Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2512.23962

Lectures on insulating and conducting quantum spin liquids

Subir Sachdev
View original source ↗Read source document ↗Export metadata ↓

Abstract

Two of the iconic phases of the hole-doped cuprate materials are the intermediate temperature pseudogap metal and the lower temperature $d$-wave superconductor. Following the suggestion of P. W. Anderson, there were early theories of these phases as doped quantum spin liquids. However, these theories have had difficulties with two prominent observations: (i) angle-dependent magnetoresistance measurements (ADMR) in the pseudogap metal, including observation of the Yamaji effect, present convincing evidence of small hole pockets which can tunnel coherently between square lattice layers (Fang et al., Nature Physics 18, 558 (2022); Chan et al., Nature Physics 21, 1753 (2025)) and (ii) the velocities of the nodal Bogoliubov quasiparticles in the $d$-wave superconductor are highly anisotropic, with $v_F \gg v_\Delta$ (Chiao et al., Phys. Rev. B 62, 3554 (2000)). These notes review how the fractionalized Fermi Liquid (FL*) state, which dopes quantum spin liquids with gauge-neutral electron-like quasiparticles, resolves both difficulties. Theories of insulating quantum spin liquids employing fractionalization of the electron spin into bosonic or fermionic partons are discussed. Doping the bosonic parton theory leads to a holon metal theory: while not appropriate for the cuprate pseudogap, this theory is argued to apply to ultracold atom experiments on the Lieb lattice. Doping the fermionic parton theory leads to a $d$-wave superconductor with nearly isotropic quasiparticle velocities. The construction of the FL* state in a single band Hubbard-type model is described using a quantum dimer model, followed by a more realistic description using the Ancilla Layer Model (ALM), which is then used to obtain the theory of the pseudogap and the $d$-wave superconductor. The ALM also leads to a wavefunction for the FL* state of the Hubbard model, which agrees with ultracold atom observations.

Explore related subjects

cond-mat.str-elcond-mat.quant-gascond-mat.supr-conhep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Subir Sachdev. 2025-12-30. Lectures on insulating and conducting quantum spin liquids. https://arxiv.org/abs/2512.23962

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↗