We study two (very) weakly coupled Hubbard chains in the half-filled case, and especially the situation where the intrachain Mott scale m is much larger than the (bare) single-electron interchain hopping ${t}_{\ensuremath{\perp}}.$ First, we find that the divergence of the intrachain umklapp channel at the Mott transition results in the complete vanishing of the single-electron interchain hopping: this is significant of a strong confinement of coherence along the chains. Excitations are usual charge fermionic solitons and spinon-(anti)spinon pairs of the Heisenberg chain. Then, we show rigorously how the tunneling of spinon-(anti)spinon pairs produces an antiferromagnetic interchain exchange of the order of ${J}_{\ensuremath{\perp}}{=t}_{\ensuremath{\perp}}^{2}/m.$ In the ``confined'' phase and in the far infrared, the system behaves as a pure spin ladder. The final result is an insulating ground state with spin-gapped excitations exactly as in the opposite ``delocalized'' limit (i.e., for rather large interchain hoppings) where the two-leg ladder is in the well-known insulating $D\ensuremath{-}\mathrm{Mott}$ phase. Unlike materials with an infinite number of coupled chains (Bechgaard salts), the confinement/deconfinement transition at absolute zero is here a simple crossover: no metallic phase is found in undoped two-leg ladders. This statement might be generalized for N-leg ladders with
N=3,4,… (but not too large).
Extraction of antiferromagnetic (AF) exchange constants J and J\ensuremath{'} in two-leg spin-1/2 nearest-neighbor (NN) Heisenberg ladders from experimental magnetic spin susceptibility \ensuremath{\chi}(T) data is studied, where J\ensuremath{'} is the NN exchange constant in the rungs and J is that in the legs. Two low-T (T\ensuremath{\ll}J/
kB) approximations of Troyer, Tsunetsugu, and W\"urtz [Phys. Rev. B 50, 13 515 (1994)] for \ensuremath{\chi}(T) of the isolated spin-1/2 two-leg ladder with J\ensuremath{'}/J=1 are shown to be accurate to \ensuremath{\sim}10% when extrapolated to T\ensuremath{\sim}J\ensuremath{'}/
kB. The variations in the magnetic excitation dispersion relation parameters [which enter the low-T expression of Troyer et al. for \ensuremath{\chi}(T)] for J\ensuremath{'}/J1 are inferred from previous theoretical results. Next, the values of the maxima in \ensuremath{\chi}(T)\ensuremath{\equiv}${\mathrm{\ensuremath{\chi}}}^{\mathrm{max}}$ from many numerical calculations in the literature for various nonfrustrated spin-1/2 NN Heisenberg antiferromagnets are considered. The values of the product ${\mathrm{\ensuremath{\chi}}}^{\mathrm{max}}$
zeff are found to depend systematically and almost uniqely on an effective magnetic coordination number
zeff, defined in the text, but are nearly independent of the dimensionality of the spin lattice and of the magnitude of any gap in the magnetic excitation spectrum. This observation allows accurate bounds on the exchange coupling constants in arbitrary quasi-low-dimensional spin-1/2 antiferromagnets to be inferred from experimental ${\mathrm{\ensuremath{\chi}}}^{\mathrm{max}}$ values. Finally, a mean-field-type expression for \ensuremath{\chi}(T) for arbitrary quasi-low-dimensional spin-1/2 Heisenberg antiferromagnets is derived, using the above ${\mathrm{\ensuremath{\chi}}}^{\mathrm{max}}$ phenomenology as input, which allows the influence of intersystem coupling on \ensuremath{\chi}(T) to be evaluated. These results, and the \ensuremath{\chi}(T) calculations of Barnes and Riera [Phys. Rev. B 50, 6817 (1994)] for isolated two-leg spin-1/2 Heisenberg ladders, are used to analyze the experimental \ensuremath{\chi}(T) data of Azuma et al. [Phys. Rev. Lett. 73, 3463 (1994)] for the spin-1/2 two-leg ladder compound
SrCu2O3. The analyses together suggest that J\ensuremath{'}/J\ensuremath{\sim}0.5, contrary to the expectation that J\ensuremath{'}/J\ensuremath{\approxeq}1, and that J is very large (\ensuremath{\sim}2000 K), similar to the value of J in the linear-chain cuprate
Sr2CuO3. \textcopyright{} 1996 The American Physical Society.
We study two (very) weakly-coupled Hubbard chains in the half-filled case, and especially the situation where the intrachain Mott scale
m is much larger than the bare single-electron interchain hopping
t⊥. First, we find that the divergence of the intrachain Umklapp channel at the Mott transition results in the complete vanishing of the single-electron interchain hopping: This is significant of a strong confinement of coherence along the chains. Excitations are usual charge fermionic solitons and spinon pairs of the Heisenberg chain. Then, we show rigorously how the tunneling of spinon-pairs produces a magnetic interchain exchange
J⊥=t⊥2/m>0. The result is an insulating state with spin-gapped excitations as in the delocalized limit (i.e. for rather large interchain hoppings), where the two-leg ladder is in the well-known D-Mott phase. Unlike for Bechgaard salts, the confinement/deconfinement transition at absolute zero is here a simple crossover: no metallic phase is found in undoped two-leg ladders. This statement might be generalized for N-leg ladders with N=3,4... (but not too large).
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a
T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-
Tc cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
In strongly correlated quantum materials, the behavior of charge carriers is dominated by strong electron-electron interactions. These can lead to insulating states with spin order, and upon doping to competing ordered states including unconventional superconductivity. The underlying pairing mechanism remains poorly understood however, even in strongly simplified theoretical models. Recent advances in quantum simulation allow to study pairing in paradigmatic settings, e.g. in the t-J t − J and t-J_z t − J z Hamiltonians. Even there, the most basic properties of paired states of only two dopants, such as their dispersion relation and excitation spectra, remain poorly studied in many cases. Here we provide new analytical insights into a possible string-based pairing mechanism of mobile holes in an antiferromagnet. We analyze an effective model of partons connected by a confining string and calculate the spectral properties of bound states. Our model is equally relevant for understanding Hubbard-Mott excitons consisting of a bound doublon-hole pair or confined states of dynamical matter in lattice gauge theories, which motivates our study of different parton statistics. Although an accurate semi-analytic estimation of binding energies is challenging, our theory provides a detailed understanding of the internal structure of pairs. For example, in a range of settings we predict heavy states of immobile pairs with flat-band dispersions - including for the lowest-energy d d -wave pair of fermions. Our findings shed new light on the long-standing question about the origin of pairing and competing orders in high-temperature superconductors.
To make the transition from the quasi-long-range order in a chain of antiferromagnetically coupled S = 1/2 spins to the true long-range order that occurs in a plane, one can assemble chains to make ladders of increasing width. Surprisingly, this crossover between one and two dimensions is not at all smooth. Ladders with an even number of legs have purely short-range magnetic order and a finite energy gap to all magnetic excitations. Predictions of this ground state have now been verified experimentally. Holes doped into these ladders are predicted to pair and possibly superconduct.