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Register a new userMetallic and insulating stripes and their relation with superconductivity in the doped Hubbard model
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Added by
Luca Fausto Tocchio
Publication date
2019
fields
Physics
and research's language is
English
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The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and possibly coexist in a wide regime of electron dopings for both weak and strong couplings. Here, we investigate this antagonism within a variational approach that is based upon Jastrow-Slater wave functions, including backflow correlations, which can be treated within a quantum Monte Carlo procedure. We focus on clusters having a ladder geometry with $M$ legs (with $M$ ranging from $2$ to $10$) and a relatively large number of rungs, thus allowing us a detailed analysis in terms of the stripe length. We find that stripe order with periodicity $lambda=8$ in the charge and $2lambda=16$ in the spin can be stabilized at doping $delta=1/8$. Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with $lambda=6$, appears at $delta=1/6$. Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at $delta=1/12$ and metallic with strong superconducting correlations at $delta=1/10$, as well as for intermediate (incommensurate) dopings. Remarkably, we observe that spin modulation plays a major role in stripe formation, since it is crucial to obtain a stable striped state upon optimization. The relevance of our calculations for previous density-matrix renormalization group results and for the two-dimensional case is also discussed.
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The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models, they differ on which is the actual ground state. Finite cluster methods typically indicate that stripe order dominates while embedded quantum cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate for the first time that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides a new opportunity to study the influence of fluctuating stripe correlations on the models pairing correlations within a unified numerical framework.
We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our Ansatz is an optimized linear superposition of Affleck-Kennedy-Lieb-Tasaki valence bond states, rendering the combination a valence bond liquid dubbed Orbital Resonant Valence Bond. We show that the undoped (one electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Andersons resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths -- W the carriers bandwidth -- could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.
We explore the ground-state properties of the two-band Hubbard model with degenerate electronic bands, parametrized by nearest-neighbor hopping $t$, intra- and inter-orbital on-site Coulomb repulsions $U$ and $U^prime$, and Hund coupling $J$, focusing on the case with $J>0$. Using Jastrow-Slater wave functions, we consider both states with and without magnetic/orbital order. Electron pairing can also be included in the wave function, in order to detect the occurrence of superconductivity for generic electron densities $n$. When no magnetic/orbital order is considered, the Mott transition is continuous for $n=1$ (quarter filling); instead, at $n=2$ (half filling), it is first order for small values of $J/U$, while it turns out to be continuous when the ratio $J/U$ is increased. A significant triplet pairing is present in a broad region around $n=2$. By contrast, singlet superconductivity (with $d$-wave symmetry) is detected only for small values of the Hund coupling and very close to half filling. When including magnetic and orbital order, the Mott insulator acquires antiferromagnetic order for $n=2$; instead, for $n=1$ the insulator has ferromagnetic and antiferro-orbital orders. In the latter case, a metallic phase is present for small values of $U/t$ and the metal-insulator transition becomes first order. In the region with $1<n<2$, we observe that ferromagnetism (with no orbital order) is particularly robust for large values of the Coulomb repulsion and that triplet superconductivity is strongly suppressed by the presence of antiferromagnetism. The case with $J=0$, which has an enlarged SU(4) symmetry due to the interplay between spin and orbital degrees of freedom, is also analyzed.
The interplay between thermal and quantum fluctuations controls the competition between phases of matter in strongly correlated electron systems. We study finite-temperature properties of the strongly coupled two-dimensional doped Hubbard model using the minimally-entangled typical thermal states (METTS) method on width $4$ cylinders. We discover that a phase characterized by commensurate short-range antiferromagnetic correlations and no charge ordering occurs at temperatures above the half-filled stripe phase extending to zero temperature. The transition from the antiferromagnetic phase to the stripe phase takes place at temperature $T/t approx 0.05$ and is accompanied by a step-like feature of the specific heat. We find the single-particle gap to be smallest close to the nodal point at $mathbf{k}=(pi/2, pi/2)$ and detect a maximum in the magnetic susceptibility. These features bear a strong resemblance to the pseudogap phase of high-temperature cuprate superconductors. The simulations are verified using a variety of different unbiased numerical methods in the three limiting cases of zero temperature, small lattice sizes, and half-filling. Moreover, we compare to and confirm previous determinantal quantum Monte Carlo results on incommensurate spin-density waves at finite doping and temperature.
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.
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