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Abstract
Tools of quantum information theory offer a new perspective to characterize phases and phase transitions in interacting many-body quantum systems. The Hubbard model is the archetypal model of such systems and can explain rich phenomena of quantum matter with minimal assumptions. Recent measurements of entanglement-related properties of this model using ultracold atoms in optical lattices hint that entanglement could provide the key to understanding open questions of the doped Hubbard model, including the remarkable properties of the pseudogap phase. These experimental findings call for a theoretical framework and new predictions. Here we approach the doped Hubbard model in two dimensions from the perspective of quantum information theory. We study the local entropy and the total mutual information across the doping-driven Mott transition within plaquette cellular dynamical mean-field theory. We find that upon varying doping these two entanglement-related properties detect the Mott insulating phase, the strongly correlated pseudogap phase, and the metallic phase. Imprinted in the entanglement-related properties we also find the pseudogap to correlated metal first-order transition, its finite temperature critical endpoint, and its supercritical crossovers. Through this footprint we reveal an unexpected interplay of quantum and classical correlations. Our work shows that sharp variation in the entanglement-related properties and not broken symmetry phases characterizes the onset of the pseudogap phase at finite temperature.
Highlights
Quantum information theory [1,2] provides new concepts, based on the nature of the entanglement, for characterizing phases of matter and phase transitions in correlated many-body systems [3,4,5,6]
Our work shows that sharp variation in the entanglement-related properties and not broken symmetry phases characterizes the onset of the pseudogap phase at finite temperature
III we briefly review the thermodynamic description of the normal-state phase diagram of the two-dimensional Hubbard model
Summary
Quantum information theory [1,2] provides new concepts, based on the nature of the entanglement, for characterizing phases of matter and phase transitions in correlated many-body systems [3,4,5,6]. Recent experimental work of Cocchi et al [10] with ultracold atoms has probed key measures of quantum correlations in the two-dimensional fermionic Hubbard model, paving the way for probing the role of the entanglement in the description of the complex phases of the model. By tuning the level of doping, we use local entropy and mutual information to characterize the Mott insulator, the strongly correlated pseudogap phase, and the metallic state. III we briefly review the thermodynamic description of the normal-state phase diagram of the two-dimensional Hubbard model Additional figures for the analysis of local entropy, thermodynamic entropy, and total mutual information can be found in the appendices
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