Estimating phase transition of perturbed Heisenberg quantum chain in mixtures of ground and first excited states

Abstract

We show that the nearest neighbour entanglement in a mixture of ground and first excited states—a subjacent state—of the $J_1-J_2$ Heisenberg quantum spin chain can be used as an order parameter to detect the phase transition of the chain from a gapless spin fluid to a gapped dimer phase. We study the effectiveness of the order parameter for varying relative mixing probabilities between the ground and first excited states in the subjacent state for different system sizes, and extrapolate the results to the thermodynamic limit. We observe that the nearest neighbour concurrence can play a role of a good order parameter even if the system is in the ground state, but with a small finite probability of leaking into the first excited state. Moreover, we apply the order parameter of the subjacent state to investigate the response to separate introductions of anisotropy and of glassy disorder on the phase diagram of the model, and analyse the corresponding finite-size scale exponents and the emergent tricritical point in the former case. The anisotropic $J_1-J_2$ chain has a richer phase diagram which is also clearly visible by using the same order parameter.

Keywords

• quantum spin models
• quantum cooperative phenomena
• J 1-J 2 models
• entanglement in many-body quantum systems
• finite temperature effects
• finite-size scaling exponents