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Register a new userDimensional-crossover-driven Mott transition in the frustrated Hubbard model
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We study the Mott transition in a frustrated Hubbard model with next-nearest neighbor hopping at half-filling. The interplay between interaction, dimensionality and geometric frustration closes the one-dimensional Mott gap and gives rise to a metallic phase with Fermi surface pockets. We argue that they emerge as a consequence of remnant one-dimensional Umklapp scattering at the momenta with vanishing interchain hopping matrix elements. In this pseudogap phase, enhanced d-wave pairing correlations are driven by antiferromagnetic fluctuations. Within the adopted cluster dynamical mean-field theory on the $8times 2$ cluster and down to our lowest temperatures the transition from one to two dimensions is continuous.
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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.
We discuss the solution of the Mott transition problem in a fully frustrated lattice with a semicircular density of states in the limit of infinite dimensions from the point of view of a Landau free energy functional. This approach provides a simple relation between the free energy of the lattice model and that of its local description in terms of an impurity model. The character of the Mott transition in infinite dimensions, (as reviewed by Georges Kotliar Krauth and Rozenberg, RMP 68, 1996, 13) follows simply from the form of the free energy functional and the physics of quantum impurity models. At zero temperature, below a critical value of the interaction U, a Mott insulator with a finite gap in the one particle spectrum, becomes unstable to the formation of a narrow band near the Fermi energy. Using the insights provided by the Landau approach we answer questions raised about the dynamical mean field solution of the Mott transition problem, and comment on its applicability to three dimensional transition metal oxides.
We consider the one-band Hubbard model on the square lattice by using variational and Greens function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction $U$, we can identify a hidden critical point $U_{rm Mott}$, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of $U$), where magnetism induces a potential energy gain, and a Mott insulator (at large values of $U$), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of $U_{rm Mott}$ has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above $U_{rm Mott}$, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above $U_{rm Mott}$ shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.
We apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction~$U$ equals the band width, $U_{rm c}=W$, where the single-particle gap opens linearly, $Delta(Ugeq W)=U-W$. The simple nature of the elementary excitations permits to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution $n_k$ at the Fermi wave number $k_{rm F}=0$ cannot be used to locate accurately $U_{rm c}$ from finite-size systems. However, the slope of $n_k$ at the band edges, $k_{rm B}=pm pi$, reveals the formation of a single-particle bound state which can be used to determine $U_{rm c}$ reliably from $n_k$ using accurate finite-size data.
Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Motivated by recent cold atom experiments, which are now able to measure the corresponding information-theoretic quantities, we study the Mott transition in the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory, and focus on two key measures of quantum correlations: entanglement entropy and mutual information. We show that they detect the first-order nature of the transition, the universality class of the endpoint, and the crossover emanating from the endpoint.
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