scholarly journals Many-body localization in a finite-range Sachdev-Ye-Kitaev model and holography

2019 ◽  
Vol 99 (5) ◽  
Author(s):  
Antonio M. García-García ◽  
Masaki Tezuka
Keyword(s):  
Finite Range ◽  
Many Body ◽  
Kitaev Model

scholarly journals Many-Body Chaos in the Sachdev-Ye-Kitaev Model

2021 ◽  
Vol 126 (3) ◽  
Author(s):  
Bryce Kobrin ◽  
Zhenbin Yang ◽  
Gregory D. Kahanamoku-Meyer ◽  
Christopher T. Olund ◽  
Joel E. Moore ◽  
...  
Keyword(s):  
Many Body ◽  
Kitaev Model

scholarly journals Many-body quantum dynamics slows down at low density

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Xiao Chen ◽  
Yingfei Gu ◽  
Andrew Lucas
Keyword(s):  
Lyapunov Exponent ◽  
Density Dependence ◽  
Quantum Dynamics ◽  
Chemical Potential ◽  
Quantum Circuits ◽  
Many Body ◽  
Many Body Quantum Dynamics ◽  
Energy Conserving ◽  
Kitaev Model ◽  
Many Body Systems

We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of N interacting fermions with charge conservation, or N interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger than any Lieb-Robinson bound. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model. We also study random automaton quantum circuits and Brownian Sachdev-Ye-Kitaev models, each of which exhibit a different density dependence for the Lyapunov exponent, and explain the discrepancy. We propose that our results are a cartoon for understanding Planckian-limited energy-conserving dynamics at finite temperature.

scholarly journals Dissipation-induced topological insulators: A no-go theorem and a recipe

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Moshe Goldstein
Keyword(s):  
Topological Insulators ◽  
Hamiltonian Dynamics ◽  
Cold Atom ◽  
Atomic Gases ◽  
Finite Range ◽  
Many Body ◽  
Topological States ◽  
Range Dynamics ◽  
Nonequilibrium Conditions ◽  
General Answer

Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantum-coherent many-body phenomena, and much effort is often devoted to their elimination. Recently this approach has changed: It has been realized that driven-dissipative dynamics could be used as a resource. By proper engineering of the reservoirs and their couplings to a system, one may drive the system towards desired quantum-correlated steady states, even in the absence of internal Hamiltonian dynamics. An intriguing category of equilibrium many-particle phases are those which are distinguished by topology rather than by symmetry. A natural question thus arises: which of these topological states can be achieved as the result of dissipative Lindblad-type (Markovian) evolution? Beside its fundamental importance, it may offer novel routes to the realization of topologically-nontrivial states in quantum simulators, especially ultracold atomic gases. Here I give a general answer for Gaussian states and quadratic Lindblad evolution, mostly concentrating on the example of 2D Chern insulator states. I prove a no-go theorem stating that a finite-range Lindbladian cannot induce finite-rate exponential decay towards a unique topological pure state above 1D. I construct a recipe for creating such state by exponentially-local dynamics, or a mixed state arbitrarily close to the desired pure one via finite-range dynamics. I also address the cold-atom realization, classification, and detection of these states. Extensions to other types of topological insulators and superconductors are also discussed.

scholarly journals Page curve from non-Markovianity

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Kaixiang Su ◽  
Pengfei Zhang ◽  
Hui Zhai
Keyword(s):  
Many Body ◽  
Thermal Entropy ◽  
Initial Stage ◽  
Environment Temperature ◽  
Exactly Solvable ◽  
Long Time ◽  
Kitaev Model ◽  
Many Body Systems ◽  
Near Future ◽  
System Entropy

Abstract In this paper, we use the exactly solvable Sachdev-Ye-Kitaev model to address the issue of entropy dynamics when an interacting quantum system is coupled to a non-Markovian environment. We find that at the initial stage, the entropy always increases linearly matching the Markovian result. When the system thermalizes with the environment at a sufficiently long time, if the environment temperature is low and the coupling between system and environment is weak, then the total thermal entropy is low and the entanglement between system and environment is also weak, which yields a small system entropy in the long-time steady state. This manifestation of non-Markovian effects of the environment forces the entropy to decrease in the later stage, which yields the Page curve for the entropy dynamics. We argue that this physical scenario revealed by the exact solution of the Sachdev-Ye-Kitaev model is universally applicable for general chaotic quantum many-body systems and can be verified experimentally in near future.

scholarly journals Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model

2019 ◽  
Vol 99 (19) ◽  
Author(s):  
Jan Behrends ◽  
Jens H. Bardarson ◽  
Benjamin Béri
Keyword(s):  
Many Body ◽  
Zero Modes ◽  
Kitaev Model
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