Quantum criticality in the two-dimensional Hubbard model

We investigate the two-dimensional Hubbard model with next-nearest-neighbor hopping, ${t}^{\ensuremath{'}}$, using the dynamical cluster approximation. We confirm the existence of a first-order phase-separation transition terminating at a second-order critical point at filling ${n}_{c}({t}^{\ensuremath{'}})$ and temperature ${T}_{ps}({t}^{\ensuremath{'}})$. We find that as ${t}^{\ensuremath{'}}$ approaches zero, ${T}_{ps}({t}^{\ensuremath{'}})$ vanishes and ${n}_{c}({t}^{\ensuremath{'}})$ approaches the filling associated with the quantum critical point separating the Fermi liquid from the pseudogap phase. We propose that the quantum critical point under the superconducting dome is the zero-temperature limit of the line of second-order critical points.We investigate the two-dimensional Hubbard model with next-nearest-neighbor hopping, ${t}^{\ensuremath{'}}$, using the dynamical cluster approximation. We confirm the existence of a first-order phase-separation transition terminating at a second-order critical point at filling ${n}_{c}({t}^{\ensuremath{'}})$ and temperature ${T}_{ps}({t}^{\ensuremath{'}})$. We find that as ${t}^{\ensuremath{'}}$ approaches zero, ${T}_{ps}({t}^{\ensuremath{'}})$ vanishes and ${n}_{c}({t}^{\ensuremath{'}})$ approaches the filling associated with the quantum critical point separating the Fermi liquid from the pseudogap phase. We propose that the quantum critical point under the superconducting dome is the zero-temperature limit of the line of second-order critical points.

arXiv:0909.0759Physical Review BMay 19, 201052 citations

Quantum criticality in the Hubbard model

Mark Jarrell

Bulletin of the American Physical SocietyMar 25, 20111 citation

Quantum criticality in the 2D Hubbard: from weak to strong coupling

Dimitrios Galanakis, Karlis Mikelsons, Ehsan Khatami +4 more

Bulletin of the American Physical SocietyMar 15, 20100 citations

Universal thermodynamics of the one-dimensional attractive Hubbard model

Song Cheng, Yi-Cong Yu, Murray T. Batchelor +1 more

The one-dimensional (1D) Hubbard model, describing electrons on a lattice with an on-site repulsive interaction, provides a paradigm for the physics of quantum many-body phenomena. Here, by solving the thermodynamic Bethe ansatz equations, we study the universal thermodynamics, quantum criticality, and magnetism of the 1D attractive Hubbard model. We show that the compressibility and the susceptibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state obey simple additivity rules at low temperatures, indicating an existence of two free quantum fluids. The magnetic properties, such as magnetization and susceptibility, reveal three physical regions: quantum fluids at low temperatures, a non-Fermi liquid at high temperatures, and the quantum fluid to non-Fermi liquid crossover in between. The lattice interaction is seen to significantly influence the nature of the FFLO-like state in 1D. Furthermore, we show that the dimensionless Wilson ratio provides an ideal parameter to map out the various phase boundaries and to characterize the two free fluids of the FLLO-like state. The quantum scaling functions for the thermal and magnetic properties yield the same dynamic critical exponent $z=2$ and correlation critical exponent $\ensuremath{\nu}=1/2$ in the quantum critical region whenever a phase transition occurs. Our results provide a rigorous understanding of quantum criticality and free fluids of many-body systems on a 1D lattice.The one-dimensional (1D) Hubbard model, describing electrons on a lattice with an on-site repulsive interaction, provides a paradigm for the physics of quantum many-body phenomena. Here, by solving the thermodynamic Bethe ansatz equations, we study the universal thermodynamics, quantum criticality, and magnetism of the 1D attractive Hubbard model. We show that the compressibility and the susceptibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state obey simple additivity rules at low temperatures, indicating an existence of two free quantum fluids. The magnetic properties, such as magnetization and susceptibility, reveal three physical regions: quantum fluids at low temperatures, a non-Fermi liquid at high temperatures, and the quantum fluid to non-Fermi liquid crossover in between. The lattice interaction is seen to significantly influence the nature of the FFLO-like state in 1D. Furthermore, we show that the dimensionless Wilson ratio provides an ideal parameter to map out the various phase boundaries and to characterize the two free fluids of the FLLO-like state. The quantum scaling functions for the thermal and magnetic properties yield the same dynamic critical exponent $z=2$ and correlation critical exponent $\ensuremath{\nu}=1/2$ in the quantum critical region whenever a phase transition occurs. Our results provide a rigorous understanding of quantum criticality and free fluids of many-body systems on a 1D lattice.

arXiv:1708.07784Physical review. B./Physical review. BMar 26, 20185 citations

Universality class of quantum criticality in the two-dimensional Hubbard model at intermediate temperatures ( t2/U≪T≪t )

Kaden R. A. Hazzard, Ana María Rey, Richard T. Scalettar

By using numerically exact determinantal Monte Carlo we show that the dilute Fermi gas quantum critical theory quantitatively describes the behavior of the density and compressibility along the Mott/metal crossover in the two-dimensional Hubbard model for temperatures somewhat less than (roughly half) the tunneling but greater than (roughly twice) the superexchange energy. In contrast, we find that other observables such as the kinetic energy, doubly occupied sites, and magnetization in a finite Zeeman field are poorly described by the same dilute Fermi gas universality class. In addition to these findings' fundamental interest, they are relevant to cold atom systems, where the intermediate temperature regime is currently in experimental reach.By using numerically exact determinantal Monte Carlo we show that the dilute Fermi gas quantum critical theory quantitatively describes the behavior of the density and compressibility along the Mott/metal crossover in the two-dimensional Hubbard model for temperatures somewhat less than (roughly half) the tunneling but greater than (roughly twice) the superexchange energy. In contrast, we find that other observables such as the kinetic energy, doubly occupied sites, and magnetization in a finite Zeeman field are poorly described by the same dilute Fermi gas universality class. In addition to these findings' fundamental interest, they are relevant to cold atom systems, where the intermediate temperature regime is currently in experimental reach.

arXiv:1106.2330Physical Review BJan 7, 20134 citations

z=2

and correlation critical exponent $\ensuremath{\nu}=1/2$ in the quantum critical region whenever a phase transition occurs. Our results provide a rigorous understanding of quantum criticality and free fluids of many-body systems on a 1D lattice.