Strong-coupling phases of frustrated bosons on a two-leg ladder with ring exchange
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 "N-leg ladder" systems. Characteristic of each parent 2D quantum liquid would be a precise pattern of one-dimensional (1D) gapless modes on the N-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 d-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.
Additional Information© 2008 The American Physical Society. (Received 7 May 2008; published 26 August 2008). Editor's suggestion. We would like to thank L. Balents, T. Senthil, and A. Vishwanath for useful discussions. This work was supported by DOE Grant No. DE-FG02-06ER46305 (D.N.S.), the National Science Foundation through Grants No. DMR-0605696 (D.N.S.) and No. DMR-0529399 (MPAF), and the A.P. Sloan Foundation (O.I.M.). Some of our numerical simulations were based on the ALPS libraries.
Published - SHEprb08.pdf
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