Complexity of frustration - Trieste 12/2022
Abstract
In this talk, I will present recent results on the topic of integrable topologically frustrated quantum spin chains. In particular, I will discuss entanglement properties of frustrated Ising chains with assumed frustrated boundary conditions that imply periodic boundary conditions, an odd number of spins, and antiferromagnetic coupling. The topologically frustrated ground state is a unique example of a state associated with a local and nearest-neighbor coupling Hamiltonian that violates the area-law scaling of entanglement with the subsystem size. Frustrated boundary conditions induce an excess of long-range entanglement that can be analytically described in the thermodynamic limit using the single-particle interpretation. Using an entanglement cooling (disentangling) algorithm, represented by a particular stochastic quantum circuit, we show that the frustration-induced entanglement is robust against the application of local gates. In this process, we additionally demonstrate, how with different choices of local gates the quantum circuit can induce a transition in the entanglement spectrum from the uncorrelated Poissonian distributed eigenvalue spacings to the correlated Wigner-Dyson distribution. Moreover, we advance the characterization of complexity in quantum many-body systems by examining W -state, a well-known state within the quantum information community. Such a state admits an amount of non-stabilizerness or magic (measured as the Stabilizer Renyi Entropy – SRE) that grows logarithmically with the number of qubits/spins. We show that topologically frustrated ground states have a value of SRE that is the sum of that of the W-state plus an extensive local contribution. Our work reveals that W-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.
