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

Abstract

The recent results of [J. Dubail, J.-M. Stéphan, 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 \boldsymbol{n}𝐧-particle function \boldsymbol{\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.

Fine structure of heating in a quasiperiodically driven critical quantum system

“…where T 00 (x) is the energy density of the CFT. These inhomogeneous conformal field theories have been studied in the context of quantum quenches [34][35][36][37][38] and out-of-equilibrium dynamics [39,40]. In terms of the Virasoro generators L n and L n , in the Euclidean framework with imaginary time τ , the uniform (2).…”

Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps

“…where χ F may be considered as the corresponding susceptibility. The cancellation of the linear term in the expansion (15) is essentially related to the fact that the fidelity is bounded, i.e., 0 ≤ F ≤ 1. The fidelity susceptibility gives a quantitative idea of the speed of the flow of ground states within the global Hilbert space of the quantum states, when varying the trap size.…”

“…By expanding it as in Eq. (15), we obtain the corresponding susceptibility, which is given by FIG. 1: The fidelity susceptibility for two-dimensional harmonic traps with respect to a variation of the trap size ℓ.…”

“…Some aspects related to this issue have been discussed in the literature, such as the time dependence of the particle density and fixed-time correlation functions, spatial entanglement, etc..., in particular for one-dimensional systems, see, e.g., Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Entanglement spreading and quasiparticle picture beyond the pair structure

“…Above, N can be any real number, but later on we restrict to the case of integers N . In general, entanglement entropies are not easy to compute: apart from free systems [37], progresses can be made in critical systems taking advantage of conformal invariance [38,39] with extensions to out-of-equilibrium setups [33] and recently to inhomogeneous cases [40][41][42][43][44]. In particular, bringing a low-entanglement state out-of-equilibrium will result in the entanglement growing with time: a powerful method to describe (the scaling part of) the entanglement spreading is provided by the quasi-particle picture.…”