We present the phase diagram of the
S=1/2 Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.
The ground-state phase diagram of a Heisenberg $\text{spin}\ensuremath{-}\frac{1}{2}$ system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides the usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low-energy dispersions and ground-state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.
Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.
We study the spin-1/2 two-leg Heisenberg ladder with four-spin ring exchanges under a magnetic field. We introduce an exact duality transformation which is an extension of the spin-chirality duality developed previously and yields a new self-dual surface in the parameter space. We then determine the magnetic phase diagram using the numerical approaches of the density-matrix renormalization-group and exact diagonalization methods. We demonstrate the appearance of a magnetization plateau and the Tomonaga-Luttinger liquid with dominant vector-chirality quasi-long-range order for a wide parameter regime of strong ring exchange. A "nematic" phase, in which magnons form bound pairs and the magnon-pairing correlation functions dominate, is also identified.
A spin-1/2 Heisenberg model with a chirality-chirality interaction (CCI) on a two-leg ladder provides a minimal setup to explore an interplay between spin and chirality degrees of freedom. This model is potentially relevant for understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a comprehensive ground-state phase diagram that includes previously unexplored cases of a ferromagnetic rung exchange
J⊥<0 or a negative CCI
Kch<0. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Moreover, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties.
Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg
SU(N) spin ladders. Two-leg ladders provide a rich and highly nontrivial extension of the single chain case on the way towards the relatively little explored two-dimensional situation. Focusing on the experimentally relevant limit of one fermion per site, antiferromagnetic exchange interactions, and $2\ensuremath{\le}N\ensuremath{\le}6$, we show that the phase diagrams as a function of the interchain (rung) to intrachain (leg) coupling ratio, ${J}_{\ensuremath{\perp}}/{J}_{\ensuremath{\parallel}}$, strongly differ for even versus odd
N. For even
N=4 and 6, we demonstrate that the phase diagram consists of a single valence bond crystal (VBC) with a spatial period of
N/2 rungs. For odd
N=3 and 5, we find surprisingly rich phase diagrams exhibiting three distinct phases. For weak rung coupling, we obtain a VBC with a spatial period of
N rungs, whereas for strong coupling we obtain a critical phase related to the case of a single chain. In addition, we encounter intermediate phases for odd
N, albeit of a different nature for
N=3 as compared to
N=5. For
N=3, we find a novel gapless intermediate phase with ${J}_{\ensuremath{\perp}}$-dependent incommensurate spatial fluctuations in a sizeable region of the phase diagram. For
N=5, there are strong indications for a narrow potentially gapped intermediate phase, whose nature is not entirely clear. Our results are based on (i) field theoretical techniques, (ii) qualitative symmetry considerations, and (iii) large-scale density matrix renormalization group (DMRG) simulations keeping beyond a million of states by fully exploiting and thus preserving the
SU(N) symmetry.