Random-singlet phases beyond one spatial dimension

N. E. Bonesteel, Kun Yang

One-dimensional chains of non-Abelian quasiparticles described by SU(2)k Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to k-->infinity). For k=2 this phase provides a random singlet description of the infinite-randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size L in these phases scales as S(L) approximately lnd/3 log(2)L for large L, where d is the quantum dimension of the particles.

Yu-Rong Shu, Dao‐Xin Yao, Chih-Wei Ke +2 more

Courtney Lanert, Gil Refael

Daniel S. Fisher

The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a generalization of that introduced by Dasgupta and Ma. Random-singlet phases occur in which each spin is paired with one other spin that may be very far away; more exotic phases also occur. The behavior of typical and mean correlation functions is analyzed and found to be very different, with very small sets of spins dominating the latter at long distances as well as the low-temperature thermodynamics. Some of the phase transitions that occur between antiferromagnetically ordered phases and random singlet or other antiferromagnetic phases are also analyzed. For example, if a small uniaxial anisotropy perturbation is added to a random Heisenberg antiferromagnetic chain, a transition occurs from a random-singlet phase to an Ising antiferromagnetic phase, as the anisotropy changes sign from easy plane to easy axis. The staggered magnetization vanishes at the transition with critical exponent \ensuremath{\beta}=8/(1+ \ensuremath{\surd}7 ). Possible implications for the properties of random quantum magnetic systems in higher dimensions are briefly discussed.

José A. Riera

Effective models of hard-core hole pair bosons and triplets are derived from the $t\ensuremath{-}J$ model in ladders and on the square lattice by performing a change from site to dimer basis. The Hilbert space is truncated by projecting out single-occupied electron states and only nearest-neighbor interactions are retained. The resulting effective models in one and two dimensions are studied by numerical techniques. In both spatial dimensions, the main result is that each hole pair is surrounded by a singlet cloud expelling triplet excitations from its vicinity. It is suggested an interpretation of this feature as a phase-separated state between a hole-pair-rich singlet phase and an undoped triplet phase with antiferromagnetic correlations. The possible relevance of this result to other theoretical scenarios and experimental results is discussed.

J. D. Fan, Y. M. Malozovsky