Phases In Spin Systems Research Articles

Genuine Tripartite Entanglement as a Probe of Quantum Phase Transitions in a Spin‐1 Heisenberg Chain with Single‐Ion Anisotropy

AbstractThe quantum phase transitions of spin‐1 Heisenberg chains with an easy‐axis anisotropy Δ and a uniaxial single‐ion anisotropy D are studied using a multipartite entanglement approach. The genuine tripartite entanglement between the spin blocks, measured by the tripartite qutrit hyperdeterminant, is calculated within the quantum renormalization group method. Using this approach, the phase boundaries between the topological Haldane, large‐D, and anti‐ferromagnetic Néel phases are determined in the half plane with . When the size of the spin blocks increases, the genuine tripartite entanglement between the blocks exhibits a nonzero plateau in the topological Haldane phase, and experiences abrupt drops at both the phase boundaries between the Haldane–large‐D and Haldane–Néel phases, which suggests the usage of genuine multipartite entanglement as a probe of topological phases in spin systems.

Many-body localization: Transitions in spin models

We study the transitions between ergodic and many-body localized phases in spin systems, subject to quenched disorder, including the Heisenberg chain and the central spin model. In both cases systems with common spin lengths $1/2$ and $1$ are investigated via exact numerical diagonalization and random matrix techniques. Particular attention is paid to the sample-to-sample variance $(\Delta_sr)^2$ of the averaged consecutive-gap ratio $\langle r\rangle$ for different disorder realizations. For both types of systems and spin lengths we find a maximum in $\Delta_sr$ as a function of disorder strength, accompanied by an inflection point of $\langle r\rangle$, signaling the transition from ergodicity to many-body localization. The critical disorder strength is found to be somewhat smaller than the values reported in the recent literature. Further information about the transitions can be gained from the probability distribution of expectation values within a given disorder realization.

From symmetry-protected topological order to Landau order

Focusing on the particular case of the discrete symmetry group Z_N x Z_N, we establish a mapping between symmetry protected topological phases and symmetry broken phases for one-dimensional spin systems. It is realized in terms of a non-local unitary transformation which preserves the locality of the Hamiltonian. We derive the image of the mapping for various phases involved, including those with a mixture of symmetry breaking and topological protection. Our analysis also applies to topological phases in spin systems with arbitrary continuous symmetries of unitary, orthogonal and symplectic type. This is achieved by identifying suitable subgroups Z_N x Z_N in all these groups, together with a bijection between the individual classes of projective representations.

Quadrupolar spin phases in the presence of biquadratic exchange

A generalized mean field approximation is used to find sufficient conditions for the existence of stable quadrupole phases in spin systems with atomic spin s and described by isotropic nearest-neighbour bilinear and biquadratic exchange. Quadrupolar phases are defined as having thermal averages such that (si.ii)0=0 while ((si.ui)2)0 has a value different than its paramagnetic value, ui is a unit vector at site i in the direction of the local mean field. By determining the ui variationally, phases not previously discussed are found.