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arXiv:cond-mat/0606691 · Physical Review B

Competing orders and hidden duality symmetries in two-leg spin ladder systems

P. Lecheminant, Kiyohito Totsuka

Published Dec 21, 2006• 27 citations
arXivHTMLPDF

Abstract

A unifying approach to competing quantum orders in generalized two-leg spin ladders is presented. Hidden relationship and quantum phase transitions among the competing orders are thoroughly discussed by means of a low-energy field theory starting from an SU(4) quantum multicritical point. Our approach reveals that the system has a relatively simple phase structure in spite of its complicated interactions. On top of the U(1) symmetry which is known from previous studies to mix up antiferromagnetic order parameter with that of the $p$-type nematic, we find an emergent U(1) symmetry which mixes order parameters dual to the above. On the basis of the field-theoretical and variational analysis, we give a qualitative picture for the global structure of the phase diagram. Interesting connection to other models (e.g., the bosonic $t\text{\ensuremath{-}}J$ model) is also discussed.

DOI
10.1103/physrevb.74.224426

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A unifying approach to competing quantum orders in generalized two-leg spin ladders is presented. Hidden relationship and quantum phase transitions among the competing orders are thoroughly discussed by means of a low-energy field theory starting from an SU(4) quantum multicritical point. Our approach reveals that the system has a relatively simple phase structure in spite of its complicated interactions. On top of the U(1) symmetry which is known from previous studies to mix up antiferromagnetic order parameter with that of the ppp-type nematic, we find an emergent U(1) symmetry which mixes order parameters dual to the above. On the basis of the field-theoretical and variational analysis, we give a qualitative picture for the global structure of the phase diagram. Interesting connection to other models (e.g., the bosonic t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model) is also discussed.
The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point that unifies different competing dimerized orders and a scalar chirality phase that breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is dominated by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of a U(1)\mathrm{U}(1)U(1) self-duality symmetry.
Abstract We studied quantum phase transitions in the antiferromagnetic dimerized spin- 1 2 XY chain and two-leg ladders. From analysis of several spin models we present our main result: the framework to deal with topological orders and hidden symmetries within the Landau paradigm. After mapping of the spin Hamiltonians onto the tight-binding models with Dirac or Majorana fermions and, when necessary, the mean-field approximation, the analysis can be done analytically. By utilizing duality transformations the calculation of nonlocal string order parameters is mapped onto the local order problem in some dual representation and done without further approximations. Calculated phase diagrams, phase boundaries, order parameters and their symmetries for each of the phases provide a comprehensive quantitative Landau description of the quantum critical properties of the models considered. Complementarily, the phases with hidden orders can also be distinguished by the Pontryagin (winding) numbers which we have calculated as well. This unified framework can be straightforwardly applied for various spin chains and ladders, topological insulators and superconductors. Applications to other systems are under way.
We analyzed quantum phase transitions in the antiferromagnetic dimerized spin-1/2 XY chain and two-leg ladders. Their gapped phases possess distinct nonlocal string order parameters (SOPs) and the hidden symmetry breaking in each phase is identified. After mapping of the original spin Hamiltonians onto the tight-binding models with Dirac or Majorana fermions and the mean-field approximation (for ladders), the essential physics of nonlocal orders can be grasped analytically. By utilizing duality transformations the calculation of SOPs is mapped onto the local order problem in some dual representation and done without further approximations. The phases with hidden orders can also be distinguished by topological winding numbers. The latter provide a complimentary description. Our main result is the framework to treat nonlocal orders and hidden symmetries which unifies the key elements of the Landau paradigm with the new concept of topological order. This unified framework can be straightforwardly applied for spin chain and ladders, topological insulators and superconductors. Applications of this theory to other systems are under way.
Abstract Finding the Kitaev spin liquid in candidate materials involves understanding the entire phase diagram, including other allowed interactions. One of these interactions, called the Gamma (Γ) interaction, causes magnetic frustration and its interplay with the Kitaev (K) interaction is crucial to comprehend Kitaev materials. Due to the complexity of the combined KΓ model, quasi-one-dimensional models have been investigated. While several disordered phases are found in the 2-leg ladder, the nature of the phases are yet to be determined. Here we focus on the disordered phase near the antiferromagnetic Γ limit (denoted by AΓ phase) next to the ferromagnetic Kitaev phase. We report a distinct non-local string order parameter characterizing the AΓ phase, different from the string order parameter in the Kitaev phase. This string order parameter becomes evident only after two unitary transformation, referred to as a twice hidden string order parameter. The related entanglement spectrum, edge states, magnetic field responses, and the symmetry protecting the phase are presented, and its relevance to the two-dimensional Kitaev materials is discussed. Two newly identified disordered phases in the phase diagram of KΓ ladder is also reported.
We discuss duality relations in correlated electronic ladder systems to clarify mutual relations between various conventional and unconventional phases. For the generalized two-leg Hubbard ladder, we find two exact duality relations, and also one asymptotic relation which holds in the low-energy regime. These duality relations show that unconventional (exotic) density-wave orders such as staggered flux or circulating spin-current are directly mapped to conventional density-wave orders, which establishes the appearance of various exotic states with time-reversal and/or spin symmetry breaking. We also study duality relations in the SO(5) symmetry that was proposed to unify antiferromagnetism and d-wave superconductivity. We show that the same SO(5) symmetry also unifies circulating spin current order and s-wave superconductivity.
We investigate a frustrated four-leg spin-1/2 ladder using density matrix renormalization group calculations. The uniform system displays three regimes: short-range antiferromagnetic legs, short-range ferromagnetic legs, and an effective spin-2 Heisenberg chain, separated by a crossover and a first-order transition. The spin-2 regime is confirmed through its finite string order parameter, edge-localized excitations, and excellent agreement with a projected Sr = 2 effective Hamiltonian. Recasting the model as two frustrated two-leg ladders coupled by rung and diagonal interactions, we track how the trivial and Haldane phases of an isolated ladder evolve as interladder couplings are introduced. The resulting phase diagrams reveal crossover and first-order lines whose locations are captured by the spin-2 projection and show how singlet- and triplet-dominated regimes reorganize when two ladders merge into a four-leg structure, clarifying the emergence of effective spin-1 versusspin-2 behavior.