## SciPost Submission Page

# Conformal field theory on top of a breathing one-dimensional gas of hard core bosons

### by Paola Ruggiero, Yannis Brun, Jérome Dubail

### Submission summary

As Contributors: | Yannis Brun · Jerome Dubail · Paola Ruggiero |

Arxiv Link: | https://arxiv.org/abs/1901.08132v3 |

Date accepted: | 2019-04-11 |

Date submitted: | 2019-04-04 |

Submitted by: | Brun, Yannis |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Condensed Matter Physics - Theory |

### Abstract

The recent results of [J. Dubail, J.-M. St\'ephan, J. Viti, P. Calabrese, Scipost Phys. 2, 002 (2017)], which aim at providing access to large scale correlation functions of inhomogeneous critical one-dimensional quantum systems -- e.g. a gas of hard core bosons in a trapping potential -- are extended to a dynamical situation: a breathing gas in a time-dependent harmonic trap. Hard core bosons in a time-dependent harmonic potential are well known to be exactly solvable, and can thus be used as a benchmark for the approach. An extensive discussion of the approach and of its relation with classical and quantum hydrodynamics in one dimension is given, and new formulas for correlation functions, not easily obtainable by other methods, are derived. In particular, a remarkable formula for the large scale asymptotics of the bosonic $n$-particle function $\left< \Psi^\dagger (x_1,t_1) \dots \Psi^\dagger (x_n,t_n) \Psi(x_1',t_1') \dots \Psi(x_n',t_n') \right>$ is obtained. Numerical checks of the approach are carried out for the fermionic two-point function -- easier to access numerically in the microscopic model than the bosonic one -- with perfect agreement.

###### Current status:

### Author comments upon resubmission

Manuscript modified according to the referees recommendations, see answers to report 1 and 2.

### List of changes

-upper-case letters in "Galilean", "Lagrangian", "Euclidean", etc. fixed.

-slight expansion of the introduction to emphasize that multi-point functions at equal time in classical hydrodynamics would be zero

-discussion of LDA/hydrostatics added in section 2.2

-reorganization of sections 2.4, 2.5, 2.6 in order to clarify some technical aspects about Jacobian factors in the calculation of CFT correlation functions

-formatting of long equations (for instance (68)) fixed

-some typos fixed