Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0309377

String order in spin liquid phases of spin ladders

G. Fath·O. Legeza·J. Solyom
View original source ↗Read source document ↗Export metadata ↓

Abstract

Two-leg spin ladders have a rich phase diagram if rung, diagonal and plaquette couplings are allowed for. Among the possible phases there are two Haldane-type spin liquid phases without local order parameter, which differ, however, in the topology of the short range valence bonds. We show that these phases can be distinguished numerically by two different string order parameters. We also point out that long range string- and dimer orders can coexist.

Explore related subjects

cond-mat.str-elcond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

G. Fath, O. Legeza, J. Solyom. 2003-09-16. String order in spin liquid phases of spin ladders. https://doi.org/10.1103/physrevb.63.134403

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Symmetry-Protected Topological Structures in Quantum Many-Body Scar Subspaces

We investigate how symmetry-associated topological properties, originally defined for ground states, can be consistently extended to dynamically isolated subspaces of quantum many-body systems. Focusing on quantum many-body scars (QMBS), we show that a scar subspace is invariant under the relevant symmetries, and it can support well-defined topological properties inherited from an underlying symmetry-protected topological (SPT) ground state, even though individual scar states need not themselves be symmetric. We refer to such structures as SPT-like scar subspaces, emphasizing that the topological properties are defined at the level of the symmetry-invariant subspace rather than on a state-by-state basis. As a concrete example, we analyze the spin-$1$ Affleck--Kennedy--Lieb--Tasaki (AKLT) model, where a restricted spectrum-generating algebra (rSGA) generates a tower of QMBS on top of a nontrivial SPT ground state admitting a matrix product state (MPS) representation. We demonstrate that the resulting symmetry-invariant scar subspace inherits well-defined topological characteristics, encoded in bond-space symmetry representations, expectation values of symmetry-twist operators, and long-range string order in the dilute regime. We further show that these features persist in a broader class of models, including deformations and higher-spin generalizations that preserve the relevant symmetries and admit nontrivial SPT ground states with MPS representations. Our results provide a general framework in which symmetry-associated topological properties, while inherited from the ground state, are consistently realized at the level of symmetry-invariant nonthermal subspaces. This perspective clarifies how topological structures can be meaningfully defined beyond individual eigenstates.

cond-mat.str-el↗
arXiv2026

Non-invertible symmetries and mixed anomalies from equations of motion in (3+1)D twisted $BF$ topological quantum field theories

We develop a systematic study on the topological operators that generate invertible and non-invertible higher-form symmetries in $\left(3+1\right)D$ twisted $BF$ topological quantum field theories (TQFTs). We focus on the twisted $BF$ theories with gauge group $G=\prod_i \mathbb{Z}_{N_i}$ and an $a\wedge a\wedge b$ twist, where $a$'s and $b$ are 1-form and 2-form gauge fields, respectively. These theories realize non-Abelian $(3+1)$D TQFTs supporting Borromean-Rings braiding and describe three-dimensional non-Abelian topological orders in condensed matter. For $G=(\mathbb{Z}_2)^3$, a microscopic realization is given by the $\mathbb{D}_4$ Kitaev quantum double model. Starting from the equations of motion (EoMs), we construct gauge invariant operators that are supported on closed submanifolds, hence are genuine topological operators. Some of them are associated with nontrivial Hilbert spaces which are the projective representation spaces of specific gauge subgroups, thus being non-invertible. The others are invertible topological operators with group-like fusion rules. The fusion rules of non-invertible topological operators correspond to the decomposition of the product of the projective representation spaces. We provide a field-theoretical algorithm to calculate the fusion rules. Besides, we identify an obstruction to retaining a non-invertible topological operator after gauging an invertible symmetry, and derive the constraints on pairs of non-invertible operators relevant to simultaneous gauging. Our results give a unified and practical approach for identifying and characterizing higher-form symmetries and mixed anomalies, which can be extended to more general TQFTs and topological orders.

cond-mat.str-el↗
arXiv2026

For any static interaction the self-energy and vertex corrections to the electron-gas polarizability combine exactly into one integrand free of the Coulomb singularity

The first-order corrections to the polarizability of the uniform electron gas are a self-energy insertion and a vertex correction. For the Coulomb interaction the coefficient of q^2 in each diverges logarithmically at small wave vector, and the two divergences have opposite signs and cancel in their sum. This Note shows that for any interaction that depends only on the momentum it transfers, the two integrands combine exactly into one before any integration is done. At zero temperature the combined integrand has no Coulomb singularity and no chemical-potential counterterm. For screened interactions, which must be integrated numerically, it should be computed in place of the two diagrams. The Note gives the derivation and its physical reason, the one term added at finite temperature, and checks for bare, Yukawa and screened interactions. With a frequency-dependent interaction the combination is no longer exact.

cond-mat.str-el↗