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Thermal and dissipative effects on the heating transition in a driven critical system

by Kenny Choo, Bastien Lapierre, Clemens Kuhlenkamp, Apoorv Tiwari, Titus Neupert, Ramasubramanian Chitra

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Submission summary

Authors (as registered SciPost users): Bastien Lapierre · Apoorv Tiwari
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-09-15
Date submitted: 2022-09-01 14:35
Submitted by: Lapierre, Bastien
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approaches: Theoretical, Computational


We study the dissipative dynamics of a periodically driven inhomogeneous critical lattice model in one dimension. The closed system dynamics starting from pure initial states is well-described by a driven Conformal Field Theory (CFT), which predicts the existence of both heating and non-heating phases in such systems. Heating is inhomogeneous and is manifested via the emergence of black-hole like horizons in the system. The robustness of this CFT phenomenology when considering thermal initial states and open systems remains elusive. First, we present analytical results for the Floquet CFT time evolution for thermal initial states. Moreover, using exact calculations of the time evolution of the lattice density matrix, we demonstrate that for short and intermediate times, the closed system phase diagram comprising heating and non-heating phases, persists for thermal initial states on the lattice. Secondly, in the fully open system with boundary dissipators, we show that the nontrivial spatial structure of the heating phase survives particle-conserving and non-conserving dissipations through clear signatures in mutual information and energy density evolution.

Author comments upon resubmission

Dear Editor,

For ease of reading, as our reply contains several figures, we wrote it as a pdf file which can be accessed here:

The authors

List of changes

1. The abstract and introduction were partially rewritten to make explicit mention of the new results on the CFT side at finite initial temperature.

2. Caption of Fig. 1 was changed according to the comment from Referee 2.

3. The Refs. [47,48] were added to the manuscript, as suggested by Referee 2.

4. Section 4 was fully rewritten. In particular, we added Sec. 4.1 "Thermal Floquet CFT" that deals with the analytic computation of the energy evolution starting from thermal initial state using CFT techniques.

5. Figure 2 was changed to make direct comparison between CFT and lattice results at finite temperature. Plots showing long time evolution of the energy in the non-heating phase were also added in Fig. 2(c,d).

6. In Sec. 4.2, the analysis of the total energy growth was rewritten to discuss CFT comparison as well as energy damping effects in the non-heating phase.

7. Figure 3 was changed according to the comment of Referee 1: the initial temperatures now displayed are $\beta=\{0,0.05,0.1\}$, in order to have explicit comparison between Fig. 3(a,b) and Fig. 2.

8. Figure 7 was added as suggested by Referee~2, together with a paragraph on page 16.

9. A paragraph was added on page 18 about adding both dissipation and dephasing, as suggested by Referee 1

10. The conclusion was partially rewritten to take into account the new changes in both Sec. 4 and 5. In particular, Figure 11 was added, as suggested by Referee 2.

Published as SciPost Phys. 13, 104 (2022)

Reports on this Submission

Anonymous Report 2 on 2022-9-6 (Invited Report)


The authors have made a number of changes to the manuscript, which have strengthened it. In particular they have addressed the issues I flagged with regards to Figs 1 and 3. In their reply to my first report they state their case for publication in SciPost Physics, and on balance I am minded to agree that the manuscript warrants publication there.

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Anonymous Report 1 on 2022-9-1 (Invited Report)


I'm happy with the author's reply. Therefore I recommend the paper for publication in its current form.

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Bastien Lapierre  on 2022-09-01  [id 2782]

Dear Editor,

For ease of reading, as our reply contains several figures, we wrote it as a pdf file which can be accessed from this comment.

The authors