PIRSA:19020071

Decay of correlations in long-range interacting systems at non-zero temperature

Hernandez Santana, S. (2019). Decay of correlations in long-range interacting systems at non-zero temperature. Perimeter Institute. https://pirsa.org/19020071

Hernandez Santana, Senaida. Decay of correlations in long-range interacting systems at non-zero temperature. Perimeter Institute, Feb. 13, 2019, https://pirsa.org/19020071 

          @misc{ pirsa_PIRSA:19020071,
            doi = {10.48660/19020071},
            url = {https://pirsa.org/19020071},
            author = {Hernandez Santana, Senaida},
            keywords = {Quantum Information},
            language = {en},
            title = {Decay of correlations in long-range interacting systems at non-zero temperature},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020071 see, \url{https://pirsa.org}}
          }

Senaida Hernandez Santana

Institute of Photonic Sciences (ICFO)

Talk number
PIRSA:19020071
Collection
Talk Type
Subject
Abstract

We study correlations in fermionic systems with long-range interactions in thermal equilibrium. We prove an upper-bound on the correlation decay between anti-commut-ing operators based on long-range Lieb-Robinson type bounds. Our result shows that correlations between such operators in fermionic long-range systems of spatial dimension $D$ with at most two-site interactions decaying algebraically with the distance with an exponent $\alpha \geq 2\,D$, decay at least algebraically with an exponent arbitrarily close to $\alpha$. Our bound is asymptotically tight, which we demonstrate by numerically analysing density-density correlations in a 1D quadratic (free, exactly solvable) model, the Kitaev chain with long-range interactions. Away from the quantum critical point correlations in this model are found to decay asymptotically as slowly as our bound permits.