Ground State Phase Diagram of Frustrated S = 1 XXZ chains: Chiral Ordered Phases

Abstract

The ground-state phase diagram of frustrated S = 1 XXZ spin chains with the competing nearest-and next-nearest-neighbor antiferromagnetic couplings is studied using the infinitesystem density-matrix renormalization-group method. We find six different phases, namely, the Haldane, gapped chiral, gapless chiral, double Haldane, Néel, and double Néel (uudd) phases. The gapped and gapless chiral phases are characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κ l =S , whereas the spin correlation decays either exponentially or algebraically. These chiral ordered phases appear in a broad region in the phase diagram for ∆ < 0.95, where ∆ is an exchange-anisotropy parameter. The critical properties of phase transitions are also studied.KEYWORDS: frustration, spin-1 chain, ground-state phase diagram, density-matrix renormalization-group method, chiral ordering §1. Introduction Frustrated antiferromagnetic quantum spin systems have attracted considerable attention over the decades since they exhibit a wealth of fascinating phenomena in their ground states and lowlying excitations. In general, frustration supresses antiferromagnetic correlations and the tendency towards the Néel order. Classical systems, for example, often show a helical ordered state in their ground states in the presence of strong frustration. In quantum systems, the interplay of frustration and quantum fluctuations plays an important role which causes exotic phenomena, e.g., a spin-liquid state and a novel type of spontaneous symmetry breaking.In this paper, we study a one-dimensional anisotropic spin system with the antiferromagnetic nearest-neighbor coupling J 1 and the frustrating next-nearest-neighbor coupling J 2 . The model is * E-mail address: hikihara@phys03.phys.sci.kobe-u.ac. where S l is a spin-S spin operator at site l and ∆ ≥ 0 represents an exchange anisotropy. Hereafter, we put j ≡ J 2 /J 1 (j ≥ 0).In the classical limit, S → ∞, the system exhibits a magnetic long-range order (LRO) characterized by a wavenumber q. The order parameter is defined bywhere L is the total number of spins. While the magnetic LRO is of the Néel-type (q = π) when j is smaller than a critical value, j ≤ 1/4, it becomes of helical-type for j > 1/4 with q = cos −1 (−1/4j).It should be noticed that both the time-reversal and parity symmetries are broken in this helical ordered state. When the system has an XY -like anisotropy (∆ < 1), the helical ordered state possesses a two-fold discrete degeneracy according as the helix is either right-or left-handed, in addition to a continuous degeneracy associated with the original U (1) symmetry of the XY spin.This discrete degeneracy is characterized by mutually opposite signs of the total chirality definedNote that this chirality is distinct from the scalar chirality of the Heisenberg spin often discussed in the literature 2) defined by χ l = S l−1 · S l × S l+1 : The chirality O κ changes its sign under the parity operation but is invariant under the time-reversal op...

Kaleidoscope of quantum phases in a long-range interacting spin-1 chain

“…However, we point out that the full 1/r α long-range interactions, frustrated or not, will result in power-law decaying correlation functions in the gapped phases (see Ref. 57 for details); such correlations are absent in models with next-nearest-neighbor interactions [76][77][78][79] . For J xy = −1, where long-range interactions in the x − y plane are not frustrated, the phase diagram [ Fig.…”

O17andV51NMR for the zigzag spin-1 chain compoundZong1, Suh2, Niazi3 et al. 2008Phys. Rev. B

“…In a zigzag spin chain system with spin S = 1, the ground state phase diagram ͑at temperature T =0͒ as a function of XXZ anisotropy and ratio between nearest-neighbor ͑NN͒ and next-nearest-neighbor ͑NNN͒ interactions exhibits six different phases. 2,3 In addition to two Néel ordered phases and two phases with a Haldane gap, there exists a large phase region called a gapless chiral phase where the chirality exhibits long-range order without accompanying spin order, and a small phase region where there is a gapped chiral phase.…”

Synthesis and structural, magnetic, thermal, and transport properties of several transition metal oxides and aresnides

“…Theoretical calculations have shown that for a one-dimensional spin S = 1 chain with antiferromagnetic nearest-neighbor interaction J 1 and frustrating nextnearest-neighbor antiferromagnetic interaction J 2 , the magnetic ground state shows gapped or gapless chiral ordering depending on the the anisotropy of the spin chain being XY or XXZ and on the ratio J 2 /J 1 . [37][38][39] The system does not show any long-range ordering of the spins.…”

“…However, numerical calculations have shown that the influence of frustrating next-nearest-neighbor (NNN, J 2 ) interactions play a significant role and depending on the J 2 /J 1 ratio, can lead to incommensurate helical spin structures which may be gapped or gapless. [37,38,[146][147][148]] Such a system is described by the XXZ Hamiltonian…”