TY - JOUR

T1 - RG boundaries and Cardy’s variational ansatz for multiple perturbations

AU - Konechny, Anatoly

N1 - Funding Information:
I would like to thank Gabor Takács and Des Johnston for comments on the draft version of the paper. This work was supported by EPSRC grant “Renormalisation group interfaces in Tricritical Ising Model”, grant reference number: EP/W010283/1. All numerical calculations were done using Wolfram Mathematica 13.1.
Publisher Copyright:
© 2023, The Author(s).

PY - 2023/11/2

Y1 - 2023/11/2

N2 - We consider perturbations of 2D CFTs by multiple relevant operators. The massive phases of such perturbations can be labeled by conformal boundary conditions. Cardy’s variational ansatz approximates the vacuum state of the perturbed theory by a smeared conformal boundary state. In this paper we study the limitations and propose generalisations of this ansatz using both analytic and numerical insights based on TCSA. In particular we analyse the stability of Cardy’s ansatz states with respect to boundary relevant perturbations using bulk-boundary OPE coefficients. We show that certain transitions between the massive phases arise from a pair of boundary RG flows. The RG flows start from the conformal boundary on the transition surface and end on those that lie on the two sides of it. As an example we work out the details of the phase diagram for the Ising field theory and for the tricritical Ising model perturbed by the leading thermal and magnetic fields. For the latter we find a pair of novel transition lines that correspond to pairs of RG flows. Although the mass gap remains finite at the transition lines, several one-point functions change their behaviour. We discuss how these lines fit into the standard phase diagram of the tricritical Ising model. We show that each line extends to a two-dimensional surface ξσ,c in a three coupling space when we add perturbations by the subleading magnetic field. Close to this surface we locate symmetry breaking critical lines leading to the critical Ising model. Near the critical lines we find first order phase transition lines describing two-phase coexistence regions as predicted in Landau theory. The surface ξσ,c is determined from the CFT data using Cardy’s ansatz and its properties are checked using TCSA numerics.

AB - We consider perturbations of 2D CFTs by multiple relevant operators. The massive phases of such perturbations can be labeled by conformal boundary conditions. Cardy’s variational ansatz approximates the vacuum state of the perturbed theory by a smeared conformal boundary state. In this paper we study the limitations and propose generalisations of this ansatz using both analytic and numerical insights based on TCSA. In particular we analyse the stability of Cardy’s ansatz states with respect to boundary relevant perturbations using bulk-boundary OPE coefficients. We show that certain transitions between the massive phases arise from a pair of boundary RG flows. The RG flows start from the conformal boundary on the transition surface and end on those that lie on the two sides of it. As an example we work out the details of the phase diagram for the Ising field theory and for the tricritical Ising model perturbed by the leading thermal and magnetic fields. For the latter we find a pair of novel transition lines that correspond to pairs of RG flows. Although the mass gap remains finite at the transition lines, several one-point functions change their behaviour. We discuss how these lines fit into the standard phase diagram of the tricritical Ising model. We show that each line extends to a two-dimensional surface ξσ,c in a three coupling space when we add perturbations by the subleading magnetic field. Close to this surface we locate symmetry breaking critical lines leading to the critical Ising model. Near the critical lines we find first order phase transition lines describing two-phase coexistence regions as predicted in Landau theory. The surface ξσ,c is determined from the CFT data using Cardy’s ansatz and its properties are checked using TCSA numerics.

KW - Boundary Quantum Field Theory

KW - Field Theories in Lower Dimensions

KW - Phase Transitions

KW - Renormalization Group

UR - http://www.scopus.com/inward/record.url?scp=85175718932&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2023)004

DO - 10.1007/JHEP11(2023)004

M3 - Article

AN - SCOPUS:85175718932

SN - 1126-6708

VL - 2023

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 11

M1 - 4

ER -