@article {2638, title = {Conformal field theories are magical}, journal = {Physical Review B}, volume = {103}, year = {2021}, month = {2/25/2021}, pages = {075145}, abstract = {

\"Magic\" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model\&$\#$39;s critical point, and that this mana resides in the system\&$\#$39;s correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.

}, doi = {https://journals.aps.org/prb/pdf/10.1103/PhysRevB.103.075145}, url = {https://arxiv.org/abs/2007.01303}, author = {Christopher David White and ChunJun Cao and Brian Swingle} } @article {2374, title = {Chaos in a quantum rotor model}, year = {2019}, month = {01/29/2019}, abstract = {

We study scrambling in a model consisting of a number N of M-component quantum rotors coupled by random infinite-range interactions. This model is known to have both a paramagnetic phase and a spin glass phase separated by second order phase transition. We calculate in perturbation theory the squared commutator of rotor fields at different sites in the paramagnetic phase, to leading non-trivial order at large N and large M. This quantity diagnoses the onset of quantum chaos in this system, and we show that the squared commutator grows exponentially with time, with a Lyapunov exponent proportional to 1M. At high temperature, the Lyapunov exponent limits to a value set by the microscopic couplings, while at low temperature, the exponent exhibits a T4 dependence on temperature T.\ 

}, url = {https://arxiv.org/abs/1901.10446}, author = {Gong Cheng and Brian Swingle} } @article {2372, title = {A characterization of quantum chaos by two-point correlation functions}, year = {2019}, month = {02/28/2019}, abstract = {

We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

}, url = {https://arxiv.org/abs/1902.11086}, author = {Hrant Gharibyan and Masanori Hanada and Brian Swingle and Masaki Tezuka} }