[Paper Review] Weak Mott insulators on the triangular lattice: possibility of a gapless nematic quantum spin liquid

Tarun Grover, Nandini Trivedi+2 more|arXiv (Cornell University)|Jul 10, 2009

Advanced Condensed Matter Physics5 citations

TL;DR

This paper proposes a gapless nematic quantum spin liquid ground state in weak Mott insulators on the triangular lattice, stabilized by four-body ring exchange interactions. Using variational Monte Carlo, it identifies a Gutzwiller-projected $d_{x^2-y^2}$ paired state as energetically favorable, breaking lattice rotational symmetry while preserving translational invariance, and explains key experimental features in organic Mott insulators like $κ$-CN and DMIT.

ABSTRACT

We study the energetics of Gutzwiller projected BCS states of various symmetries for the triangular lattice antiferromagnet with a four particle ring exchange using variational Monte Carlo methods. In a range of parameters the energetically favored state is found to be a projected $d_{x^2-y^2}$ paired state which breaks lattice rotational symmetry. We show that the properties of this nematic or orientationally ordered paired spin liquid state as a function of temperature and pressure can account for many of the experiments on organic materials. We also study the ring-exchange model with ferromagnetic Heisenberg exchange and find that amongst the studied ansätze, a projected $f-$wave state is the most favorable.

Motivation & Objective

• To identify the most stable spin liquid phase in weak Mott insulators on the triangular lattice with ring exchange interactions.
• To explain the anomalous low-temperature behavior observed in organic Mott insulators such as $κ-(ET)_2Cu_2(CN)_3$ and DMIT, including linear T-dependent specific heat and finite spin susceptibility.
• To explore the connection between the proposed spin liquid state and the pressure-induced superconducting phase in these materials.
• To analyze the finite-temperature phase transitions associated with nematic order and their experimental signatures.
• To investigate the stability of paired spin liquid states under varying Heisenberg and ring exchange parameters, including ferromagnetic $J_2$ cases.

Proposed method

• Employed variational Monte Carlo (VMC) to evaluate the energy of Gutzwiller-projected BCS wavefunctions with different pairing symmetries on the triangular lattice.
• Used the $J_2$-$J_4$ Hamiltonian with antiferromagnetic Heisenberg exchange and four-particle ring exchange on elementary plaquettes.
• Evaluated the $d_{x^2-y^2}$, $d_{x^2-y^2}+id_{xy}$, and $f_{x^3-3xy^2}$ paired states as variational ansätze.
• Analyzed the effective field theory of the nematic order parameter using a 2D XY model with 6-fold anisotropy to determine universality class.
• Applied the Kosterlitz-Thouless (K-T) theory to classify finite-temperature phase transitions in the nematic order parameter.
• Assessed the impact of lattice anisotropy and disorder on the stability of the nematic transition using random field and pinning effects.

Experimental results

Research questions

• RQ1 What is the most energetically favorable spin liquid state in the $J_2$-$J_4$ model on the triangular lattice with ring exchange?
• RQ2 How does the nematic order parameter associated with $d_{x^2-y^2}$ pairing affect the finite-temperature phase diagram and experimental observables?
• RQ3 Can the proposed gapless $Z_2$ spin liquid state explain the linear T-dependent specific heat and finite spin susceptibility in $κ$-CN and DMIT?
• RQ4 What is the nature of the pressure-induced superconducting state in relation to the underlying spin liquid?
• RQ5 How do weak lattice anisotropy and disorder affect the visibility of the nematic phase transition in experiments?

Key findings

• The Gutzwiller-projected $d_{x^2-y^2}$ paired state is energetically favored over other paired states in a range of $J_4/J_2$ values with both $J_2$ and $J_4$ antiferromagnetic.
• The $d_{x^2-y^2}$ state breaks discrete rotational symmetry of the triangular lattice, forming a gapless nematic quantum spin liquid with nodal fermionic spinons and gapped visons.
• The state exhibits a finite-temperature transition at $T_{c3}$ in the inverted Kosterlitz-Thouless universality class due to power-law correlations in the nematic order parameter.
• The phase transition is expected to be weakly first-order or crossover-like in real materials due to lattice anisotropy and disorder, which may pin the nematic order.
• The model with ferromagnetic $J_2$ and antiferromagnetic $J_4$ favors a projected $f$-wave state as the lowest-energy variational state.
• The proposed gapless $Z_2$ spin liquid state predicts a flux trapping effect and can be probed via Josephson tunneling experiments with spin-liquid barriers.