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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 derive higher-order error bounds with small prefactors for a general Trotter product formula, generalizing a result of Childs et al. [Phys. Rev. X 11, 011020 (2021)]. We then apply these bounds to the real-time quantum time evolution…

Quantum Physics · Physics 2023-11-06 Ansgar Schubert , Christian B. Mendl

The dynamics of quantum systems strongly depends on the local structure of the Hamiltonian. For short-range interacting systems, the well-known Lieb-Robinson bound defines the effective light cone with an exponentially small error with…

Quantum Physics · Physics 2016-05-31 Tomotaka Kuwahara

The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson…

Statistical Mechanics · Physics 2018-06-20 Zhiqiang Huang , Xiao-Kan Guo

We prove an analogue of the Lieb--Thirring inequality for many-body quantum systems with the kinetic operator $\sum_i (-\Delta_i)^s$ and the interaction potential of the form $\sum_i \delta_i^{-2s}$ where $\delta_i$ is the nearest-neighbor…

Mathematical Physics · Physics 2025-01-03 G. K. Duong , Phan Thành Nam

Recent works have revealed the intricate effect of long-range interactions on information transport in quantum many-body systems: In $D$ spatial dimensions, interactions decaying as a power-law $r^{-\alpha}$ with $\alpha > 2 D+1$ exhibit a…

Mathematical Physics · Physics 2025-09-23 Marius Lemm , Tom Wessel

The Lieb-Robinson correlation function is the norm of a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum…

Quantum Physics · Physics 2024-06-25 Brendan J. Mahoney , Craig S. Lent

We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from…

Mathematical Physics · Physics 2015-06-03 Rupert L. Frank , Robert Seiringer

Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Intuitively, Lieb-Robinson bounds state that with local or exponentially decaying interactions, the correlation that can be built up between two sites…

Quantum Physics · Physics 2026-01-27 Ben T. McDonough , Chao Yin , Andrew Lucas , Carolyn Zhang

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

We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems.

Mathematical Physics · Physics 2009-02-03 Bruno Nachtergaele , Hillel Raz , Benjamin Schlein , Robert Sims

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

Lieb-Robinson bounds show that the speed of propagation of information under the Heisenberg dynamics in a wide class of non-relativistic quantum lattice systems is essentially bounded. We review work of the past dozen years that has turned…

Mathematical Physics · Physics 2019-06-25 Bruno Nachtergaele , Robert Sims , Amanda Young

We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using…

High Energy Physics - Theory · Physics 2024-10-01 Holger Gies , Philip Heinzel , Johannes Laufkötter , Marta Picciau

For quantum lattice systems with local interactions, the Lieb-Robinson bound acts as an alternative for the strict causality of relativistic systems and allows to prove many interesting results, in particular when the energy spectrum…

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected…

Quantum Physics · Physics 2018-02-01 Minh Cong Tran , James R. Garrison , Zhe-Xuan Gong , Alexey V. Gorshkov

We study the integrable model of one-dimensional bosons with contact repulsion. In the limit of weak interaction, we use the microscopic hydrodynamic theory to obtain the excitation spectrum. The statistics of quasiparticles changes with…

Quantum Gases · Physics 2014-07-04 Zoran Ristivojevic

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

Estimating extensive combinations of local parameters in distributed quantum systems is a central problem in quantum sensing, with applications ranging from magnetometry to timekeeping. While optimal strategies are known for sensing…

We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving…

Quantum Physics · Physics 2020-09-29 Amikam Levy , Wenjie Dou , Eran Rabani , David T. Limmer