Quantum simulation of long-range XY quantum spin glass with strong area-law violation using trapped ions

Abstract

Ground states of local Hamiltonians are known to obey the entanglement entropy area law. While area-law violation of a mild kind (logarithmic) is commonly encountered, strong area-law violation (more than logarithmic) is rare. In this paper, we study the long-range quantum spin glass in one dimension whose couplings are disordered and fall off with distance as a power law. We show that this system exhibits more than logarithmic area-law violation in its ground state. Strikingly this feature is found to be true even in the short-range regime, in sharp contrast to the spinless long-range disordered fermionic model. This necessitates the study of large systems for the quantum $XY$ spin glass model, which is challenging since these numerical methods depend on the validity of the area law. This situation lends itself naturally to the exploration of a quantum simulation approach. We present a proof-of-principle implementation of this nontrivially interacting spin model using trapped ions and provide a detailed study of experimentally realistic parameters.