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arXiv:1806.04014 · Physical Review Research

Extended Coulomb liquid of paired hardcore boson model on a pyrochlore lattice

Chun-Jiong Huang, Changle Liu, Zi Yang Meng, Yue Yu, Youjin Deng, Gang Chen

Published Oct 30, 2020• 16 citations
arXivHTMLPDF

Abstract

There is growing interest in the U (1) Coulomb liquid in both quantum materials in pyrochlore ice and cluster Mott insulators and cold-atom systems.We explore a paired hardcore boson model on a pyrochlore lattice.This model is equivalent to the XYZ spin model that was proposed for rare-earth-metal pyrochlores with "dipoleoctupole" doublets.Since our model has no sign problem for quantum Monte Carlo (QMC) simulations in a large parameter regime, we carry out both analytical and QMC calculations.We find that the U (1) Coulomb liquid is quite stable and spans a rather large portion of the phase diagram with boson pairing.Moreover, we numerically find a thermodynamic evidence that the boson pairing could induce a possible Z 2 liquid in the vicinity of the phase boundary between Coulomb liquid and Z 2 symmetry-broken phase.Besides the materials' relevance with quantum spin ice, we point to quantum simulation with cold atoms on optical lattices.

DOI
10.1103/physrevresearch.2.042022

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There is growing interest in the U (1) Coulomb liquid in both quantum materials in pyrochlore ice and cluster Mott insulators and cold-atom systems.We explore a paired hardcore boson model on a pyrochlore lattice.This model is equivalent to the XYZ spin model that was proposed for rare-earth-metal pyrochlores with "dipoleoctupole" doublets.Since our model has no sign problem for quantum Monte Carlo (QMC) simulations in a large parameter regime, we carry out both analytical and QMC calculations.We find that the U (1) Coulomb liquid is quite stable and spans a rather large portion of the phase diagram with boson pairing.Moreover, we numerically find a thermodynamic evidence that the boson pairing could induce a possible Z 2 liquid in the vicinity of the phase boundary between Coulomb liquid and Z 2 symmetry-broken phase.Besides the materials' relevance with quantum spin ice, we point to quantum simulation with cold atoms on optical lattices.
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The low-energy physics of quantum spin ice is known to support an emergent form of quantum electrodynamics (QED), where magnetic monopoles exist and the fine-structure constant is material dependent. In this article, we show how this QED is modified via a coupling to dynamical matter on the centered pyrochlore lattice, a structure that has recently been synthesized using metal-organic frameworks. Specifically, we study the low-energy properties of the S = 1 / 2 quantum XXZ model on the centered pyrochlore lattice, with a focus on the sign-problem-free region. At fourth order in degenerate perturbation theory, this model hosts a quantum spin liquid distinct from the well-known U(1) quantum spin ice on the pyrochlore because of the presence of dynamical matter in the ground state. Exact diagonalization results are consistent with this quantum spin liquid over an extended region of the ground-state phase diagram, although potential quantum critical points within this region could indicate a richer phase structure. Our work thus expands the physics of quantum spin ice in an experimentally motivated geometry, showing how the emergent QED can be coupled to dynamical matter at zero temperature.
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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.
Quantum Monte Carlo (QMC) simulation has uncovered nonzero Berry curvature and bosonic edge states in the hardcore-Bose-Hubbard model on the gapped honeycomb lattice. The competition between the chemical potential and staggered onsite potential leads to an interesting quantum phase diagram comprising the superfluid phase, Mott insulator, and charge density wave insulator. In this paper, we present a semiclassical perspective of this system by mapping to a spin-1/2 quantum XY model. We give an explicit analytical origin of the quantum phase diagram, the Berry curvatures, and the edge states using semiclassical approximations. We find very good agreement between the semiclassical analyses and the QMC results. Our results show that the topological properties of the hardcore-Bose-Hubbard model are the same as those of magnon in the corresponding quantum spin system. Our results are applicable to systems of ultracold bosonic atoms trapped in honeycomb optical lattices.
We study the physics of hard-core bosons with unfrustrated hopping (t) and nearest-neighbor repulsion (V) on the three dimensional pyrochlore lattice. At half-filling, we demonstrate that the small V/t superfluid state eventually becomes unstable at large enough V/t to an unusual insulating state which displays no broken lattice translation symmetry. Equal time and static density correlators in this insulator are well described by a mapping to electric field correlators in the Coulomb phase of a U(1) lattice gauge theory, allowing us to identify this insulator with a U(1) fractionalized Mott-insulating state. The possibility of observing this phase in suitably designed atom-trap experiments with ultracold atoms is also discussed, as are specific experimental signatures.