater than two. Building upon our previous work which introduced quaternionic representations for studying Floquet dynamics in higher-dimensional CFTs, we now explore more general square pulse drive protocols that go beyond a single SU(1,1) S U ( 1 , 1 ) subgroup. We demonstrate that, for multi-step drive protocols, the system exhibits distinct dynamical phases characterized by the nature of the eigenvalues of the quaternionic matrix representing time evolution in a single cycle, leading to different stroboscopic responses. Our analysis establishes a fundamental geometric interpretation where these dynamical phases directly correspond to the presence or absence of Killing horizons in the base space of the CFT and in a higher dimensional AdS space on which a putative dual lives. The heating phase is associated with a non-extremal horizon, the critical phase with an extremal horizon which disappears in the non-heating phase. We develop perturbative approaches to compute the Floquet Hamiltonians in different regimes and show, how tuning drive parameters can lead to horizons, providing a geometric framework for understanding heating phenomena in driven conformal systems.
This paper investigates the dynamical phases of Floquet Conformal Field Theories (CFTs) in space-time dimensions greater than two. Building upon our previous work [1] which introduced quaternionic representations for studying Floquet dynamics in higher dimensional CFTs, we now explore more general square pulse drive protocols that go beyond a single SU(1,1) subgroup. We demonstrate that, for multi-step drive protocols, the system exhibits distinct dynamical phases characterized by the nature of the eigenvalues of the quaternionic matrix representing time evolution in a single cycle, leading to different stroboscopic responses. Our analysis establishes a fundamental geometric interpretation where these dynamical phases directly correspond to the presence or absence of Killing horizons in the base space of the CFT and in a higher dimensional AdS space on which a putative dual lives. The heating phase is associated with a non-extremal horizon, the critical phase with an extremal horizon which disappears in the non-heating phase. We develop perturbative approaches to compute the Floquet Hamiltonians in different regimes and show, how tuning drive parameters can lead to horizons, providing a geometric framework for understanding heating phenomena in driven conformal systems.
A bstract We will explore the dynamical property of non-equilibrium phenomena induced by two-dimensional holographic conformal field theory (2d holographic CFT) Hamiltonian on the curved spacetime by studying the time dependence of the entanglement entropy and mutual information. Here, holographic CFT is the CFT having the gravity dual. We will start from the boundary and thermofield double states, evolve the systems in Euclidean time with the Hamiltonian on the curved background, and then evolve them in real-time with the same Hamiltonian. We found that the early- and late-time entanglement structure depends on the curved background, while the entanglement growth does not, and is linear. Furthermore, in the gravity dual for the thermofield double state, this entanglement growth is due to the linear growth of the wormhole, while in the one for the boundary state, it is due to the in-falling of the end of the world brane to the black hole. We discussed the low temperature system can be regarded as the dynamical system induced by the multi-joining quenches. We also discussed the effective description of the high temperature system, called line tension picture.
In this paper, we study the quantum information-geometric structure underlying short-time nonequilibrium relaxation in quantum Markov dynamics, and derive bounds on the nonequilibrium correction to the short-time relaxation curvature. These bounds generalize the information-geometric structure underlying Auconi's classical nonequilibrium relaxation inequality to quantum Markov dynamics. We consider the von Neumann relative entropy as quantum divergence, and parametrize perturbations through the Kubo-Mori map, which converts the second-order expansion of the relative entropy into the Bogoliubov-Kubo-Mori (BKM) inner product at all temperatures. For a quantum Markov semigroup with full-rank stationary state, the induced tangent-space generator admits a canonical decomposition into a BKM-symmetric and a BKM-antisymmetric part, and the leading nonequilibrium curvature correction takes the exact form of the expectation of the commutator between the dissipative and the transport part of the generator. This correction is bounded by the product of a BKM-symmetric dissipative activity and a transport-sector activity. The bound is verified on a noncommuting qubit model and a driven-dissipative qutrit, and the full chain is confirmed numerically on a two-dimensional Fokker-Planck steady state. In the high-temperature and overdamped limit the quantum formula reduces to the position-space Fokker-Planck expression and reproduces Auconi's entropy-production bound with the correct temperature factor.
We unify two emergent aspects of quantum theory within a single information-geometricframework based on the Araki relative entropy and the associated Bogoliubov–Kubo–Mori(BKM) metric on a von Neumann algebra state manifold.First, we show that in the commutative reduction to a spatial density subalgebra, theBKM metric becomes the classical Fisher information metric. Its trace gives, after a singlenormalization choice, the expectation value of the Bohmian quantum potential, and thecorresponding Bohmian trajectories arise as Jacobi geodesics of a conformally related metric.The guidance equation is then recovered from the polar decomposition of states satisfyingthe emergent Schr¨odinger equation.Second, we show that the modular flow of the reference state yields the Heisenbergand von Neumann equations, and that the physical Schr¨odinger equation follows under astandard unitary state implementation. In the finite regulated K¨ahler sector, geometricprequantization of the BKM state manifold leads to a discrete horizon area spectrum and touncertainty relations, with an induced gravitational coupling derived from the Seeley–DeWittcoefficient [1].No continuum limit is taken, and no identification with the observed Newton constantis assumed. The results exhibit a common information-geometric framework for Bohmianmechanics, quantum dynamics, and emergent gravitational structures.
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by their conformal symmetry. We reveal the underlying quantum geometry by considering finite many-body systems driven by time-dependent conformal transformations. For small deformations, perturbation theory predicts absorption rates and linear responses that probe the quantum geometric tensor. For arbitrarily large but adiabatic deformations, we show that periodic drives give rise to nontrivial return amplitudes involving the quantum metric, beyond the familiar leading order that only features a Berry phase. The former is less sensitive to decoherence than the latter, so it can provide robust experimental signatures of our predictions. Our field-theoretic findings are universal, comprising general relations between measurable quantities and quantum geometry that only depend on the emergent effective description. This is supported both by numerical simulations of gapless lattice models, and by exact results for quantum dynamics under certain Floquet drives, probing the full dynamical parameter space.