Ground-state phase diagram of dipolar-octupolar pyrochlores

Owen Benton

doi:10.1103/physrevb.102.104408

Abstract

The dipolar-octupolar pyrochlore oxides R$_2$M$_2$O$_7$ (R=Ce, Sm, Nd) represent an important opportunity in the search for three dimensional Quantum Spin Liquid (QSL) ground states. Their low energy physics is governed by an alluringly simple XYZ Hamiltonian, enabling theoretical description with only a small number of free parameters. Meanwhile, recent experiments on Ce pyrochlores strongly suggest QSL physics. Motivated by this, we present here a complete analysis of the ground state phase diagram of dipolar-octupolar pyrochlores. Combining cluster mean field theory, variational arguments and exact diagonalization we find multiple U(1) QSL phases which together occupy a large fraction of the parameter space. These results give a comprehensive picture of the ground state physics of an important class of QSL candidates and support the possibility of a $U(1)$ QSL ground state in Ce$_2$Zr$_2$O$_7$ and Ce$_2$Sn$_2$O$_7$.

Highlights

The pursuit of quantum spin liquid (QSL) ground states has not gone unrewarded
It has been realized that an enormous diversity of QSL states are possible [1,2] and several physically relevant models are known to have QSL ground states [3,4,5,6,7,8,9,10,11]
Some materials studied as potential QSLs order at low temperature [17,18,19], and others are complicated by chemical or structural disorder [20,21,22,23]

Summary

INTRODUCTION

The pursuit of quantum spin liquid (QSL) ground states has not gone unrewarded. On the theory side, it has been realized that an enormous diversity of QSL states are possible [1,2] and several physically relevant models are known to have QSL ground states [3,4,5,6,7,8,9,10,11]. We calculate the ground-state phase diagram of Eq (2), by combining cluster mean-field theory (CMFT), a variational extension to CMFT (CVAR) [52] and exact diagonalization (ED). The four U (1) QSLs all host gapless photons and gapped fractionalized charges, and are realizations of emergent electromagnetism [4,6,47,49] They are labeled dipolar/octupolar-U (1)0/π with the dipolar/octupolar label referring to whether the emergent electric field transforms like a magnetic dipole or octupole [56,57], and the 0/π subscript referring to the U (1) flux penetrating elementary plaquettes in the ground state.

DUALITIES OF THE MODEL AND REDUCED PARAMETER SPACE

CMFT Calculation

Cluster variational calculation

Boundary between QSLs

CONSTRUCTION OF COMPLETE PHASE DIAGRAM

SUMMARY AND OUTLOOK