Locality of temperature for 1D lattice systems
JAN 09, 2018 | 11:00 AM TO 1:30 PM
The Graduate Center
365 Fifth Avenue
January 09, 2018: 11:00 AM-1:30 PM
Initiative for the Theoretical Sciences and the PhD Program in Physics
Speaker: Anatoly Dymarsky (University of Kentucky)
We discuss how the thermal physics of 1D lattice models depends on the size of the system. As is suggested by intuition local physics should not be sensitive to the overall system size provided the model exhibits a finite correlation length. We devleop a new representation for the reduced density matrix of a system in thermal state which makes this manifest by respecting the locality of interaction. This new representation immediately shows that local thermal physics is exponentially insensitive to the overall size not only for local observables, but also for the non-local ones, such as Renyi entropies. For the chaotic systems satisfying Eigenstate Thermalization Hypothesis our results prove, for the first time, that the density of the entanglement Renyi entropies in an eigenstate are equal to those of the thermal state. Furthermore, it proves that an individual sufficiently excited energy eigenstate "encodes the full Hamiltonian" in the sense that it reproduces local and non-local observables at all temperatures.