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

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 mixes 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. bosonic t-J model) is also discussed.

Quantum magnetism on the Cairo pentagonal lattice

“…18). 50,51 The details of this approach are provided in App. E and follow closely in spirit the treatment by Lecheminant and Totsuka 51 of a very similar situation in a two-leg ladder system where a different pair of plaquette triplets emerges at low energies.…”

Semiclassical approach to competing orders in a two-leg spin ladder with ring exchange

“…40 In this basis, the spin-chirality transformation (2) has a simple interpretation as the U(1) gauge transformation of the bosons. 36 The next step of the approach is to perform a simple mean-field approximation of the phases of the bosonic model. We then incorporate quantum fluctuations by constructing semiclassical low-energy Hamiltonians which describe the competition of the RS and the VC orders as well as the usual rotational fluctuations.…”

“…spinchirality) part reduces to the Tomonaga-Luttinger model as is expected from the previous results. 35,36 Now we proceed to a more interesting case of the chiralitydominant phase realized in the large-K 4 region. In this phase, φ 0 is locked at φ = ±π/2 and the effective action (49) describes the short-range (staggered) fluctuations in the chirality channel; the staggered component of the B-field plays a role of the order-parameter field: Ω ∼ (S 1 ×S 2 ) q=π .…”

“…16). The model (1) is interesting in its own right and has been studied extensively over the years and its phase diagram [26][27][28][29][30] , ground-state-and dynamical properties 14,[31][32][33] , quantum phase transitions [34][35][36] , and entanglement properties [37][38][39] have been explored by both analytical and numerical approaches.…”

On the ground state energy scaling in quasi-rung-dimerized spin ladders

“…INTRODUCTION Phase structure of frustrated spin ladders and spin ladders with four-spin terms has been intensively studied in the last decade both theoretically and numerically [1][2][3] . Among other phases the mathematically most simple one and at the same time, probably, the one most interesting for physical applications is the so called rung-singlet (or rung-dimerized) phase 4,5 .…”