Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9910224

Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems

T. Senthil·Matthew P. A. Fisher
View original source ↗Read source document ↗Export metadata ↓

Abstract

We develop a new theoretical framework for describing and analyzing exotic phases of strongly correlated electrons which support excitations with fractional quantum numbers. Starting with a class of microscopic models believed to capture much of the essential physics of the cuprate superconductors, we derive a new gauge theory - based upon a {\it discrete} Ising or Z_2 symmetry - which interpolates naturally between an antiferromagnetic Mott insulator and a conventional d-wave superconductor. We explore the intervening regime, and demonstrate the possible existence of an exotic fractionalized insulator - the nodal liquid - as well as various more conventional insulating phases exhibiting broken lattice symmetries. A crucial role is played by vortex configurations in the Z_2 gauge field. Fractionalization is obtained if they are uncondensed. Within the insulating phases, the dynamics of these Z_2 vortices in two dimensions (2d) is described, after a duality transformation, by an Ising model in a transverse field - the Ising spins representing the Z_2 vortices. The presence of an unusual Berry's phase term in the gauge theory, leads to a doping-dependent "frustration" in the dual Ising model, being fully frustrated at half-filling. The Z_2 gauge theory is readily generalized to a variety of different situations - in particular, it can also describe 3d insulators with fractional quantum numbers. We point out that the mechanism of fractionalization for d>1 is distinct from the well-known 1d spin-charge separation. Other interesting results include a description of an exotic fractionalized superconductor in two or higher dimensions.

Explore related subjects

cond-mat.str-elcond-mat.supr-con

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

T. Senthil, Matthew P. A. Fisher. 1999-10-21. Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems. https://doi.org/10.1103/physrevb.62.7850

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

KEEP EXPLORING

Related papers

arXiv2026

Real-space determination of orbital states driving successive phase transitions in FeV2O4

Direct experimental access to orbital states in strongly correlated materials remains a major challenge, despite their central role in driving coupled structural and magnetic phase transitions. In systems where electronic correlations, electron-lattice coupling, and relativistic spin-orbit interactions compete on comparable energy scales, even first-principles calculations often yield multiple metastable solutions, hindering the unambiguous identification of the ground state. Here, we demonstrate that the orbital states of the spinel oxide FeV2O4, which possesses active orbital degrees of freedom on both Fe and V ions, are uniquely resolved by combining valence electron density (VED) analysis based on state-of-the-art synchrotron x-ray diffraction with spin-polarized density-functional-theory calculations. Our results reveal that temperature-dependent rearrangements of orbital occupations drive successive structural transitions that accompany collinear and noncoplanar ferrimagnetic orders, establishing a direct correspondence between orbital anisotropy and spin structure. More broadly, this work shows that experimentally determined VED provides a decisive real-space constraint on competing theoretical solutions, offering a powerful and broadly applicable framework for elucidating the microscopic mechanisms of complex phase transitions in strongly correlated electron systems.

cond-mat.str-el↗
arXiv2026

Textures as a phase-transition probe for quantum spin chains

The idea of quantum texture has been recently proposed and used as a tool for quantifying coherences and for quantum gate identification. In this work we offer a study on its usage to quantum phase transitions, demonstrating the rugosity metric as a simple tool for effective phase-transition probing. We establish the link between rugosity in the computational basis and the hierarchy of spin correlators, and analyze rugosities defined in the global ground-state and in ground-states belonging to different magnetization sectors (to which we refer to as global vs symmetry-resolved rugosities) to study the phase diagram of the Heisenberg XXZ model. We find distinct rugosity signatures at both transition points. In particular, a sharp feature appears at $Δ=1$ already for small systems, revealing a pronounced sensitivity of the correlation hierarchy encoded by the texture to this point. Since the BKT transition coincides with the isotropic $SU(2)$ point of the XXZ model, this behavior may reflect a particular sensitivity of rugosity to the structure of the spin-correlation hierarchy at isotropy.

cond-mat.str-el↗
arXiv2026

Exact selection of a toric-code vison crystal in a flux-conditioned Kitaev model

We construct an exactly solvable extension of the spin-$1/2$ Kitaev honeycomb model in which conserved $\mathbb{Z}_2$ fluxes determine not only the signs but also the connectivity of nearest-neighbor Majorana hopping. At a tuned loop point, hopping survives only across opposite-flux plaquettes, so every vertex has active degree zero or two and the matter Hamiltonian fragments in each flux sector into independent Majorana rings and isolated zero modes. Exact ring spectra and bond counting then bound the matter energy over all local flux configurations and all four Wilson-loop sectors, and split it exactly into a frustrated triangular-lattice Ising term, whose extensively degenerate ground states are the fully packed loop coverings, and a non-negative Majorana residual. On admissible commensurate tori, the residual selects precisely the three translation-related $2/3$-vison crystals, which saturate the bound, and an exact fermion-parity identity shows that for antiferromagnetic coupling their vacua also survive projection, making them rigorous ground states of the spin model. Within a single crystal, a depth-one local unitary then maps the ground space onto that of a sheared square-lattice toric code, giving fourfold topological degeneracy. The model thus realizes exact nonperturbative gauge-matter feedback: the flux fixes where the Majorana fermions may move, and their zero-point energy selects in return a topologically ordered vison crystal with spontaneously broken translation symmetry.

cond-mat.str-el↗