scholarly journals Flow equations for disordered Floquet systems

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Steven Thomson ◽  
Duarte Magano ◽  
Marco Schiro'
Keyword(s):  
Flow Equation ◽  
Two Dimensional ◽  
Many Body ◽  
Integrals Of Motion ◽  
Exact Methods ◽  
New Approach ◽  
Flow Equations ◽  
Periodically Driven ◽  
Floquet Modes ◽  
Many Body Systems

In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.

scholarly journals Self-consistent effective Hamiltonian theory for fermionic many-body systems

2020 ◽  
pp. 2150019
Author(s):  
Xindong Wang ◽  
Hai-Ping Cheng
Keyword(s):  
Hubbard Model ◽  
Order Parameter ◽  
Cooper Pair ◽  
Effective Hamiltonian ◽  
Two Dimensional ◽  
Body System ◽  
Many Body ◽  
Hamiltonian Theory ◽  
Self Consistent ◽  
Many Body Systems

Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional (2D) Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2D, a highly unconventional quadruple-fermion non-Cooper pair order parameter is discovered.

scholarly journals Cooling and entangling ultracold atoms in optical lattices

Science ◽  
2020 ◽  
Vol 369 (6503) ◽  
pp. 550-553 ◽  
Author(s):  
Bing Yang ◽  
Hui Sun ◽  
Chun-Jiong Huang ◽  
Han-Yi Wang ◽  
Youjin Deng ◽  
...  
Keyword(s):  
Large Scale ◽  
Thermal Fluctuations ◽  
Two Dimensional ◽  
Many Body ◽  
Quantum Phases ◽  
Atom Pairs ◽  
Speed Up ◽  
Quantum Simulator ◽  
Many Body Systems ◽  
Qubit Gate

Scalable, coherent many-body systems can enable the realization of previously unexplored quantum phases and have the potential to exponentially speed up information processing. Thermal fluctuations are negligible and quantum effects govern the behavior of such systems with extremely low temperature. We report the cooling of a quantum simulator with 10,000 atoms and mass production of high-fidelity entangled pairs. In a two-dimensional plane, we cool Mott insulator samples by immersing them into removable superfluid reservoirs, achieving an entropy per particle of 1.9−0.4+1.7×10−3kB. The atoms are then rearranged into a two-dimensional lattice free of defects. We further demonstrate a two-qubit gate with a fidelity of 0.993 ± 0.001 for entangling 1250 atom pairs. Our results offer a setting for exploring low-energy many-body phases and may enable the creation of large-scale entanglement.

scholarly journals Universal flow equations and chaos bound saturation in 2d dilaton gravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
D. Grumiller ◽  
R. McNees
Keyword(s):  
Fixed Point ◽  
Chaotic Behavior ◽  
Broad Class ◽  
Flow Equation ◽  
Two Dimensional ◽  
Maximal Lyapunov Exponent ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Flow Equations ◽  
Universal Properties

Abstract We show that several features of the Jackiw-Teitelboim model are in fact universal properties of two-dimensional Maxwell-dilaton gravity theories with a broad class of asymptotics. These theories satisfy a flow equation with the structure of a dimensionally reduced $$ T\overline{T} $$ T T ¯ deformation, and exhibit chaotic behavior signaled by a maximal Lyapunov exponent. One consequence of our results is a no-go theorem for smooth flows from an asymptotically AdS2 region to a de Sitter fixed point.

scholarly journals Polynomial filter diagonalization of large Floquet unitary operators

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
David J. Luitz
Keyword(s):  
Quantum Chaos ◽  
System Size ◽  
Complex Polynomial ◽  
Many Body ◽  
Unitary Evolution ◽  
Filter Diagonalization ◽  
Periodically Driven ◽  
Nonequilibrium Phenomena ◽  
Many Body Systems ◽  
Static Systems

Periodically driven quantum many-body systems play a central role for our understanding of nonequilibrium phenomena. For studies of quantum chaos, thermalization, many-body localization and time crystals, the properties of eigenvectors and eigenvalues of the unitary evolution operator, and their scaling with physical system size LL are of interest. While for static systems, powerful methods for the partial diagonalization of the Hamiltonian were developed, the unitary eigenproblem remains daunting. % In this paper, we introduce a Krylov space diagonalization method to obtain exact eigenpairs of the unitary Floquet operator with eigenvalue closest to a target on the unit circle. Our method is based on a complex polynomial spectral transformation given by the geometric sum, leading to rapid convergence of the Arnoldi algorithm. We demonstrate that our method is much more efficient than the shift invert method in terms of both runtime and memory requirements, pushing the accessible system sizes to the realm of 20 qubits, with Hilbert space dimensions \geq 10^6≥106.

scholarly journals Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

scholarly journals Universal Chiral Quasisteady States in Periodically Driven Many-Body Systems

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Netanel H. Lindner ◽  
Erez Berg ◽  
Mark S. Rudner
Keyword(s):  
Many Body ◽  
Periodically Driven ◽  
Many Body Systems

scholarly journals Polaritons in an Electron Gas—Quasiparticles and Landau Effective Interactions

Atoms ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 81
Author(s):  
Miguel Angel Bastarrachea-Magnani ◽  
Jannie Thomsen ◽  
Arturo Camacho-Guardian ◽  
Georg M. Bruun
Keyword(s):  
Light Transmission ◽  
Landau Theory ◽  
Effective Interaction ◽  
Electron Gas ◽  
Ladder Approximation ◽  
Two Dimensional ◽  
Many Body ◽  
Strong Light ◽  
Exciton Polaritons ◽  
Many Body Systems

Two-dimensional semiconductors inside optical microcavities have emerged as a versatile platform to explore new hybrid light–matter quantum states. A strong light–matter coupling leads to the formation of exciton-polaritons, which in turn interact with the surrounding electron gas to form quasiparticles called polaron-polaritons. Here, we develop a general microscopic framework to calculate the properties of these quasiparticles, such as their energy and the interactions between them. From this, we give microscopic expressions for the parameters entering a Landau theory for the polaron-polaritons, which offers a simple yet powerful way to describe such interacting light–matter many-body systems. As an example of the application of our framework, we then use the ladder approximation to explore the properties of the polaron-polaritons. Furthermore, we show that they can be measured in a non-demolition way via the light transmission/reflection spectrum of the system. Finally, we demonstrate that the Landau effective interaction mediated by electron-hole excitations is attractive leading to red shifts of the polaron-polaritons. Our work provides a systematic framework to study exciton-polaritons in electronically doped two-dimensional materials such as novel van der Waals heterostructures.

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