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Register a new userMagnetic and spin-liquid phases in the frustrated $t-t^prime$ Hubbard model on the triangular lattice
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Added by
Luca Fausto Tocchio
Publication date
2020
fields
Physics
and research's language is
English
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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.
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We investigate melting of stripe phases in the overdoped regime x>0.3 of the two-dimensional t-t-U Hubbard model, using a spin rotation invariant form of the slave boson representation. We show that the spin and charge order disappear simultaneously, and discuss a mechanism stabilizing bond-centered and site-centered stripe structures.
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.
The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard (TLU) model, while the nature of the state is under debate. Using the density matrix renormalization group with SU(2)$_{rm{spin}} otimes $U(1)$_{rm{charge}}$ symmetries implemented, we study the TLU model defined on the long cylinder geometry with circumference $W=4$. A gapped quantum spin liquid, with on-site interaction $9 lesssim U / t lesssim 10.75$, is identified between the metallic and the antiferromagnetic Mott insulating phases. In particular, we find that this spin liquid develops a robust long-range spin scalar-chiral correlation as the system length $L$ increases, which unambiguously unveils the spontaneous time-reversal symmetry breaking. In addition, the large degeneracy of the entanglement spectrum supports symmetry fractionalization and spinon edge modes in the obtained ground state. The possible origin of chiral order in this intermediate spin liquid and its relation to the rotonlike excitations have also been discussed.
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