Finite-temperature properties of the frustrated Hubbard model are theoretically examined by using the recently proposed thermal pure quantum state, which is an unbiased numerical method for finite-temperature calculations. By performing systematic calculations for the frustrated Hubbard model, we show that the geometrical frustration controls the characteristic energy scale of the metal-insulator transitions. We also find that entropy remains large even at moderately high temperature around the region where the quantum spin liquid is expected to appear at zero temperature. We propose that this is a useful criterion whether the target systems have a chance to be the quantum spin liquid or the non-magnetic insulator at zero temperature.
Finite-temperature properties of the frustrated Hubbard model are theoretically examined by using the recently proposed thermal pure quantum state, which is an unbiased numerical method for finite-temperature calculations. By performing systematic calculations for the frustrated Hubbard model, we show that the geometrical frustration controls the characteristic energy scale of the metal-insulator transitions. We also find that entropy remains large even at moderately high temperature around the region where the quantum spin liquid is expected to appear at zero temperature. We propose that this is a useful criterion whether the target systems have a chance to be the quantum spin liquid or the non-magnetic insulator at zero temperature.
Abstract We investigate the finite temperature properties of the half filled Hubbard model in two dimensions, with onsite interaction ( U ), in presence of (frustrating) next nearest neighbor hopping ( t ′) using a semiclassical approximation scheme. We show that introduction of t ′ results in a finite temperature pseudogapped (PG) phase that separates the small U Fermi liquid and large U Mott insulator. We map out the PG to normal metal crossover temperature scale ( T *) as a function of U and t ′. We demonstrate that in the PG phase, the quadratic dependence of resistivity on temperature is violated due to thermally induced spin fluctuations. We conclude with exact diagonalization calculations, that complement our finite temperature results, and indicate the presence of a frustration driven PG state between the Fermi liquid and the Mott insulator at zero temperature as well.
Unique features of the nonmagnetic insulator phase are revealed, and the phase diagram of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model containing the diagonal transfers ${t}^{\ensuremath{'}}$ on a square lattice is presented. Using the path-integral renormalization group method, we find an antiferromagnetic phase for small next-nearest-neighbor transfer ${t}^{\ensuremath{'}}$ and a stripe (or collinear) phase for large ${t}^{\ensuremath{'}}$ in the Mott insulating region of the strong on-site interaction U. For intermediate ${t}^{\ensuremath{'}}∕t\ensuremath{\sim}0.7$ at large U∕t>7, we find a longer-period antiferromagnetic-insulator phase with $2\ifmmode\times\else\texttimes\fi{}4$ structure. In the Mott insulating region, we also find a quantum spin liquid (in other words, a nonmagnetic insulator) phase near the Mott transition to paramagnetic metals for the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model on the square lattice as well as on the anisotropic triangular lattice. Correlated electrons often crystallize to the Mott insulator usually with some magnetic orders, whereas the ``quantum spin liquid" has been a long-sought issue. We report numerical evidence that a nonmagnetic insulating phase gets stabilized near the Mott transition with remarkable properties: The two-dimensional Mott insulators on geometrically frustrated lattices contain a phase with gapless spin excitations and degeneracy of the ground state in the whole Brillouin zone of the total momentum. The obtained vanishing spin renormalization factor suggests that spin excitations do not propagate coherently in contrast to conventional phases, where there exist either magnons in symmetry-broken phases or particle-hole excitations in paramagnetic metals. It imposes a constraint on the possible pictures of quantum spin liquids and supports an interpretation for the existence of an unconventional quantum liquid. The present concept is useful in analyzing a variety of experimental results in frustrated magnets including organic BEDT-TTF compounds and 3He atoms adsorbed on graphite.
We study the ground-state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping t and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. By using the path-integral renormalization-group method, we study the phase diagram in the parameter space of the Hubbard interaction U and the frustration-control parameter ${t}^{\ensuremath{'}}/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution, and the spin- and charge-correlation functions allow us to determine the phase diagram at zero temperature, at which the plaquette-singlet insulator emerges besides the antiferromagnetic insulator and the paramagnetic metal. Spin-liquid insulating states without any kind of symmetry breaking cannot be found in our frustrated model.
Over the past few decades, magnetic frustration has been under intense debate due to its unusual properties. For instance, frustration in the kagome lattice suppresses long-range spin correlations, and it is expected to be a candidate for a spin liquid system. Therefore, with the advent of experiments with ultracold atoms, the interest in frustrated geometries has increased. Given this, in the present work we investigate the repulsive Hubbard model on the kagome lattice using unbiased quantum Monte Carlo simulations. We examine its thermodynamic properties, as well as the magnetic and transport response of the system at finite temperatures and different values of the repulsive interaction. From these results, we discuss the possible occurrence of adiabatic cooling, a quite important feature in ultracold systems, and the presence of a metal-to-insulator transition at a finite interaction strength. Our findings may guide future experiments in ultracold fermionic atoms on the kagome lattice.
The Kagome lattice Fermi-Hubbard model is one of the most physically rich, and at the same time most challenging, models to study in strongly-correlated physics. Among its special features are geometric frustration and a flat energy band that create conditions favorable to ferromagnetism near the band insulating limit. Here, we utilize two exact finite-temperature methods, the numerical linked-cluster expansion and the determinant quantum Monte Carlo, to study the extent as well as doping and interaction dependence of ferromagnetic correlations and other thermodynamic properties of the model. We find that repulsive interactions enhance ferromagnetic correlations at high electron densities and that increasing the interaction strength, extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. We also use the charge compressibility to obtain an accurate estimate for the critical interaction strength for the metal-insulator transition at half filling. These results improve our understanding of the magnetic tendencies of the model away from half filling and pave the way for further studies, including with ultracold atoms in optical lattices.
A spin liquid is a novel quantum state of matter with no conventional order parameter where a finite charge gap exists even though the band theory would predict metallic behavior. Finding a stable spin liquid in two or higher spatial dimensions is one of the most challenging and debated issues in condensed matter physics. Very recently, it has been reported that a model of graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin liquid ground state in a wide region of the phase diagram, between a semi-metal (SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically exact quantum Monte Carlo simulations, we extend the previous study to much larger clusters (containing up to 2592 sites), and find, if any, a very weak evidence of this spin liquid region. Instead, our calculations strongly indicate a direct and continuous quantum phase transition between SM and AFMI.