Strong Rung Limit Research Articles

Partial Ferrimagnetism in S = 1/2 Heisenberg Ladders with a Ferromagnetic Leg, an Antiferromagnetic Leg, and Antiferromagnetic Rungs

Ground-state and finite-temperature properties of $S=1/2$ Heisenberg ladders with a ferromagnetic leg, an antiferromagnetic leg, and antiferromagnetic rungs are studied. It is shown that a partial ferrimagnetic phase extends over a wide parameter range in the ground state. The numerical results are supported by an analytical calculation based on a mapping onto the nonlinear $\sigma$ model and a perturbation calculation from the strong-rung limit. It is shown that the partial ferrimagnetic state is a spontaneously magnetized Tomonaga--Luttinger liquid with incommensurate magnetic correlation, which is confirmed by a DMRG calculation. The finite-temperature magnetic susceptibility is calculated using the thermal pure quantum state method. It is suggested that the susceptibility diverges as $T^{-2}$ in the ferrimagnetic phases as in the case of ferromagnetic Heisenberg chains.

Nature of a single doped hole in two-leg Hubbard and t−J ladders

In this paper, we have systematically studied the single hole problem in two-leg Hubbard and $t$-$J$ ladders by large-scale density-matrix renormalization group calculations. We found that the doped hole in both models behaves similarly with each other while the three-site correlated hopping term is not important in determining the ground state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, its spin and charge components are only loosely bound together with a nontrivial mutual statistics inside the quasiparticle. Our results show that this mutual statistics can lead to an important residual effect which dramatically changes the local structure of the ground state wavefunction.

Quasiparticle collapsing in an anisotropict−Jladder

Quasiparticle collapsing is a central issue in the study of strongly correlated electron systems. In the one-dimensional case, the quasiparticle collapsing in a form of spin-charge separation has been well established, but the problem remains elusive in dimensions higher than one. By using the density matrix renormalization group (DMRG) algorithm, we show that in an anisotropic two-leg $t\ensuremath{-}J$ ladder, an injected single hole behaves like a well-defined quasiparticle in the strong rung limit but undergoes a ``phase transition'' with the effective mass diverging at a quantum critical point (QCP) towards the isotropic limit. After the transition, the quasiparticle collapses into a loosely bound object of a charge (holon) and a spin-1/2 (spinon) accompanied by an unscreened phase string as well as a substantially enhanced binding energy between two doped holes. A phase diagram of multileg ladders is further obtained, which extrapolates the QCP towards the two-dimensional limit. The underlying mechanism generic for any dimensions is also discussed.

Berry phase investigation of spin-Sladders

We investigate the properties of antiferromagnetic spin-$S$ ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time-reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of nonfrustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains, with the surprising conclusion that, at least far enough from dimerized chains, they define different domains in parameter space. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated with a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated with a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes $2S$ times. By analogy with the fully frustrated ladder, these changes are interpreted as crossovers between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to $2S$ in the weak rung limit. This interpretation is further supported by the observation that these crossovers turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin $2S$ impurity.

Frustration-induced plateaus inS≥12Heisenberg spin ladders

We study the T = 0 magnetization of frustrated two-leg spin ladders with arbitrary value of the spin S. In the strong rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaux at fractional values of the magnetization for all spins S, and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaux. These ratios depend both on the plateau and on the spin. To confirm these results, and to investigate the properties of these ladders away from the strong coupling limit, we have performed extensive density matrix renormalization group (DMRG) calculations for S <= 2. For large enough inter-rung couplings, all plateaux simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.