Solvable model for a dynamical quantum phase transition from fast to slow scrambling

By S. Banerjee, E. Altman. 2016

215 citations recorded by the source corpus.

We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a quantum phase transition from the previously identified non-Fermi-liquid fixed point to a Fermi-liquid-like state, while still allowing an exact solution in a suitable large-$N$ limit. The extended model involves coupling the interacting $N$-site SYK model to a new set of $pN$ peripheral sites with only quadratic hopping terms between them. The conformal fixed point of the SYK model remains a stable low-energy phase below a critical ratio of peripheral sites $pl{p}_{c}(n)$ that depends on the fermion filling $n$. The scrambling dynamics throughout the non-Fermi-liquid (NFL) phase is characterized by a universal Lyapunov exponent ${\ensuremath{\lambda}}_{\mathrm{L}}\ensuremath{\rightarrow}2\ensuremath{\pi}T$ in the low-temperature limit; however, the temperature scale marking the crossover to the conformal regime vanishes continuously at the critical point ${p}_{c}$. The residual entropy at $T\ensuremath{\rightarrow}0$, nonzero in the NFL, also vanishes continuously at the critical point. For $pg{p}_{c}$ the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low-temperature and low-frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent ${\ensuremath{\lambda}}_{\mathrm{L}}\ensuremath{\propto}{T}^{2}$.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3bb4b672a38bfe306522d2101c9b35cfde08c49b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Brian Swingle
2. A. Nahum
3. S. Vijay
4. Shenglong Xu
5. Xiao-Liang Qi
6. D. Chowdhury
7. Jeongwan Haah
8. B. Yoshida

In Condensed Matter Physics

1. Brian Swingle
2. A. Nahum
3. S. Vijay
4. Xiao-Liang Qi
5. J. Maldacena
6. B. Yoshida
7. D. Chowdhury
8. Norman Y. Yao

In Nuclear and High Energy Physics

1. B. Yoshida
2. A. Nahum
3. Brian Swingle
4. Xiao-Liang Qi
5. J. Maldacena
6. T. Takayanagi
7. A. Altland
8. Alex Kamenev

Citations in the corpus

• Power-law out of time order correlation functions in the SYK model (2017, background): “The potential realization of a holographic principle of lowest possible dimension has triggered a surge of research activity on the SYK model and its quantum dynamics [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20].”
• Eternal traversable wormhole (2018, background): “It should be noted that various models with interplay of SYK interaction and bilinear terms have been studied in the literature, such as[10, 11, 12].”
• Operator Spreading in Random Unitary Circuits (2017, background): “[34] Sumilan Banerjee and Ehud Altman, “Solvable model for a dynamical quantum phase transition from fast to slow scrambling,” Phys.”
• Scrambling and thermalization in a diffusive quantum many-body system (2016, background): “This bound is saturated in strongly coupledfield theories with a gravity dual [6] and in disorderedmodels describing a strangemetal [7, 11, 12].”
• Disentangling Scrambling and Decoherence via Quantum Teleportation (2018, background): “Recent studies on the dynamics of such information scrambling have sharpened our understanding of chaos in quantum many-body systems [5–27], and have led to new insights on a variety of questions ranging from the black-hole information paradox [5,11,15,28,29] to transport phenomena in non-Fermi liqu”
• Onset of many-body chaos in the $O(N)$ model (2017, background): “There has been a flurry of recent calculations of out-of-time-order correlators in a variety of models [34, 35, 36, 37, 38, 39, 40].”