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Register a new userMetal-insulator transition and strong-coupling spin liquid in the $t{-}t^prime$ Hubbard model
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We study the phase diagram of the frustrated $t{-}t^prime$ Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and have been used for describing various interacting systems on the continuum (like liquid $^3$He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate {it ansatz} can be achieved both at weak and strong coupling. We present the evidence that an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^prime/t$.
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The Hubbard model and its strong-coupling version, the Heisenberg one, have been widely studied on the triangular lattice to capture the essential low-temperature properties of different materials. One example is given by transition metal dichalcogenides, as 1T$-$TaS$_2$, where a large unit cell with $13$ Ta atom forms weakly-coupled layers with an isotropic triangular lattice. By using accurate variational Monte Carlo calculations, we report the phase diagram of the $t-t^prime$ Hubbard model on the triangular lattice, highlighting the differences between positive and negative values of $t^prime/t$; this result can be captured only by including the charge fluctuations that are always present for a finite electron-electron repulsion. Two spin-liquid regions are detected: one for $t^prime/t<0$, which persists down to intermediate values of the electron-electron repulsion, and a narrower one for $t^prime/t>0$. The spin-liquid phase appears to be gapless, though the variational wave function has a nematic character, in contrast to the Heisenberg limit. We do not find any evidence for non-magnetic Mott phases in the proximity of the metal-insulator transition, at variance with the predictions (mainly based upon strong-coupling expansions in $t/U$) that suggest the existence of a weak-Mott phase that intrudes between the metal and the magnetically ordered insulator.
We calculate the Landau interaction function f(k,k) for the two-dimensional t-t Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface.
We present a systematic study of the phase diagram of the $t{-}t^prime{-}J$ model by using the Greens function Monte Carlo (GFMC) technique, implemented within the fixed-node (FN) approximation and a wave function that contains both antiferromagnetic and d-wave pairing. This enables us to study the interplay between these two kinds of order and compare the GFMC results with the ones obtained by the simple variational approach. By using a generalization of the forward-walking technique, we are able to calculate true FN ground-state expectation values of the pair-pair correlation functions. In the case of $t^prime=0$, there is a large region with a coexistence of superconductivity and antiferromagnetism, that survives up to $delta_c sim 0.10$ for $J/t=0.2$ and $delta_c sim 0.13$ for $J/t=0.4$. The presence of a finite $t^prime/t<0$ induces a strong suppression of both magnetic (with $delta_c lesssim 0.03$, for $J/t=0.2$ and $t^prime/t=-0.2$) and pairing correlations. In particular, the latter ones are depressed both in the low-doping regime and around $delta sim 0.25$, where strong size effects are present.
We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site non-random repulsion, the Hubbard $U$. We argue that recent numerical results of Cha et al. (arXiv:2002.07181) can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large $M$ theory which generalizes the SU(2) spin symmetry to SU($M$), and obtain exponents for the electron and spin correlators which agree with those of Cha et al. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small $U$.
Using a self-consistent Hartree-Fock approximation we investigate the relative stability of various stripe phases in the extended $t$-$t$-$U$ Hubbard model. One finds that a negative ratio of next- to nearest-neighbor hopping $t/t<0$ expells holes from antiferromagnetic domains and reinforces the stripe order. Therefore the half-filled stripes not only accommodate holes but also redistribute them so that the kinetic energy is gained, and these stripes take over in the regime of $t/tsimeq -0.3$ appropriate for YBa$_2$Cu$_3$O$_{6+delta}$.
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