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 Physics , 2005, DOI: 10.1103/PhysRevB.73.012411 Abstract: We study the low-energy excitations of the spin-1/2 antiferromagnetic Heisenberg chain and $N$-leg ($N$=2, 3, 4) ladders in a staggered magnetic field $h_s$. We show that $h_s$ induces gap and midgap states in all the cases and examine their field scaling behavior. A modified boundary scheme is devised to extract accurate bulk excitation behavior. The gap values converge rapidly as $N$ increases, leading to a field scaling exponent $\gamma=1/2$ for both the longitudinal and transverse gaps of the square lattice ($N \to \infty$). The midgap states induced by the boundary edge effects share the bulk gap scaling exponents but their overall scaling behavior in the large-N limit needs further investigation.
 Physics , 2000, DOI: 10.1103/PhysRevB.63.100402 Abstract: We have synthesized and characterized a new spin-1/2 Heisenberg antiferromagnetic ladder: bis 5-iodo-2-aminopyridinium tetrabromocuprate(II) dihydrate. X-ray diffraction studies show the structure of the compound to consist of well isolated stacked ladders and the interaction between the Cu(2+) atoms to be due to direct Br...Br contacts. Magnetic susceptibility and magnetization studies show the compound to be in the strong-coupling limit, with the interaction along the rungs (J' ~ 13 K) much greater than the interaction along the rails (J ~ 1 K). Magnetic critical fields are observed near 8.3 T and 10.4 T, respectively, establishing the existence of the energy gap.
 Physics , 1999, DOI: 10.1016/S0921-4526(99)02869-0 Abstract: We have determined the ground state for both a ladder array of Josephson junctions and a ladder of thin superconducting wires. We find that the repulsive interaction between vortices falls off exponentially with separation. The fact that the interaction is short-range leads to novel phenomena. The ground state vortex density exhibits a complete devil's staircase as the applied magnetic field is increased, each step producing a pair of metal-insulator transitions. The critical fields in the staircase are all calculated analytically and depend only on the connectivity of the ladder and the area of the elementary plaquette. In particular the normal square ladder contains no vortices at all until the flux per plaquette reaches 0.5/sqrt{3} flux quanta.
 Physics , 2007, DOI: 10.1103/PhysRevLett.99.117201 Abstract: We examine the influence of weak anisotropic interactions on the T=0 phase diagram of the frustrated two-leg Heisenberg ladder, a well-studied spin model exhibiting integer and fractional magnetization plateaux separated by gapless incommensurate states. We find that the Dzyaloshinskii--Moriya coupling may substantially modify the phase diagram so that the half-integer plateau and the surrounding gapless phases merge into a single Ising-ordered phase breaking the translational symmetry of the lattice. A different Ising order is found for a weakly frustrated ladder. Implications for experimental ladder and dimer systems are discussed.
 Gaoyong Sun Physics , 2015, Abstract: In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting many-body states were observed. Motivated by these experiments, we extend the uniform synthetic magnetic field to a periodic case and show that a commensurate synthetic magnetic field offers an alternative scheme to realize topological phases in many-body systems of ultra-cold Fermi gases in ladder-like optical lattices. Using the exact diagonalization, we numerically determine the topological band structure, edge states, non-zero Chern numbers, Hofstadter-like-butterfly spectrum, and a complete phase diagram of non-interacting fermionic ladders.
 Physics , 2000, DOI: 10.1103/PhysRevB.63.144503 Abstract: We report on a theoretical analysis, consisting of both numerical and analytic work, of the stability of synchronization of a ladder array of Josephson junctions under the influence of current induced magnetic fields. Surprisingly, we find that as the ratio of the mutual to self inductance of the cells of the array is increased a region of unstable behavior occurs followed by reentrant stable synchronization. Analytic work tells us that in order to understand fully the cause of the observed instabilities the behavior of the vertical junctions, sometimes ignored in analytic analyses of ladder arrays, must be taken into account.
 Frederic Mila Physics , 1998, DOI: 10.1007/s100510050542 Abstract: We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase ($H_c^1$, $H_c^2$, the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration.