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The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone…

Quantum Physics · Physics 2020-09-08 Zhiyuan Wang , Kaden R. A. Hazzard

Quantum-disordered models provide a versatile platform to explore the emergence of quantum excitations in many-body systems. The engineering of spin models at the atomic scale with scanning tunneling microscopy and the local imaging of…

Mesoscale and Nanoscale Physics · Physics 2023-08-23 Netta Karjalainen , Zina Lippo , Guangze Chen , Rouven Koch , Adolfo O. Fumega , Jose L. Lado

We investigate the dynamical spreading of correlations in many-body quantum systems with competing short- and global-range couplings. We monitor the non-equilibrium dynamics of the correlations following a quench, showing that for strong…

We study the velocity of the propagation of information for a class of local dissipative quantum dynamics. This finite velocity is expressed by the so-called Lieb-Robinson bound. Besides the properties of the already studied dynamics, we…

Mathematical Physics · Physics 2013-09-17 Benoît Descamps

By using a Generalized Hubbard model for bosons, the energy transfer in a nonlinear quantum lattice is studied, with special emphasis on the interplay between local and nonlocal nonlinearity. For a strong local nonlinearity, it is shown…

Other Condensed Matter · Physics 2009-11-11 Cyril Falvo , Vincent Pouthier , J. C. Eilbeck

In this work, we leverage atomistic spin-lattice simulations to examine how magnetic interactions impact the propagation of sound waves through a ferromagnetic material. To achieve this, we characterize the sound wave velocity in BCC iron,…

Materials Science · Physics 2022-04-27 P. Nieves , J. Tranchida , S. Nikolov , A. Fraile , D. Legut

The Lieb-Robinson bound (LRB) states that the range and strength of interactions between the constituents of a complex many-body system impose upper limits to how fast the signal can propagate. It manifests in a light cone-like growth of…

Quantum Physics · Physics 2024-09-12 Piotr Wysocki , Jan Chwedeńczuk

We study equilibration of an isolated quantum system by mapping it onto a network of classical oscillators in Hilbert space. By choosing a suitable basis for this mapping, the degree of locality of the quantum system reflects in the…

Quantum Physics · Physics 2019-05-14 Daniel Nickelsen , Michael Kastner

We study the propagation of sound waves in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the velocity of propagation of sound wavepackets decreases with increasing optical lattice depth, as predicted…

Soft Condensed Matter · Physics 2009-11-10 C. Menotti , M. Kramer , A. Smerzi , L. Pitaevskii , S. Stringari

We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which…

Mathematical Physics · Physics 2007-05-23 Bruno Nachtergaele , Yoshiko Ogata , Robert Sims

Several recent works have derived Lieb-Robinson bounds (LRBs) for Bose-Hubbard-type Hamiltonians. For certain structured initial states, e.g., vacuum perturbations or near-stationary states, information propagates with velocity $v \leq C$ .…

Mathematical Physics · Physics 2025-07-10 Tomotaka Kuwahara , Marius Lemm

We consider a general class of spatially local non-Markovian open quantum lattice models, with a bosonic environment that is approximated as Gaussian. Under the assumption of a finite environment memory time, formalized as a finite total…

Quantum Physics · Physics 2025-11-04 Rahul Trivedi , Xiehang Yu , Mark Rudner

We consider a one-dimensional mono-atomic lattice with random perturbations of masses spread over a finite number of particles. Assuming Newtonian dynamics and linear nearest-neighbour interactions and allowing for a provision of pinning…

Probability · Mathematics 2024-01-30 Josselin Garnier , Basant Lal Sharma

It has been recently suggested that the dynamics of a quantum spin system may provide a natural mechanism for transporting quantum information. We show that one dimensional rings of qubits with fixed (time-independent) interactions,…

Quantum Physics · Physics 2007-05-23 Tobias J. Osborne , Noah Linden

We study the transport of a quantum particle through square lattices of various sizes by employing the tight-binding Hamiltonian from quantum percolation. Input and output semi-infinite chains are attached to the lattice either by diagonal…

Statistical Mechanics · Physics 2009-11-10 E. Cuansing , H. Nakanishi

Information theory establishes the ultimate limits on performance for noisy communication systems [Shannon48]. An accurate model of a physical communication device must include quantum effects, but typically including these makes the theory…

Quantum Physics · Physics 2013-12-20 Graeme Smith , John A. Smolin

Strong disorder often has drastic consequences for quantum dynamics. This is best illustrated by the phenomenon of Anderson localization in non-interacting systems, where destructive quantum wave interference leads to the complete absence…

Disordered Systems and Neural Networks · Physics 2025-10-15 Ben T. McDonough , Marius Lemm , Andrew Lucas

We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…

Quantum Physics · Physics 2009-11-13 Christina V. Kraus , Michael M. Wolf , J. Ignacio Cirac

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance $r$ as a power law,…

The coherent transfer of excitations between different locations of a quantum many-body system is of primary importance in many research areas, from transport properties in spintronics and atomtronics to quantum state transfer in quantum…

Quantum Physics · Physics 2020-03-31 Wayne Jordan Chetcuti , Claudio Sanavio , Salvatore Lorenzo , Tony J. G. Apollaro