Competing orders in coupled Luttinger liquids

Congjun Wu, W. Vincent Liu, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review


We consider the problem of two-coupled Luttinger liquids both at half filling and at low doping levels, to investigate the problem of competing orders in quasi-one-dimensional strongly correlated systems. We use bosonization and renormalization group equations to investigate the phase diagrams, to determine the allowed phases, and to establish approximate boundaries among them. Because of the chiral translation and reflection symmetries in the charge mode away from half filling, orders of charge-density wave (CDW) and spin Peierls (SP), diagonal current (DC), and d-density wave (DDW) form two doublets and thus can be at most quasi-long-range ordered. At half filling, Umklapp terms break this symmetry down to a discrete group and thus Ising-type ordered phases appear as a result of spontaneous breaking of the residual symmetries. Quantum disordered Haldane phases are also found, with finite amplitudes of pairing orders and triplet counterparts of CDW, SP, DC, and DDW. Relations with recent numerical results and implications to similar problems in two dimensions are discussed.

Original languageEnglish (US)
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
StatePublished - 2003

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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