Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.
Krylov Complexity and Mixed-State Phase Transition
The Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Graduate School of Informatics, Nagoya University（名古屋大学情报学研究科）；Department of Physics, College of Humanities and Sciences, Nihon University（日本大学人文学部理科系物理学教室）
Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University（莫斯科国立大学理论与数学物理研究所）；Department of Physics, Indian Institute of Technology Roorkee（鲁尔基印度理工学院物理系）
Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas
National Taiwan University（国立台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；National Sun Yat-sen University（国立中山大学）；Gwangju Institute of Science and Technology（光州科学技术院）
Krylov Complexity Under Hamiltonian Deformations and Toda Flows
University of Luxembourg（卢森堡大学）；Mie University（三重大学）；Kanazawa University（金泽大学）；Vrije Universiteit Brussel (VUB)（布鲁塞尔自由大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科理论与数学科学中心）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
Julius-Maximilians-Universität Würzburg（维尔茨堡大学）；Institute for Theoretical Physics and Astrophysics（理论物理与天体物理研究所）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群 ct.qmat）；Perimeter Institute for Theoretical Physics（理论物理珀金斯研究所）；Yukawa Institute for Theoretical Physics（汤川理论物理研究所）；Kyoto University（京都大学）；Center for Gravitational Physics and Quantum Information（引力物理与量子信息研究中心）
Holographic Krylov Complexity for Conformal Quiver Gauge Theories
Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University（莫斯科国立大学理论与数学物理研究所）；Centre for Quantum Fields and Gravity, Department of Physics, Swansea University（斯旺西大学物理系量子场与引力中心）；Instituto de Física Teórica, UNESP-Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）；Department of Physics, Indian Institute of Technology Roorkee（鲁尔基印度理工学院物理系）
Geometric-phase control of Krylov complexity in adiabatic dynamics
Beihang University（北京航空航天大学）；China West Normal University（西华师范大学）；Jishou University（吉首大学）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武研究院）
Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory
School of Physics and Astronomy, China West Normal University（西华师范大学物理与天文学院）；Department of Physics, College of Physics, Mechanical and Electrical Engineering, Jishou University（吉首大学物理机电工程学院物理学系）；Center for Gravitational Physics, Department of Space Science, Beihang University（北京航空航天大学空间科学学院引力物理中心）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武协作研究中心）
Krylov Complexity for Open Quantum System: Dissipation and Decoherence
Indian Institute of Technology, Gandhinagar（印度理工学院甘德纳格尔分校）；University of Cape Town（开普敦大学）；The National Institute for Theoretical and Computational Sciences（理论与计算科学国家研究所）
Explicit Connections Between Krylov and Nielsen Complexity
The International Solvay Institutes（索尔维国际研究所）；School of Physics, Peking University（北京大学物理学院）；Center of High Energy Physics, Peking University（北京大学高能物理中心）
Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Gwangju Institute of Science and Technology（光州科学技术院）；National Institute of Technology, Yuge College（国立丰桥技术大学宇部学院）
