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Register a new userGeneric short-range interactions in two-leg ladders
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We derive a Hamiltonian for a two-leg ladder which includes an arbitrary number of charge and spin interactions. To illustrate this Hamiltonian we consider two examples and use a renormalization group technique to evaluate the ground state phases. The first example is a two-leg ladder with zigzagged legs. We find that increasing the number of interactions in such a two-leg ladder may result in a richer phase diagram, particularly at half-filling where a few exotic phases are possible when the number of interactions are large and the angle of the zigzag is small. In the second example we determine under which conditions a two-leg ladder at quarter-filling is able to support a Tomanaga-Luttinger liquid phase. We show that this is only possible when the spin interactions across the rungs are ferromagnetic. In both examples we focus on lithium purple bronze, a two-leg ladder with zigzagged legs which is though to support a Tomanaga-Luttinger liquid phase.
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We consider the effects of Umklapp processes in doped two-leg fermionic ladders. These may emerge either at special band fillings or as a result of the presence of external periodic potentials. We show that such Umklapp processes can lead to profound changes of physical properties and in particular stabilize pair-density wave phases.
Motivated by the recent experiment on $rm{K_2Cu_3Oleft(SO_4right)_3}$, an edge-shared tetrahedral spin-cluster compound [M. Fujihala textit{et al.}, Phys. Rev. Lett. textbf{120}, 077201 (2018)], we investigate two-leg spin-cluster ladders with the plaquette number $n_p$ in each cluster up to six by the density-matrix renormalization group method. We find that the phase diagram of such ladders strongly depends on the parity of $n_p$. For even $n_p$, the phase diagram has two phases, one is the Haldane phase, and the other is the cluster rung-singlet phase. For odd $n_p$, there are four phases, which are a cluster-singlet phase, a cluster rung-singlet phase, a Haldane phase and an even Haldane phase. Moreover, in the latter case the region of the Haldane phase increases while the cluster-singlet phase and the even Haldane phase shrink as $n_p$ increases. We thus conjecture that in the large $n_p$ limit, the phase diagram will become independent of $n_p$. By analysing the ground-state energy and entanglement entropy we obtain the order of the phase transtions. In particular, for $n_p=1$ there is no phase transition between the even Haldane phase and the cluster-singlet phase while for other odd $n_p$ there is a first-order phase transition. Our work provides comprehensive phase diagrams for these cluster-based models and may be helpful to understand experiments on related materials.
In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the divergent logarithmic length $l_d$ and a set of renormalization-group exponents, also works rather well. The superconducting phases in a doped two-leg ladder are studied and classified by these renormalization-group exponents as demonstration. Finally, non-trivial constraints among the exponents are derived and explained.
We study the dynamical spin response of doped two-leg Hubbard-like ladders in the framework of a low-energy effective field theory description given by the SO(6) Gross Neveu model. Using the integrability of the SO(6) Gross-Neveu model, we derive the low energy dynamical magnetic susceptibility. The susceptibility is characterized by an incommensurate coherent mode near $(pi,pi)$ and by broad two excitation scattering continua at other $k$-points. In our computation we are able to estimate the relative weights of these contributions. All calculations are performed using form-factor expansions which yield exact low energy results in the context of the SO(6) Gross-Neveu model. To employ this expansion, a number of hitherto undetermined form factors were computed. To do so, we developed a general approach for the computation of matrix elements of semi-local SO(6) Gross-Neveu operators. While our computation takes place in the context of SO(6) Gross-Neveu, we also consider the effects of perturbations away from an SO(6) symmetric model, showing that small perturbations at best quantitatively change the physics.
Magnetic excitations in two-leg S=1/2 ladders are studied both experimentally and theoretically. Experimentally, we report on the reflectivity, the transmission and the optical conductivity sigma(omega) of undoped La_x Ca_14-x Cu_24 O_41 for x=4, 5, and 5.2. Using two different theoretical approaches (Jordan-Wigner fermions and perturbation theory), we calculate the dispersion of the elementary triplets, the optical conductivity and the momentum-resolved spectral density of two-triplet excitations for 0.2 <= J_parallel/J_perpendicular <= 1.2. We discuss phonon-assisted two-triplet absorption, the existence of two-triplet bound states, the two-triplet continuum, and the size of the exchange parameters.
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