Conformal field theories (CFT) play an important role in quantum field theories as they allow for exact studies that are hard to access without the conformal symmetries in place. A remarkable recent development is the application of conformal field theory to periodically driven systems, the so-called Floquet-driven CFTs. A number of recent works have found that there are classes of periodically driven (1+1)-dimensional CFTs that can be analytically solved, and that show both heating and non-heating phases, as well as unusual properties in terms of information scrambling. Hitherto, most results have focused on the dynamics of such models at stroboscopic times, i.e. samples taken at each period of the time evolution. In this paper, we consider time-evolution at arbitrary real times and derive formulas for the exact time-propagation of heating and non-heating classes of Floquet-driven CFTs. This requires a subtle treatment of non-stroboscopic time that leads to different interpretations in terms of curved space-time dynamics in these systems compared to previous results in the literature.
We propose a general method of cooling -- periodic driving generated by spatially deformed Hamiltonians -- and study it in general one-dimensional quantum critical systems described by a conformal field theory. Our protocol is able to efficiently cool a finite-temperature Gibbs (mixed) state down to zero temperature at prescribed sub-regions exponentially rapidly in Floquet time cycles. At the same time, entropy and energy are transferred and localized to the complementary regions that shrink with time. We derive these conclusions through an exact analytic solution of the full time evolution o…
In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a $\mathfrak{sl}_2$ sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the strob…
Given a $generic$ two-dimensional conformal field theory (CFT), we propose an analytically solvable setup to study the Floquet dynamics of the CFT, i.e., the dynamics of a CFT subject to a periodic driving. A complete phase diagram in the parameter space can be analytically obtained within our setup. We find two phases: the heating phase and the non-heating phase. In the heating phase, the entanglement entropy keeps growing linearly in time, indicating that the system keeps absorbing energy; in the non-heating phase, the entanglement entropy oscillates periodically in time, i.e., the system is…
Indian Institute of Technology, Kanpur（坎普尔印度理工学院）；University of Kentucky（肯塔基大学）；Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Indian Association for the Cultivation of Science（印度科学培育协会）
Classification of the non-equilibrium quantum many-body dynamics is a challenging problem in condensed matter physics and statistical mechanics. In this work, we study the basic question that whether a (1+1) dimensional conformal field theory (CFT) is stable or not under a periodic driving with $N$ non-commuting Hamiltonians. Previous works showed that a Floquet (or periodically driven) CFT driven by certain $SL_2$ deformed Hamiltonians exhibit both non-heating (stable) and heating (unstable) phases. In this work, we show that the phase diagram depends on the types of driving Hamiltonians. In …
We study the energy and entanglement dynamics of $(1+1)$D conformal field theories (CFTs) under a Floquet drive with the sine-square deformed (SSD) Hamiltonian. Previous work has shown this model supports both a non-heating and a heating phase. Here we analytically establish several robust and `super-universal' features of the heating phase which rely on conformal invariance but not on the details of the CFT involved. First, we show the energy density is concentrated in two peaks in real space, a chiral and anti-chiral peak, which leads to an exponential growth in the total energy. The peak lo…
We study the properties {of a conformal field theory} (CFT) driven periodically with a continuous protocol characterized by a frequency $ω_D$. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator $U$. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for $U$ that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases sep…
We investigate the light-cone-like spread of electronic correlations in a laser-driven quantum chain. Using the time-dependent density matrix renormalization group, we show that high-frequency driving leads to a Floquet-engineered spread velocity that determines the enhancement of density-density correlations when the ratio of potential and kinetic energies is effectively increased both by either a continuous or a pulsed drive. For large times we numerically show the existence of a Floquet steady state at not too long distances on the lattice with minimal heating. Intriguingly, we find a disco…
Dynamical Phases of Higher Dimensional Floquet CFTs
Indian Institute of Technology, Kanpur（坎普尔印度理工学院）；University of Kentucky（肯塔基大学）；Saha Institute of Nuclear Physics（萨哈核物理研究所）；Indian Association for the Cultivation of Science（印度科学培养协会）
Scrambling and thermalisation are topics of intense study in both condensed matter and high energy physics. Random unitary dynamics form a simple testing-ground for our theoretical understanding of these processes. In this work, we derive exact expressions for the large $q$ limiting behaviour of a selection of $n$-point correlation functions, out-of-time-ordered correlators (OTOCs), and their moments. In the process we find a general principle that breaks OTOCs into small and easy to calculate pieces, and which can likely be deployed in a more general context.
Out-of-time-order correlators (OTOCs) progressively play an important role in different fields of physics, particularly in the non-equilibrium quantum many-body systems. In this paper, we show that OTOCs can be used to prob the Floquet dynamical quantum phase transitions (FDQPTs). We investigate the OTOCs of two exactly solvable Floquet spin models, namely: Floquet XY chain and synchronized Floquet XY model. We show that the border of driven frequency range, over which the Floquet XY model shows FDQPT, signals by the global minimum of the infinite-temperature time averaged OTOC. Moreover, our …
A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes depending on the drive frequency. We compute the behavior of quantities including the entanglement entropy and Loschmidt echo, confirming analytic predictions from field theory by exact numerics on the transverse field Ising model, and demonstrate universality by adding non-integrable perturbations. The dynamics naturally separate into three regimes: a slow-driving limit, which has an interpretation as multiple quantum quenches …
While driven interacting quantum matter is generically subject to heating and scrambling, certain classes of systems evade this paradigm. We study such an exceptional class in periodically driven critical (1 + 1)-dimensional systems with a spatially modulated, but disorder-free time evolution operator. Instead of complete scrambling, the excitations of the system remain well-defined. Their propagation is analogous to the evolution along light cones in a curved space-time obtained by two Schwarzschild black holes. The Hawking temperature serves as an order parameter which distinguishes between …
Many-body correlations in Floquet steady-states: Frequency-resolved renormalization group of the driven Anderson impurity
RWTH Aachen University（亚琛工业大学）；Technische Universität Braunschweig（布伦瑞克工业大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构动力学研究所）
Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the potential to uncover a whole field of new phenomena, but the theoretical and numerical understanding becomes extremely difficult. We now propose a promising numerical method by generalizing the density matrix renormalization group to a superposition of Fourier components of periodically driven many-body systems using Floquet theory. With this method we can stu…
Intense time-periodic laser fields can transform the electronic structure of a solid into strongly modified Floquet-Bloch bands. While this suggests multiple pathways to induce electronic orders such as superconductivity or charge density waves, the possibility of preparing low-energy phases of Floquet Hamiltonians remains unclear because of the energy absorption at typical experimentally accessible driving frequencies. Here we investigate a realistic pathway towards laser control of electronic orders, which is the transient enhancement of fluctuating orders. Using a conserving Keldysh Green's…
We discuss eigenstate correlations for ergodic, spatially extended many-body quantum systems, in terms of the statistical properties of matrix elements of local observables. While the eigenstate thermalization hypothesis (ETH) is known to give an excellent description of these quantities, the butterfly effect implies structure beyond ETH. We determine the universal form of this structure at long distances and small eigenvalue separations for Floquet systems. We use numerical studies of a Floquet quantum circuit to illustrate both the accuracy of ETH and the existence of our predicted additiona…
Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a one-dimensional quantum gas, modeled by a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to solve and analyze the complete set of non-equilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when multiples of driving frequen…
We propose a method to study the time evolution of correlated electrons driven by an harmonic perturbation. Combining Floquet formalism to include the time-dependent field and Cluster Perturbation Theory to solve the many-body problem in the presence of short-range correlations, we treat the electron double dressing - by photons and by e-e interaction - on the same footing. We apply the method to an extended Hubbard chain at half occupation and we show that in the regime of small field frequency and for given values of field strength the zero-mode Floquet band is no more gapped and the system …
We propose to combine the Floquet formalism for systems in ac fields with the dynamical mean-field theory to study correlated electron systems periodically driven out of equilibrium by external fields such as intense laser light. This approach has a virtue that we can nonperturbatively include both the correlation effects and nonlinear effects due to the driving field, which is imperative in analyzing recent experiments for photoinduced phase transitions. In solving the problem, we exploit a general theorem that the Hamiltonian in a Floquet matrix form can be exactly diagonalized for single-ba…
Recent works on observation of discrete time-crystalline signatures throw up major puzzles on the necessity of localization for stabilizing such out-of-equilibrium phases. Motivated by these studies, we delve into a clean interacting Floquet system, whose quasi-spectrum conforms to the ergodic Wigner-Dyson distribution, yet with an unexpectedly robust, long-lived time-crystalline dynamics in the absence of disorder or fine-tuning. We relate such behavior to a measure zero set of nonthermal Floquet eigenstates with long-range spatial correlations, which coexist with otherwise thermal states at …
Three-body correlations, which arise between spin-polarized electrons in the first excited Landau level, are believed to play a key role in the emergence of enigmatic non-Abelian fractional quantum Hall (FQH) effects. Inspired by recent advances in Floquet engineering, we investigate periodic driving of anisotropic two-body interactions as a route for controllably creating and tuning effective three-body interactions in the FQH regime. We develop an analytic formalism to describe this Floquet-FQH protocol, which is distinct from previous approaches that instead focus on bandstructure engineeri…
We propose theoretically how unconventional superconducting pairing in a repulsively interacting Hubbard ladder can be enhanced via the application of a Floquet driving. Initially the Hubbard ladder is prepared in its charge-density-wave dominated ground state. A periodic Floquet drive is applied which modulates oppositely the energy offset of the two chains and effectively reduces the tunneling along the rungs. This modulation of the energy offsets might be caused by the excitation of a suitable phononic mode in solids or a superlattice modulation in cold atomic gases. We use state-of-the-art…
The topological phase transitions in static and periodically driven Kitaev chains are investigated by means of a renormalization group (RG) approach. These transitions, across which the numbers of static or Floquet Majorana edge modes change, are accompanied by divergences of the relevant Berry connections. These divergences at certain high symmetry points in momentum space form the basis of the RG approach, through which topological phase boundaries are identified as a function of system parameters. We also introduce several aspects to characterize the quantum criticality of the topological p…
We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct a parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this g…
Prethermalization, by introducing emergent quasiconserved observables, plays a crucial role in protecting Floquet many-body phases over exponentially long time, while the ultimate fate of such quasiconserved operators can signal thermalization to infinite temperature. To elucidate the properties of prethermal quasiconservation in many-body Floquet systems, here we systematically analyze infinite temperature correlations between observables. We numerically show that the late-time behavior of the autocorrelations unambiguously distinguishes quasiconserved observables from non-conserved ones, all…
Localisation-protected quantum order extends the idea of symmetry breaking and order in ground states to individual eigenstates at arbitrary energy. Examples include many-body localised static and $π$-spin glasses in Floquet systems. Such order is inherently dynamical and difficult to detect as the order parameter typically varies randomly between different eigenstates, requiring specific superpositions of eigenstates to be targeted by the initial state. We show that two-time correlators overcome this, reflecting the presence or absence of eigenstate order even in fully-mixed, $infinite$ $temp…
We demonstrate the existence of long-lived prethermalized states in the Mott insulating Hubbard model driven by periodic electric fields. These states, which also exist in the resonantly driven case with a large density of photo-induced doublons and holons, are characterized by a nonzero current and an effective temperature of the doublons and holons which depends sensitively on the driving condition. Focusing on the specific case of resonantly driven models whose effective time-independent Hamiltonian in the high-frequency driving limit corresponds to noninteracting fermions, we show that the…
We show that the dynamics resulting from preparing a one-dimensional quantum system in the ground state of two decoupled parts, then joined together and left to evolve unitarily with a translational invariant Hamiltonian (a local quench), can be described by means of quantum field theory. In the case when the corresponding theory is conformal, we study the evolution of the entanglement entropy for different bi-partitions of the line. We also consider the behavior of one- and two-point correlation functions. All our findings may be explained in terms of a picture, that we believe to be valid mo…
We consider the time evolution of mixed state correlation measures in two-dimensional conformal field theories, such as logarithmic negativity, odd entropy, and reflected entropy, after quantum quenches of various kinds. These correlation measures, in the holographic context, are all associated to the entanglement wedge cross section. We contrast various classes of conformal field theories, both rational and irrational (pure) conformal field theories. First, for rational conformal field theories, whose dynamics can be well described by the quasi-particle picture, we find all four quantities fo…
Altermagnetic Kondo Logic via Floquet Symmetry Conversion
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理系）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Jiangsu Physical Science Research Center, Nanjing University（南京大学江苏省物理科学研究中心）；Hefei National Laboratory, Hefei 230088, People’s Republic of China（合肥国家实验室）
Correlation-Induced Topological Reconstruction in a Periodically Driven Kagome Mott Insulator
National Institute of Science Education and Research（印度科学与教育国立研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国立中心）；Technische Universität Braunschweig（布伦瑞克工业大学）
We study states of one- and two-dimensional spin systems that are constructed as correlators within the conformal field theory of a massless, free boson. In one dimension, these are good variational wave functions for XXZ spin chains and they are similar to lattice Laughlin states in two dimensions. We show that their zz correlations are determined by a modification of the original free-boson theory. An expansion to quadratic order leads to a solvable, effective theory for the correlations in these states. Compared to the massless boson, there is an additional term in this effective theory tha…
