Confinement and bound states of bound states in a transverse-field two-leg Ising ladder

A mean field theory for the spin ladder system

In the present paper, we propose a mean field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean field level that ladders with even number legs open a energy gap in their low energy excitation with a magnitude close to the corresponding experimental values, whereas the low energy excitation of the odd-number-leg ladders are gapless. It supports the validity of our approach. We then calculate the gap size and the excitation spectra of 2-leg-ladder system. Our result is in good agreement with both the experimental data and…

Phase diagram of S=1/2 two-leg XXZ spin ladder systems

We investigate the ground state phase diagram of the S=1/2 two-leg $XXZ$ spin ladder system with an isotropic interchain coupling. In this model, there is the Berezinskii-Kosterlitz-Thouless transition which occurs at the XY-Haldane and the XY-rung singlet phase boundaries. It was difficult to determine the transition line using traditional methods. We overcome this difficulty using the level spectroscopy method combined with the twisted boundary condition method, and we check the consistency. We find out that the phase boundary between XY phase and Haldane phase lies on the $Δ=0$ line. And we…

Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions

In this work, we investigate an exactly solvable two-leg spin ladder with three-spin interactions. We obtain analytically the finite-size corrections of the low-lying energies and determine the central charge as well as the scaling dimensions. The model considered in this work has the same universality class of critical behavior of the XX chain with central charge c=1. By using the correlation matrix method, we also study the finite-size corrections of the Renyi entropy of the ground state and of the excited states. Our results are in agreement with the predictions of the conformal field theor…

Four-spin-exchange- and magnetic-field-induced chiral order in two-leg spin ladders

We propose a mechanism of a vector chiral long-range order in two-leg spin-1/2 and spin-1 antiferromagnetic ladders with four-spin exchanges and a Zeeman term. It is known that for one-dimensional quantum systems, spontaneous breakdown of continuous symmetries is generally forbidden. Any vector chiral order hence does not appear in spin-rotationally [SU(2)]-symmetric spin ladders. However, if a magnetic field is added along the S^z axis of ladders and the SU(2) symmetry is reduced to the U(1) one, the z component of a vector chiral order can emerge with the remaining U(1) symmetry unbroken. Ma…

Low-energy properties of two-leg spin-1 antiferromagnetic ladders with commensurate external fields and their extensions

This study addresses low-energy properties of 2-leg spin-1 ladders with antiferromagnetic (AF) intrachain coupling under a uniform or staggered external field $H$, and a few of their modifications. The generalization to spin-$S$ ladders is also discussed. In the strong AF rung (interchain)-coupling $J_\perp$ region, degenerate perturbation theory applied to spin-$S$ ladders predicts $2S$ critical curves in the parameter space $(J_\perp, H)$ for the staggered field case, in contrast to $2S$ finite critical regions for the uniform field case. All critical areas belong to a universality with cent…

The N-Leg spin-S Heisenberg ladders: A DMRG study

We investigate the N-leg spin-S Heisenberg Ladders by using the density matrix renormalization group method. We present estimates of the spin gap $Δ_{s}$ and of the ground state energy per site $e_{\infty}^{N}$ in the thermodynamic limit for ladders with widths up to six legs and spin $S\leq\frac{5}{2}$. We also estimate the ground state energy per site $e_{\infty}^{2D}$ for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for $N$ odd and gapped for N even. Whereas for integer spin ladders the spin…

Bond Disorder in Even-Leg Heisenberg Ladders

Random bond disorder in antiferromagnetic spin-1/2 Heisenberg ladders is investigated using the Stochastic Series Expansion Quantum Monte Carlo method. We find that the effects of individual bond impurities vary strongly, depending on their position on legs and rungs. We initially focus on how the distribution of local bond energies depends on the impurity concentration. Then we study how the phase diagram of even-leg ladders is affected by random bond doping. We observe Bose glass phases in two regimes ($h' < h \lesssim h_{c1}$ and $h" < h <h_{c2}$) and a Bose-Einstein Condensate in-between. …

受挫四腿自旋1/2梯子中的自旋1和自旋2竞争区域

Competing spin-1 and spin-2 regimes in a frustrated four-leg spin-1/2 ladder

利用密度矩阵重正化群计算，研究受挫四腿自旋1/2梯子，发现三种区域：短程反铁磁腿、短程铁磁腿和有效自旋2海森堡链，通过交叉和一阶相变分隔。

Solution of a two leg spin ladder system

A new model for a spin 1/2 ladder system with two legs is introduced. It is demonstrated that this model is solvable via the Bethe ansatz method for arbitrary values of the rung coupling J. This is achieved by a suitable mapping from the Hubbard model with appropriate twisted boundary conditions. We determine that a phase transition between gapped and gapless spin excitations occurs at the critical value J_c=1/2 of the rung coupling.

Magnetization Plateaus in a Solvable 3-Leg Spin Ladder

We present a solvable ladder model which displays magnetization plateaus at fractional values of the total magnetization. Plateau signatures are also shown to exist along special lines. The model has isotropic Heisenberg interactions with additional many-body terms. The phase diagram can be calculated exactly for all values of the rung coupling and the magnetic field. We also derive the anomalous behaviour of the susceptibility near the plateau boundaries. There is good agreement with the phase diagram obtained recently for the pure Heisenberg ladders by numerical and perturbative techniques.

Three-leg Antiferromagnetic Heisenberg Ladder with Frustrated Boundary Condition; Ground State Properties

The antiferromagnetic Heisenberg spin systems on the three-leg ladder are investigated. Periodic boundary condition is imposed in the rung direction. The system has an excitation gap for all antiferromagnetic inter-chain coupling ($J_{\perp}>0$). The estimated gap for the strong coupling limit ($J_{\perp}/J_1 \to \infty$) is 0.28$J_1$. Although the interaction is homogeneous and only nearest-neighbor, the ground states of the system are dimerized and break the translational symmetry in the thermodynamic limit. Introducing the next-nearest neighbor coupling ($J_2$), we can see that the system i…

Ground-state fidelity and quantum criticality in a two-leg ladder with cyclic four-spin exchange

We investigate a two-leg Heisenberg spin ladder with cyclic four-spin exchange by exploiting a newly-developed tensor network algorithm. The algorithm allows to efficiently compute the ground-state fidelity per lattice site, which enables us to establish the ground-state phase diagram for quantum lattice many-body systems. The latter is based on the observation that, for an infinite-size system, any singularity on a ground-state fidelity surface characterizes a critical point, at which the system undergoes a phase transition. For the two-leg Heisenberg spin-1/2 ladder with cyclic four-spin exc…

Quantum phase transition by cyclic four-spin exchange interaction for S=1/2 two-leg spin ladder

We investigate an $S=1/2$ two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by $J_4$, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by $J_{rung}$ and $J_{\rm leg}$, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet ($S_{tot}^z=0$) and the triplet ($S_{tot}^z=1$) states vanishes at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$. This result is in contrast with the fact that the $S=1/2$ antiferromagnetic Heisenberg l…