Publications Influence

Share This Author

Extended variational principle for the Sherrington-Kirkpatrick spin-glass model

- M. Aizenman, Robert Sims, S. Starr
- Philosophy
- 2 December 2003

The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy of the Sherringtun-Kirkpatrick (SK) spin-glass model could have been taken as offering some support to the… Expand

Lieb-Robinson Bounds and the Exponential Clustering Theorem

- B. Nachtergaele, Robert Sims
- Mathematics
- 10 June 2005

We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential clustering in the… Expand

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

- S. Bachmann, S. Michalakis, B. Nachtergaele, Robert Sims
- Physics, Mathematics
- 4 February 2011

Gapped ground states of quantum spin systems have been referred to in the physics literature as being ‘in the same phase’ if there exists a family of Hamiltonians H(s), with finite range interactions… Expand

An Extended Variational Principle for the SK Spin-Glass Model

- M. Aizenman, Robert Sims, S. Starr
- Mathematics
- 16 June 2003

The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as oﬀering some support to the validity of the… Expand

Propagation of Correlations in Quantum Lattice Systems

- B. Nachtergaele, Y. Ogata, Robert Sims
- Mathematics, Physics
- 24 March 2006

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… Expand

Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms

- B. Nachtergaele, Robert Sims, Amanda Young
- MathematicsJournal of Mathematical Physics
- 4 October 2018

Lieb-Robinson bounds show that the speed of propagation of information under the Heisenberg dynamics in a wide class of nonrelativistic quantum lattice systems is essentially bounded. We review works… Expand

LOCALIZATION FOR ONE DIMENSIONAL, CONTINUUM, BERNOULLI-ANDERSON MODELS

- D. Damanik, Robert Sims, G. Stolz
- Mathematics
- 14 October 2000

We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of… Expand

Lieb-Robinson Bounds in Quantum Many-Body Physics

- B. Nachtergaele, Robert Sims
- Physics
- 12 April 2010

We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.

Dynamical Localization in Disordered Quantum Spin Systems

- E. Hamza, Robert Sims, G. Stolz
- Physics
- 18 August 2011

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following… Expand

MEAN-FIELD SPIN GLASS MODELS FROM THE CAVITY-ROST PERSPECTIVE

- M. Aizenman, Robert Sims, S. Starr
- Mathematics
- 27 July 2006

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with hi ghly diversified collections of competing low energy states. The… Expand

...

1

2

3

4

5

...