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arXiv:1308.3186 · Physical Review Letters

Hubbard Model on the Pyrochlore Lattice: A 3D Quantum Spin Liquid

Bruce Normand, Zohar Nussinov

Published May 21, 2014• 24 citations
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Abstract

We demonstrate that the insulating one-band Hubbard model on the pyrochlore lattice contains, for realistic parameters, an extended quantum spin-liquid phase. This is a three-dimensional spin liquid formed from a highly degenerate manifold of dimer-based states, which is a subset of the classical dimer coverings obeying the ice rules. It possesses spinon excitations, which are both massive and deconfined, and on doping it exhibits spin-charge separation. We discuss the realization of this state in effective $S=1/2$ pyrochlore materials.

DOI
10.1103/physrevlett.112.207202

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•Sep 2, 2014•0 citations
We demonstrate that the insulating one-band Hubbard model on the pyrochlore lattice contains, for realistic parameters, an extended quantum spin-liquid phase. This is a three-dimensional spin liquid formed from a highly degenerate manifold of dimer-based states, which is a subset of the classical dimer coverings obeying the ice rules. It possesses spinon excitations, which are both massive and deconfined, and on doping it exhibits spin-charge separation. We discuss the realization of this state in effective S=1/2S=1/2S=1/2 pyrochlore materials.
We show that the highly frustrated transverse-field Ising model on the three-dimensional pyrochlore lattice realizes a first-order phase transition without symmetry breaking between the low-field Coulomb quantum spin liquid and the high-field polarized phase. The quantum phase transition is located quantitatively by comparing low- and high-field series expansions. Furthermore, the intriguing properties of the elementary excitations in the polarized phase are investigated. We argue that this model can be achieved experimentally by applying mechanical strain to a classical spin-ice material composed of non-Kramers spins such as Ho2Ti2O7{\mathrm{Ho}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}Ho2​Ti2​O7​. Taken together with our results, this provides an experimental platform to study quantum spin liquid physics.
Classical spin liquids are paramagnetic phases that feature nontrivial patterns of spin correlations within their ground-state manifold whose degeneracy scales with system size. Often they harbor fractionalized excitations, and their low-energy fluctuations are described by emergent gauge theories. In this work, we discuss a model composed of chiral three-body spin interactions on the pyrochlore lattice that realizes a novel classical chiral spin liquid whose excitations are fractonalized while also displaying a fracton-like behavior. We demonstrate that the ground-state manifold of this spin liquid is given by a subset of the so-called color-ice states. We show that the low-energy states are captured by an effective gauge theory which possesses a divergence-free condition and an additional chiral term that constrains the total flux of the fields through a single tetrahedron. The divergence-free constraint on the gauge fields results in two-fold pinch points in the spin structure factor and the identification of bionic charges as excitations of the system.
Ground state of the SSS=1/2 pyrochlore Heisenberg antiferromagnet: A quantum spin liquid emergent from dimensional reduction
The quantum antiferromagnet on the pyrochlore lattice offers an archetypal frustrated system, which potentially realizes a quantum spin liquid characterized by the absence of standard spontaneous symmetry breaking even at zero temperature, unusually as an isotropic 3D system. Despite tremendous progress in the literature, however, the nature of the ground state of the fully quantum-mechanical spin Hamiltonian on the pyrochlore lattice still remains elusive. Here, we show that an unconventional type of quantum spin liquid is born out from the pyrochlore system after the self-organized dimensional reduction leading to confined states in 2D layers. This conclusion is obtained from state-of-the-art variational Monte Carlo (VMC) simulations at zero temperature. Quantum spin liquids triggered by the emergent dimensional reduction is an unexplored route of the spin-liquid formation. The dimensional reduction from 3D to 2D is a consequence of a conventional spontaneous symmetry breaking, while the resultant decoupling of layers enables the emergence of a 2D quantum spin liquid that is adiabatically disconnected from trivial product states and exhibits strong quantum entanglement. The stabilized quantum spin liquid exhibits an algebraic decay of correlations and vanishing excitation gap in the thermodynamic limit. The wave-function structure supports the fractionalization of the spin into spinons. This spin-liquid ground state persists in the presence of spin-orbit interactions, which expands the possibilities of realizing quantum spin liquids in real pyrochlore-structured materials.
We carry out an analytical study of quantum spin ice, a U(1)(1)(1) quantum spin liquid close to the classical spin ice solution for an effective spin 1/21/21/2 model with anisotropic exchange couplings JzzJ_{zz}Jzz​, J±J_{\pm}J±​ and Jz±J_{z\pm}Jz±​ on the pyrochlore lattice. Starting from the quantum rotor model introduced by Savary and Balents in Phys. Rev. Lett. 108, 037202 (2012), we retain the dynamics of both the spinons and gauge field sectors in our treatment. The spinons are described by a bosonic representation of quantum XY rotors while the dynamics of the gauge field is captured by a phenomenological Hamiltonian. By calculating the one-loop spinon self-energy, which is proportional to Jz±2J_{z\pm}^2Jz±2​, we determine the stability region of the U(1)(1)(1) quantum spin liquid phase in the J±/JzzJ_{\pm}/J_{zz}J±​/Jzz​ vs Jz±/JzzJ_{z\pm}/J_{zz}Jz±​/Jzz​ zero temperature phase diagram. From these results, we estimate the location of the boundaries between the spin liquid phase and classical long-range ordered phases.
Three dimensional frustrated magnets realized in the rare-earth pyrochlores R_2B_2O_7, R=rare-earth ion, B transition metal ion) have attracted much interest since the discovery of spin ice in Ho_2Ti_2O_7 by Harris et al. Since then, a number of interesting phenomena in pyrochlore magnets have been observed and the interest in these systems, from an experimental and theoretical point of view, has nothing but increased. Perhaps the most appealing and unique possibility is that these systems may realize a quantum disordered phase; a so-called quantum spin ice. Theoretically, it has been predicted by Hermele et al. that a U(1) quantum spin liquid is realized in the XXZ quantum spin ice (with global U(1)xZ_2 symmetry) in the perturbative regime and more recently Savary and Balents have introduced a quantum rotor model with bosonic spinons coupled to U(1)U(1)U(1) gauge fields to describe non-peturbatively the deconfined phase predicted. They studied an anisotropic quantum spin ice (QSI) model which corresponds to the XXZ QSI with an additional anisotropic coupling. They solved the quantum rotor model using a mean-field approximation combined with a large-N approximation and predicted the possibility of a U(1) liquid in addition to an exotic ferromagnetic phase. Further work by Lee et al. has addressed the more complicated fully frustrated XXZ quantum spin ice regime, where all components of the model are frustrated, by using some insights provided by the previous perturbative results. \n \nIn this thesis, we will address the non-perturbative regime of the fully frustrated XXZ QSI beyond the simplest perturbative treatment. We will begin by mapping the quantum spin ice model to a compact U(1) gauge theory with deconfined electric and magnetic monopoles. Neglecting the interaction between the gapless photon excitation and the electric charges, we will study the matter sector with only electric charges, the so-called spinons. Building up on insights provided by high order degenerate perturbation theory calculations, we will construct some symmetric spin liquid ansatz for the static part of the gauge fields. The two novel spin liquids that we construct break time reversal symmetry and thus have a non-trivial chirality. In order to solve the matter sector of the theory and determine the stability of the deconfined phases, we will introduce a novel representation of a XY quantum rotor in terms of ``exclusive" bosons, a representation which is dynamically implemented in the dilute limit. We will benchmark this mapping in different ways by comparing our results with Quantum Monte Carlo simulations and exact diagonalization in some limiting cases. Using this mapping we will compute the region of stability of the U(1) liquid phase of XXZ QSI. Within this mapping we will reproduce qualitatively the results of previous work by finding only the so-called zero and \\pi-flux U(1) liquids in the vicinity of the classical spin ice point, while improving greatly on the estimation of the exchange coupling at which the bosonic spinons condense to form a superfluid phase. In the fully frustrated XXZ QSI, we will provide evidence, using exact diagonalization of the quantum rotor model, that one of the chiral spin liquid may be realized in the strongly correlated and frustrated QSI regime, where all previous approximations break down.