SciPost Physics

SciPost Phys. 3, 011 (2017) · published 12 August 2017

• doi: 10.21468/SciPostPhys.3.2.011
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Abstract

We propose using smeared boundary states $e^{-\tau H}|\cal B\rangle$ as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT.

• Cooper et al., Black hole microstate cosmology
  J. High Energ. Phys. 2019, 65 (2019) [Crossref]
• Tang et al., Universal entanglement signatures of interface conformal field theories
  Phys. Rev. B 109, L041104 (2024) [Crossref]
• Fukusumi et al., Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
  Phys. Rev. B 108, 085123 (2023) [Crossref]
• Nosaka et al., Quantum chaos, thermodynamics and black hole microstates in the mass deformed SYK model
  J. High Energ. Phys. 2020, 81 (2020) [Crossref]
• Lencsés et al., Chiral entanglement in massive quantum field theories in 1+1 dimensions
  J. High Energ. Phys. 2019, 177 (2019) [Crossref]
• Henderson et al., Entanglement action for the real-space entanglement spectra of chiral Abelian quantum Hall wave functions
  Phys. Rev. B 104, 195434 (2021) [Crossref]
• Ares et al., Scaling of the formation probabilities and universal boundary entropies in the quantum XY spin chain
  J. Stat. Mech. 2020, 083111 (2020) [Crossref]
• Konechny, RG boundaries and Cardy’s variational ansatz for multiple perturbations
  J. High Energ. Phys. 2023, 4 (2023) [Crossref]
• Li et al., Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
  Phys. Rev. B 110, 045118 (2024) [Crossref]
• Konechny, Properties of RG interfaces for 2D boundary flows
  J. High Energ. Phys. 2021, 178 (2021) [Crossref]
• Konechny, Critical Ising model with boundary magnetic field: RG interface and effective Hamiltonians
  J. High Energ. Phys. 2019, 1 (2019) [Crossref]
• Arildsen et al., Generalized Gibbs ensemble description of real-space entanglement spectra of (2+1) -dimensional chiral topological systems with SU(2) symmetry
  Phys. Rev. B 106, 035138 (2022) [Crossref]
• Pozsgay et al., Integrable Matrix Product States from boundary integrability
  SciPost Phys. 6, 062 (2019) [Crossref]
• Zou et al., Channeling Quantum Criticality
  Phys. Rev. Lett. 130, 250403 (2023) [Crossref]
• Piroli et al., What is an integrable quench?
  Nuclear Physics B 925, 362 (2017) [Crossref]
• Bhattacharya et al., Quantum quenches and thermalization in SYK models
  J. High Energ. Phys. 2019, 66 (2019) [Crossref]
• Prembabu et al., Boundary-deconfined quantum criticality at transitions between symmetry-protected topological chains
  Phys. Rev. B 109, L201112 (2024) [Crossref]
• Andrei et al., Boundary and defect CFT: open problems and applications
  J. Phys. A: Math. Theor. 53, 453002 (2020) [Crossref]
• Huang et al., Emergent Conformal Boundaries from Finite-Entanglement Scaling in Matrix Product States
  Phys. Rev. Lett. 132, 086503 (2024) [Crossref]
• Caceres et al., Page curves and bath deformations
  SciPost Phys. Core 5, 033 (2022) [Crossref]
• Guo, Entanglement properties of boundary state and thermalization
  J. High Energ. Phys. 2018, 44 (2018) [Crossref]
• Numasawa, Holographic complexity for disentangled states
  2020, 033B02 (2020) [Crossref]
• Fukusumi et al., Open spin chain realization of a topological defect in a one-dimensional Ising model: Boundary and bulk symmetry
  Phys. Rev. B 104, 125418 (2021) [Crossref]
• Konechny et al., On fusing matrices associated with conformal boundary conditions
  J. High Energ. Phys. 2024, 142 (2024) [Crossref]
• Choi et al., Remarks on boundaries, anomalies, and noninvertible symmetries
  Phys. Rev. D 108, 125005 (2023) [Crossref]
• Mertens, The Schwarzian theory — origins
  J. High Energ. Phys. 2018, 36 (2018) [Crossref]