Hamiltonian deformations in quantum mechanics, $T\bar{T}$, and SYK

Abstract

Motivated by $T\bar{T}$, we introduce and study a wide class of solvable deformations of quantum-mechanical theories. These deformations map the Hamiltonian to a function of itself. We solve these theories by computing all finite-temperature correlation functions of the deformed theory in terms of the correlators of the undeformed theory. Applications to AdS/CFT, SYK, and the Schwarzian theory are considered. We write down the deformed Schwarzian action for an arbitrary Hamiltonian deformation and find that the maximal Lyapunov exponent is unchanged.

arXiv comment30 pages + appendices. 3 figures. v2: Typos corrected, updated and corrected the discussion in section 2.3 and references added

References in corpus (28)

• Supersymmetry and Quantum Mechanics
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Black Holes and Random Matrices
• Fermionic Localization of the Schwarzian Theory
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• Quantum effective action from the AdS/CFT correspondence
• Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass
• Multi-Matrix Models and Tri-Sasaki Einstein Spaces
• $T\bar{T}$ Partition Function from Topological Gravity
• JT gravity as a matrix integral
• Numerical study of fermion and boson models with infinite-range random interactions
• Holography at finite cutoff with a $T^2$ deformation
• Conformal quantum mechanics as the CFT${}_1$ dual to AdS${}_2$
• $T\overline{T}$ in AdS${}_2$ and Quantum Mechanics
• Infrared Realization of dS${}_2$ in AdS${}_2$
• $T\bar{T}$ deformed CFT as a non-critical string
• De Sitter Horizons & Holographic Liquids
• Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs
• Does the SYK model have a spin glass phase?
• $T\bar{T}$ deformations and integrable spin chains
• $T\bar{T}$-deformation and long range spin chains
• A Solvable Deformation of Quantum Mechanics
• Replica-nondiagonal solutions in the SYK model

Cited by in corpus (52)

• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Global symmetry, Euclidean gravity, and the black hole information problem
• Explorations of Non-Perturbative JT Gravity and Supergravity
• Limits of JT gravity
• Classifying boundary conditions in JT gravity: from energy-branes to $\alpha$-branes
• Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models
• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• Gravitational path integral from the $T^2$ deformation
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Constructing AdS_2 flow geometries
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Nonperturbative effects and resurgence in JT gravity at finite cutoff
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Field Theory of Interacting Boundary Gravitons
• $T\bar{T}+{\Lambda }_2$ Deformed CFT on the Stretched dS${}_3$ Horizon
• Finite-cutoff JT gravity and self-avoiding loops
• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• Cutoff $\mathrm{Ad}{\mathrm{S}}_3$ versus $\mathrm{T}\bar{\mathrm{T}}$ $\mathrm{CF}{\mathrm{T}}_2$ in the large central charge sector: correlators of energy-momentum tensor
• Interpolating geometries and the stretched dS${}_2$ horizon
• Sequential Flows by Irrelevant Operators
• $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
• $T\bar{T}$-flow effects on torus partition functions
• Spacetime as a quantum circuit
• Unitarity breaking in self-averaging spectral form factors
• Building Tensor Networks for Holographic States
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• S-duality in $T\bar{T}$-deformed CFT
• Quantization of the ModMax Oscillator
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• Flat space gravity at finite cutoff
• $T\bar{T}$ and $J\bar{T}$ Deformations in Quantum Mechanics
• Flows in the Space of Interacting Chiral Boson Theories
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• $T\bar{T}$ deformation of random matrices
• $T\bar{T}+{\Lambda }_2$ from a 2d gravity path integral
• $T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions
• $T\overline{T}$-deformed free energy of the Airy model
• Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
• Holographic n-partite Information in Hyperscaling Violating Geometry
• (Half) Wormholes under Irrelevant Deformation
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs
• On SYK traversable wormhole with imperfectly correlated disorders
• $T\bar{T}$ deformations and the pp wave correspondence
• $T\bar{T}$ deformation on non-Hermitian two coupled SYK model
• On Current-Squared Flows and ModMax Theories
• $T\bar{T}$ deformation of Calogero-Sutherland model via dimensional reduction
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows
• Cost of holographic path integrals