Q+ Hangout: David Perez-Garcia
Next Q+ Hangout is on the 12th of April!
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We also encourage individuals interested in active participation—which typically involves asking questions after the talk—to join the hangout. Otherwise you can watch on the livestream. Details follow.
Title: Size-driven quantum phase transitions
Speaker: David Perez-Garcia, Universidad Complutense de Madrid
Abstract: Most of the theoretical knowledge about quantum many body systems comes from performing numerical simulations. One tries to capture the relevant physical features of a system by extrapolating to the large system size the knowledge obtained in the analysis of an increasing sequence of finite-size systems, which must be small enough for the computer to be capable of giving an answer in a reasonable amount of time. In this work we show simple examples that totally defeat any such approach. More concretely, we construct translationally invariant quantum spin models on the 2D square lattice with reasonably small local dimension exhibiting the following surprising feature that we refer to as a “size-driven phase transition”‘: For all system sizes smaller than a threshold value L, the system has a unique ground state with product structure and a constant spectral gap to the first excited state, which also has product structure. However, for all system sizes larger than L, the system has topological quantum order, meaning a finite number of ground states which are locally indistinguishable, a finite spectral gap and first excited states with anyonic statistics. Moreover, we construct examples (all of them with local dimension smaller than 10) for which the threshold size L can occur at essentially any order of magnitude. From sizes that are reachable within current experimental setups and numerical simulations (L=15 or L=84) to sizes that are beyond any present or future capability, such as L> 10^35000.