Universality of fast quenches from the conformal perturbation theory

Abstract

Abstract:We consider global quantum quenches, a protocol when a continuous field theoretic system in the ground state is driven by a homogeneous time-dependent external interaction. When the typical inverse time scale of the interaction is much larger than all relevant scales except for the UV-cutoff the system's response exhibits universal scaling behavior. We provide both qualitative and quantitative explanations of this universality and argue that physics of the response during and shortly after the quench is governed by the conformal perturbation theory around the UV fixed point. We proceed to calculate the response of one and two-point correlation functions confirming and generalizing universal scalings found previously. Finally, we discuss late time behavior after the quench and argue that all local quantities will equilibrate to their thermal values specified by an excess energy acquired by the system during the quench.

On quantum quenches at one loop

“…The universal scaling behavior has further been shown to exist in the context of free field theories [23][24][25], and it was argued that the same scaling emerges in any quantum field theory with a UV fixed point provided that the quench rate is sufficiently fast [26][27][28][29]. Finally, [29,30] used the conformal perturbation theory technique to generalize and extend these results. In particular, the universal scaling behavior of the correlation functions of spinless, spin-1 2 and spin-1 primaries was derived.…”

“…It was argued in [26][27][28][29] that if the quench rate is large compared to the other physical scales, then evolution of the system is dominated by the Gaussian fixed point. In particular, the linear response of φ 2 vanishes unless we take into account corrections associated with other relevant couplings of the model.…”

“…For instance, we will see that due to the RG flow it induces quench of the running mass. 1 The linear response vanishes because φ 2 and φ 4 have different scaling dimensions [29]. 2 In the next section we elaborate an example where the finite order conformal perturbation theory breaks down.…”

“…Furthermore, it has been argued in [26][27][28][29] that if the quench rate is the shortest scale compared to any other physical scale inherent to the system, then dynamics at early times is dominated by the UV fixed point. Thus it is tempting to employ the conformal perturbation approach to recover leading order effects associated with rapid but smooth quenches.…”

Complexity and scaling in quantum quench in 1 + 1 dimensional fermionic field theories

“…For quench rates which are slow compared to physical mass scales local quantities in many systems obey Kibble Zurek scaling [1][2][3][4]. In systems which have relativistic continuum limits there is a different scaling behavior for quench rates which are fast compared to physical mass scales, but slow compared to the UV scale [5][6][7][8][9][10]. Finally at quench rates at the scale of a UV cutoff one expects that the response saturates as a function of the rate.…”