Charge and Spin Sharpening Transitions on Dynamical Quantum Trees (2405.13894v2)
Abstract: The dynamics of monitored systems can exhibit a measurement-induced phase transition (MIPT) between entangling and disentangling phases, tuned by the measurement rate. When the dynamics obeys a continuous symmetry, the entangling phase further splits into a fuzzy phase and a sharp phase based on the scaling of fluctuations of the symmetry charge. While the sharpening transition for Abelian symmetries is well understood analytically, no such understanding exists for the non- Abelian case. In this work, building on a recent analytical solution of the MIPT on tree-like circuit architectures (where qubits are repatedly added or removed from the system in a recursive pattern), we study entanglement and sharpening transitions in monitored dynamical quantum trees obeying U (1) and SU (2) symmetries. The recursive structure of tree tensor networks enables powerful analytical and numerical methods to determine the phase diagrams in both cases. In the U (1) case, we analytically derive a Fisher-KPP-like differential equation that allows us to locate the critical point and identify its properties. We find that the entanglement/purification and sharpening transitions generically occur at distinct measurement rates. In the SU (2) case, we find that the fuzzy phase is generic, and a sharp phase is possible only in the limit of maximal measurement rate. In this limit, we analytically solve the boundaries separating the fuzzy and sharp phases, and find them to be in agreement with exact numerical simulations.
- B. Skinner, J. Ruhman, and A. Nahum, Measurement-induced phase transitions in the dynamics of entanglement, Physical Review X 9, 10.1103/physrevx.9.031009 (2019).
- Y. Li, X. Chen, and M. P. A. Fisher, Quantum zeno effect and the many-body entanglement transition, Physical Review B 98, 10.1103/physrevb.98.205136 (2018).
- M. Szyniszewski, A. Romito, and H. Schomerus, Entanglement transition from variable-strength weak measurements, Phys. Rev. B 100, 064204 (2019).
- M. Szyniszewski, A. Romito, and H. Schomerus, Universality of entanglement transitions from stroboscopic to continuous measurements, Phys. Rev. Lett. 125, 210602 (2020).
- Y. Li, X. Chen, and M. P. A. Fisher, Measurement-driven entanglement transition in hybrid quantum circuits, Phys. Rev. B 100, 134306 (2019).
- M. J. Gullans and D. A. Huse, Dynamical purification phase transition induced by quantum measurements, Physical Review X 10, 10.1103/physrevx.10.041020 (2020a).
- Y. Bao, S. Choi, and E. Altman, Theory of the phase transition in random unitary circuits with measurements, Phys. Rev. B 101, 104301 (2020).
- M. J. Gullans and D. A. Huse, Scalable probes of measurement-induced criticality, Phys. Rev. Lett. 125, 070606 (2020b).
- Q. Tang and W. Zhu, Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations, Phys. Rev. Research 2, 013022 (2020).
- X. Turkeshi, R. Fazio, and M. Dalmonte, Measurement-induced criticality in (2+1)21(2+1)( 2 + 1 )-dimensional hybrid quantum circuits, Phys. Rev. B 102, 014315 (2020).
- Y. Li and M. P. A. Fisher, Statistical mechanics of quantum error correcting codes, Phys. Rev. B 103, 104306 (2021).
- A. Lavasani, Y. Alavirad, and M. Barkeshli, Measurement-induced topological entanglement transitions in symmetric random quantum circuits, Nature Physics 17, 342 (2021).
- J. Lopez-Piqueres, B. Ware, and R. Vasseur, Mean-field entanglement transitions in random tree tensor networks, Phys. Rev. B 102, 064202 (2020).
- M. Ippoliti and V. Khemani, Postselection-free entanglement dynamics via spacetime duality, Phys. Rev. Lett. 126, 060501 (2021).
- Y. Li, S. Vijay, and M. P. Fisher, Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment, PRX Quantum 4, 010331 (2023).
- X. Feng, B. Skinner, and A. Nahum, Measurement-induced phase transitions on dynamical quantum trees, PRX Quantum 4, 030333 (2023).
- M. Ippoliti and V. Khemani, Learnability transitions in monitored quantum dynamics via eavesdropper’s classical shadows, PRX Quantum 5, 020304 (2024).
- A. A. Akhtar, H.-Y. Hu, and Y.-Z. You, Measurement-induced criticality is tomographically optimal (2023), arXiv:2308.01653 [quant-ph] .
- S. J. Garratt and E. Altman, Probing post-measurement entanglement without post-selection (2023), arXiv:2305.20092 [quant-ph] .
- M. McGinley, Postselection-free learning of measurement-induced quantum dynamics, arXiv e-prints , arXiv:2310.04156 (2023).
- L. Fidkowski, J. Haah, and M. B. Hastings, How dynamical quantum memories forget, Quantum 5, 382 (2021).
- A. C. Potter and R. Vasseur, Entanglement dynamics in hybrid quantum circuits, in Quantum Science and Technology (Springer International Publishing, 2022) pp. 211–249.
- S. Vijay, Measurement-driven phase transition within a volume-law entangled phase (2020), arXiv:2005.03052 [quant-ph] .
- R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugen. 7, 355 (1937).
- B. Derrida and D. Simon, The survival probability of a branching random walk in presence of an absorbing wall, Europhysics Letters 78, 60006 (2007).
- J. D. Miller and B. Derrida, Weak-disorder expansion for the anderson model on a tree, Journal of Statistical Physics 75, 357 (1994).
- C. Monthus and T. Garel, Anderson transition on the cayley tree as a traveling wave critical point for various probability distributions, Journal of Physics A: Mathematical and Theoretical 42, 075002 (2009).
- Y.-Y. Shi, L.-M. Duan, and G. Vidal, Classical simulation of quantum many-body systems with a tree tensor network, Phys. Rev. A 74, 022320 (2006).
- L. Tagliacozzo, G. Evenbly, and G. Vidal, Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law, Phys. Rev. B 80, 235127 (2009).
- W. Li, J. von Delft, and T. Xiang, Efficient simulation of infinite tree tensor network states on the bethe lattice, Phys. Rev. B 86, 195137 (2012).
- T. Zhou and A. Nahum, Emergent statistical mechanics of entanglement in random unitary circuits, Phys. Rev. B 99, 174205 (2019).
- Y. Bao, S. Choi, and E. Altman, Symmetry enriched phases of quantum circuits, Annals of Physics 435, 168618 (2021).
- E. Brunet and B. Derrida, Shift in the velocity of a front due to a cutoff, Physical Review E 56, 2597 (1997).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.