On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain
Abstract
We rigorously prove a new kind of anomalous (or sub-ballistic) Lieb-Robinson bound for the isotropic XY chain with Fibonacci external magnetic field at arbitrary coupling. It is anomalous in that the usual exponential decay in |x| − v|t| is replaced by exponential decay in |x| − v|t|^α with 0 < α < 1. In fact, we can characterize the values of α for which such a bound holds as those exceeding α^+_u, the upper transport exponent of the one-body Fibonacci Hamiltonian. Following the approach of [12], we relate Lieb-Robinson bounds to dynamical bounds for the one-body Hamiltonian corresponding to the XY chain via the Jordan-Wigner transformation; in our case the one-body Hamiltonian with Fibonacci potential. We can bound its dynamics by adapting techniques developed in [6, 7, 2, 3] to our purposes. We also discuss the extension to the more general class of Sturmian potentials and we explain why our method does not extend to yield anomalous Lieb-Robinson bounds of power-law type for the random dimer model.
Additional Information
© 2016 European Mathematical Society. Received September 3, 2014; revised February 22, 2015. David Damanik was supported in part by NSF grants DMS–1067988 and DMS–1361625. Milivoje Lukic was supported in part by NSF grant DMS–1301582. William Yessen was supported by NSF grant DMS–1304287.Attached Files
Submitted - 1407.4924v1.pdf
Files
Name | Size | Download all |
---|---|---|
md5:155e14e4c77f6aeef854a2555a98b275
|
243.4 kB | Preview Download |
Additional details
- Eprint ID
- 52488
- DOI
- 10.4171/JST/133
- Resolver ID
- CaltechAUTHORS:20141209-084133546
- DMS-1067988
- NSF
- DMS-1361625
- NSF
- DMS-1301582
- NSF
- DMS-1304287
- NSF
- Created
-
2014-12-09Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field