Topological transition between competing orders in quantum spin chains

Abstract

We study quantum phase transitions between competing orders in one-dimensional spin systems. We focus on systems that can be mapped to a dual-field double sine-Gordon model as a bosonized effective field theory. This model contains two pinning potential terms of dual fields that stabilize competing orders and allows different types of quantum phase transition to happen between two ordered phases. At the transition point, elementary excitations change from the topological soliton of one of the dual fields to that of the other, thus it can be characterized as a topological transition. We compute the dynamical susceptibilities and the entanglement entropy, which gives us access to the central charge, of the system using a numerical technique of infinite time-evolving block decimation and characterize the universality class of the transition as well as the nature of the order in each phase. The possible realizations of such transitions in experimental systems both for condensed matter and cold atomic gases are also discussed. arXiv:1807.06029v2 [cond-mat.str-el]

Universality of Heisenberg–Ising chain in external fields

“…The critical exponent β and central charge c are consistent with Ref. 39 where only the staggered field (h y term) is considered. We further calculate the spin-spin correlation, denoted as C(i − j) = S z i S z j − S z i S z j , for Hamiltonian Eq.…”

Topological charge pumping of bound bosonic pairs

“…up to higher-order terms. In the weak-coupling limit with g 1,2 ∼ U , g 3 ∼ t, and phenomenological Luttinger-liquid parameters K ± and velocities v ± , H − has the form of a doublesine-Gordon Hamiltonian [43]. For K − > 1/2, the cos(2θ − ) term is relevant and will open up a gap in the antisymmetric sector.…”

Experimental observations of the universal cascade of bound states in quantum Ising chain in a magnetic field and E8 symmetry

“…As the applied field is increased, the spins are canted toward the effective staggered field, and the Z 2 symmetry is eventually recovered for a strong applied field. Thus there should be a quantum phase transition at a critical field, and it turns out to be in the (1 + 1)-dimensional Ising universality class [9,10]. Concerning the critical behavior, the y and z components of the magnetic field are irrelevant.…”