Generic short-range interactions in two-leg ladders

Abstract

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.

Zigzag carbon nanotubes with generic electron-electron interactions

“…2͑c͒ is definitely a TLL as it may be some other phase which appears to converge after much renormalization and then suddenly diverges. 29 In either case, after considering a number of different values for N x,y X we conclude that TLLlike behavior only arises when the e-e spin interactions are ferromagnetic and when these spin interactions are approximately of the same order as the charge interactions. This gives a clear indication of the importance of e-e spin interactions in CNT.…”

“…The interacting two-leg ladder problem can be solved using a well-developed method, [21][22][23][24][25][26][27][28][29] although with some differences due to the absence of rungs. 23,30 The Fermi operators d qj are linearized about the Fermi momentum k F by expanding in terms of chiral left-moving and right-moving fields and rapidly varying terms are discarded.…”

Thermal Properties of Rung Disordered Two-leg Quantum Spin Ladders: Quantum Monte Carlo Study

“…Various properties of a wide range of different ladder models have been studied, like spin ladder systems with dimerization [35][36][37][38][39][40][41] , zig-zag ladders 23,[42][43][44][45] , mixed ladders [46][47][48][49][50] . A gapless phase has been found in two-leg zig-zag ladders with frustration by benefiting from exact diagonalization and density matrix renormalization group (DMRG) methods 23 .…”

Competing orders in the generalized Hund chain model at half filling

“…In this respect, the bosonization approach has been very successful to investigate the physical properties of one-dimensional quantum phases 3,4 . Within this approach, several conventional and exotic long-range ordered phases have been revealed over the years in two-leg ladder models [5][6][7][8][9][10][11][12][13][14][15][16][17][18] and carbon nanotube systems [19][20][21][22] at half-filling. Two different classes of Mott-insulating phases have been found at half-filling in these systems.…”