[Paper Review] Deconfined critical point in a doped random quantum Heisenberg magnet

Darshan G. Joshi, Chenyuan Li+3 more|arXiv (Cornell University)|Dec 18, 2019

Physics of Superconductivity and Magnetism73 references17 citations

TL;DR

This paper proposes a deconfined quantum critical point in a doped random quantum Heisenberg magnet with all-to-all random hopping and spin exchange, where a critical point at hole doping $ p_c $ separates a metallic spin glass (for $ p < p_c $) from a disordered Fermi liquid (for $ p > p_c $). Using two-loop renormalization group and large-$ M $ analysis, it identifies fractionalized spinon and holon excitations at $ p_c $, exhibiting fermion-boson duality and maximal chaos akin to Sachdev-Ye-Kitaev models, offering a unified framework for cuprate phenomenology including the pseudogap and Fermi surface evolution.

ABSTRACT

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interactions between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a non-zero critical value $p_c$ of the hole doping $p$ away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point $p_c$ is flanked by confining phases: a disordered Fermi liquid with carrier density $1+p$ for $p>p_c$, and a metallic spin glass with carrier density $p$ for $p<p_c$. Additional evidence for the critical behavior is obtained from a large $M$ analysis of a model which extends the SU(2) spin symmetry to SU($M$). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.

Motivation & Objective

• To understand the quantum phase transition in doped correlated metals with 'Mottness' and strong disorder.
• To identify a deconfined quantum critical point (QCP) with fractionalized excitations in a random t-J model with all-to-all couplings.
• To explain the observed carrier density change from $ p $ to $ 1+p $ across optimal doping in cuprates without relying on broken symmetries as the primary driver.
• To establish a connection between the critical point and the chaotic, non-Fermi liquid behavior seen in strange metals.

Proposed method

• Employing a perturbative two-loop renormalization group (RG) analysis in the $ \mathrm{SU}(2) $ spin symmetry sector.
• Extending the model to $ \mathrm{SU}(M) $ symmetry and analyzing the large-$ M $ limit to access non-perturbative critical behavior.
• Using a large-$ M $ saddle-point approach to compute self-energies, Green's functions, and correlation functions.
• Implementing a quantum impurity mapping to study the critical fixed point and its stability.
• Applying Luttinger constraints and self-consistency equations to enforce particle number and spinon/holon statistics.
• Analyzing spin and electron correlation functions to identify critical scaling and duality.

Experimental results

Research questions

• RQ1 Does a deconfined quantum critical point exist in a doped random Heisenberg magnet with all-to-all couplings, and what are its universal properties?
• RQ2 How does the carrier density evolve across the critical point, and what is the role of fractionalized spinons and holons in this transition?
• RQ3 Can the critical theory at $ p_c $ be described by a fermion-boson duality, and how does it relate to the Sachdev-Ye-Kitaev model?
• RQ4 What is the nature of the phases adjacent to the critical point: is the underdoped phase a metallic spin glass and the overdoped phase a disordered Fermi liquid?
• RQ5 How does the large-$ M $ limit support the existence of a critical point in the physical $ \mathrm{SU}(2) $ case?

Key findings

• A deconfined quantum critical point exists at a finite hole doping $ p_c $, with fractionalized spinon and holon excitations, confirmed via two-loop RG and large-$ M $ analysis.
• The critical theory exhibits exact fermion-boson duality, with the same physics described by either fermionic spinons and bosonic holons or vice versa.
• For $ p < p_c $, the system is a metallic spin glass with carrier density $ p $, while for $ p > p_c $, it is a disordered Fermi liquid with carrier density $ 1+p $, consistent with cuprate phenomenology.
• The critical point is maximally chaotic, similar to the Sachdev-Ye-Kitaev model, with spin-spin correlations decaying as $ 1/|\tau| $, indicating non-Fermi liquid behavior.
• Anomalous dimensions of operators are computed to all orders in the large-$ M $ limit, and the critical exponents are found to be universal and non-trivial.
• The critical point is flanked by confining phases: the spin glass phase for $ p < p_c $ and the Fermi liquid for $ p > p_c $, with no true fractionalization in either phase due to Higgs-like condensates.