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arXiv:cond-mat/0511458

Charge ordering in quasi-one-dimensional systems with frustrating interactions

Siddhartha Lal, M. S. Laad

Published Nov 18, 2005• 0 citations
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Abstract

Motivated by the co-existing charge and spin order found in strongly correlated ladder systems, we study an effective pseudospin model on a coupled two-leg ladder. A bosonisation analysis yields a rich phase diagram showing Wigner/Peierls charge order and Neel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled ladder systems.

DOI
10.48550/arxiv.cond-mat/0511458

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Motivated by the co-existing charge and spin order found in strongly correlated ladder systems, we study an effective pseudospin model on a coupled two-leg ladder. A bosonisation analysis yields a rich phase diagram showing Wigner/Peierls charge order and Neel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled ladder systems.
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We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion VVV using the density matrix renormalization-group technique. The ground state is homogeneous at small V,V,V, a ``checkerboard'' charge-ordered insulator at large VVV and not too small on site Coulomb repulsion U, and is phase separated for moderate or large VVV and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling, charge-ordered regime that maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.
We study the effect of dimerization (due to, e.g., spin-Peierls instability) on the phase diagram of a frustrated antiferromagnetic spin-1/2 ladder, with weak transverse and diagonal rung coupling. Our analysis focuses on a one-dimensional version of the model (i.e., a single two-leg ladder) where we consider two forms of dimerization on the legs: columnar dimers (CDs) and staggered dimers (SDs). We examine in particular the regime of parameters (corresponding to an intermediate XXZXXZXXZ anisotropy) in which the leg dimerization and the rung coupling terms are equally relevant. In both the CD and SD cases, we find that the effective field theory describing the system is a self-dual sine-Gordon model, which favors ordering and the opening of a gap to excitations. The order parameter, which reflects the interplay between the leg and rung dimerization interactions, represents a crystal of 4-spin plaquettes on which longitudinal and transverse dimers are in a coherent superposition. Depending on the leg dimerization mode, these plaquettes are closed or open, however both types spontaneously break reflection symmetry across the ladder. The closed plaquettes are stable, while the open plaquette order is relatively fragile and the corresponding gap may be tuned to zero under extreme conditions. We further find that a first-order transition occurs from the plaquette order to a valence bond crystal (VBC) of dimers on the legs. This suggests that in a higher-dimensional version of this system, this variety of distinct VBC states with comparable energies leads to the formation of domains. Effectively one-dimensional gapless spinon modes on domain boundaries may account for the experimental observation of spin-liquid behavior in a physical realization of the model.
We study a model of the stripe state in strongly correlated systems consisting of an array of antiferromagnetic spin ladders, each with n(leg) legs, coupled to each other through the spin-exchange interaction to charged stripes in between each pair of ladders. The charged stripes are assumed to be Luttinger liquids in a spin-gap regime. An effective interaction for a pair of neighboring ladders is calculated by integrating out the gapped spin degrees of freedom in the charged stripes. The low energy effective theory of each ladder is a nonlinear sigma model with additional cross couplings of neighboring ladders, which favor either in-phase or antiphase short-range spin orderings depending on the physical parameters of the charged stripe.
Developing a theoretical framework to access the quantum phases of itinerant bosons or fermions in two dimensions that exhibit singular structure along surfaces in momentum space but have no quasiparticle description remains a central challenge in the field of strongly correlated physics. In this paper we propose that distinctive signatures of such two-dimensional (2D) strongly correlated phases will be manifest in quasi-one-dimensional ``NNN-leg ladder'' systems. Characteristic of each parent 2D quantum liquid would be a precise pattern of one-dimensional (1D) gapless modes on the NNN-leg ladder. These signatures could be potentially exploited to approach the 2D phases from controlled numerical and analytical studies in quasi-one-dimension. As a first step we explore itinerant-boson models with a frustrating ring-exchange interaction on the two-leg ladder, searching for signatures of the recently proposed two-dimensional ddd-wave-correlated Bose liquid (DBL) phase. A combination of exact diagonalization, density-matrix renormalization-group, variational Monte Carlo, and bosonization analysis of a quasi-1D gauge theory provide compelling evidence for the existence of an unusual strong-coupling phase of bosons on the two-leg ladder, which can be understood as a descendant of the two-dimensional DBL. We suggest several generalizations to quantum spin and electron Hamiltonians on ladders, which could likewise reveal fingerprints of such 2D non-Fermi-liquid phases.