Reentrance of the topological phase in a spin-1 frustrated Heisenberg chain

Abstract

For the Haldane phase, the magnetic field usually tends to break the symmetry and drives the system into a topologically trivial phase. Here, we report a novel reentrance of the Haldane phase at zero temperature in the spin-1 antiferromagnetic Heisenberg model on sawtooth chain. A partial Haldane phase is induced by the magnetic field, which is the combination of the Haldane state in one sublattice and a ferromagnetically ordered state in the other sublattice. Such a partial topological order is a result of the zero-temperature entropy due to quantum fluctuations caused by geometrical frustration.Introduction. -Frustration incorporating with strong correlations usually leads to exotic quantum phenomena. A typical example in statistical physics is the reentrant phenomena, where a sequence of phase transitions, such as A-B-A-B by lowering temperature may happen, where A and B denote ordered and disordered phases, respectively. Taking the Ising model on kagomé lattice with nearest and next-nearest neighboring interactions as an example, one may find that upon lowering temperature, the system passes through four phases, a paramagnetic phase, a magnetically-ordered phase, a reentrant paramagnetic phase, and a ferromagnetic phase 1 . Such a reentrant phenomenon was experimentally confirmed 2 , and theoretically investigated with different approaches 1,3-8 . In the past decades, systematic investigations on the partially disordered phase in both classical and quantum systems at finite temperatures were performed theoretically 1,4,5,[9][10][11][12][13][14][15] and experimentally [16][17][18][19][20][21] . It has been widely recognized that the partially disordered phase is driven by the thermal entropy, in which the disordered part behaves like a "perfect" paramagnet. The reentrant phenomena can be viewed as the order-bydisorder effect 22 , which is driven by thermal fluctuations and entropy.Recently, the interests on the reentrant phenomena were renewed. The order-by-disorder effects were investigated theoretically 23-26 and experimentally 27,28 . For the spin-1/2 Heisenberg antiferromagnet on the √ 3 × √ 3disordered triangular lattice 26 , a partially disordered ground state in the weakly frustrated regime was reported. The spins on the honeycomb sublattice form a 180 • Néel order, and spins at the hexagon center sites are in a disordered state. This work is aimed at explaining the spin-liquid behaviors of LiZn 2 M o 3 O 8 29 , and shows that a partially disordered phase can be the ground state of a simple quantum isotropic Heisenberg antiferromagnet. Comparing with the classical systems, the disordered subsystem is a short range ferromagnetically correlated state instead of a paramagnet, and the mechanism is owning to the zero-point quantum fluctuations instead of the thermal ones. Furthermore, previous works 1 J 2 J : Sublattice A : Sublattice B FIG. 1. (Color online) Sawtooth chain lattice with two sublattice A and B. Two exchange interactions J1 and J2 are indicated by black and green lines, respectively.show that ...

Multiple magnetic transitions and complex magnetic structures in Fe$_2$SiSe$_4$ with the sawtooth lattice

“…Firstly, the sawtooth antiferromagnetic (AFM) chain with corner-sharing triangles of spins represents one of the fundamental models of geometrically frustrated quantum magnetism as that in triangular and kagome lattices [1,2]. Secondly, the sawtooth lattice also exhibits flat-band feature [3] which may give rise to high thermoelectric performance [4], quantum topological phase [5][6][7], flat-band spin dynamics and phonon anomalies [8]. Besides, a two-dimensional kagome lattice can be viewed as the combination of one-dimensional sawtooth chains.…”

Quantum phase transitions in the spin-1 Kitaev-Heisenberg chain

“…On the other hand, the GS of Eq. ( 3) with AFM couplings (J > 0) is a topological phase predicted by Haldane [41], which has a finite excitation gap ∆ = 0.41J and exponentially decaying spin correlation functions. More precisely, since the edge states have a finite length for an open chain, the splitting in the lowest energies is exponentially small for longer chains, resulting in fourfold quasidegenerate GSs below the Haldane gap [42].…”