Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2103.08434

Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses

Yuhai Liu·Zhenjiu Wang·Toshihiro Sato·Wenan Guo·Fakher F. Assaad
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider fermions on a honeycomb lattice supplemented by a spin invariant interaction that dynamically generates a quantum spin Hall insulator. This lattice model provides an instance of Gross-Neveu Heisenberg criticality, as realized for example by the Hubbard model on the honeycomb lattice. Using auxiliary field quantum Monte Carlo simulations we show that we can compute with unprecedented precision susceptibilities of the order parameter. In O(N) Gross-Neveu transitions, the anomalous dimension of the bosonic mode grows as a function of N such that in the large-N limit it is of particular importance to consider susceptibilities rather than equal time correlations so as to minimize contributions from the background. For the N=3 case, we obtain $1/\nu=1.11(4)$, $\eta_{\phi}=0.80(9)$, and $\eta_{\psi}=0.29(2)$ for respectively the correlation length exponent, bosonic and fermionic anomalous dimensions.

Explore related subjects

cond-mat.str-el

Keep this discovery

BibTeXRIS

Yuhai Liu, Zhenjiu Wang, Toshihiro Sato, Wenan Guo, Fakher F. Assaad. 2021-03-15. Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses. https://doi.org/10.1103/physrevb.104.035107

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

KEEP EXPLORING

Related papers

arXiv2026

Competing Interlayer Loop Currents and Superconductivity in the Bilayer $t$-$J_\perp$-$V$ Model

The recent discovery of high-$T_c$ superconductivity in pressurized and thin-film bilayer nickelates, featuring a strong interlayer exchange coupling, and their potential similarities with cuprate superconductors, has made this a very active topic in condensed matter physics. In the present paper we study the strongly correlated one-orbital ($d_{x^2-y^2}$) bilayer $t$-$J_\perp$-$V$ model for nickelates, where $V$ denotes the Coulomb interactions, using a controlled large-$N$ expansion at and beyond the mean-field level. Focusing on the out-of-plane spin exchange interaction ($J_\perp$), we find that it triggers both out-of-plane $s$-wave superconductivity and an out-of-plane bond-order phase ($z$-BOP) instability. The $z$-BOP gives rise to a complex $z$-axis hopping dominated by its imaginary component, which drives out-of-plane currents and induces in-plane ones, spontaneously forming on the vertical plaquettes a loop-current state that breaks time-reversal symmetry. Competition between this loop-current phase and superconductivity yields a dome-shaped superconducting region, with optimal superconductivity occurring near the $z$-BOP quantum critical point. The resulting phase diagram features a pure loop-current region, a low-doping coexistence phase, a pure superconducting state at higher doping, and a correlated metallic state.

cond-mat.str-el↗
arXiv2026

Optically induced metallic state with persistent monoclinic symmetry in NdNiO$_3$

Understanding whether electronic and structural order remain coupled under nonequilibrium conditions is a central challenge in correlated materials. Here, we simultaneously track metallicity and symmetry across the photoinduced insulator-to-metal transition in NdNiO$_3$ using time-resolved optical reflectivity and symmetry-sensitive second-harmonic generation. We find that metallic reflectivity emerges at significantly lower excitation fluence than restoration of the orthorhombic high-temperature symmetry. As a result, optical excitation stabilizes a metastable state that combines the reflectivity of the metallic phase with the monoclinic symmetry of the insulating phase, revealing an optically induced monoclinic metal. Only at substantially higher fluences does the symmetry fully recover to that of the high-temperature phase. These results demonstrate a nonequilibrium decoupling of metallicity and structural symmetry and establish simultaneous multiprobe spectroscopy as a powerful approach for identifying emergent phases in correlated materials.

cond-mat.str-el↗
arXiv2026

Instabilities in self-consistent diagrammatic approaches and how to cure them

While self-consistent diagrammatic approaches are widely used to compute the physical properties of correlated quantum materials, their applicability may get severely hindered precisely in the parameter regions, where the most exciting physics is observed. One of the major issues, referred to as "misleading convergence", is the tendency of iterative schemes to converge to unphysical fixed points for intermediate-to-strong electronic interactions, regardless of numerical accuracy of the computation. Here, we explicitly verify that the origin of this problem in several established self-consistent many-electron approaches, defined in the general diagrammatic framework of the boson-exchange formalism, resides exclusively in the stability condition of the respective iteration schemes, and not in an intrinsic breakdown of their self-consistent diagrammatic description. This insight enables a simple and general remedy, as recently proposed in Phys. Rev. Lett. 137, 016502 (2026): The redefinition of the iterative procedure, by inverting the unstable eigendirections of the Jacobian associated to the fixed point of the self-consistent algorithm. We illustrate the successful outcome of this procedure by means of systematic calculations performed on testbed, exactly solvable, models. Our results demonstrate that the physical fixed point of the diagrammatic schemes we considered can be stabilized, de facto, across the entire parameter range, including the most challenging nonperturbative/strong-coupling regimes.

cond-mat.str-el↗