Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

Yan Qi Qin,Yuan-Yao He,Anders W. Sandvik,Zhong-Yi Lu,Yi-Zhuang You,Zi Yang Meng,Arnab Sen,Cenke Xu

doi:10.1103/physrevx.7.031052

Abstract

Recently significant progress has been made in $(2+1)$-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities, i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly-correlated quantum-matter systems: the one relating the easy-plane noncompact CP$^1$ model (NCCP$^1$) and noncompact quantum electrodynamics (QED) with two flavors ($N = 2$) of massless two-component Dirac fermions. The easy-plane NCCP$^1$ model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while $N=2$ noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work we present strong numerical support for the proposed duality. We realize the $N=2$ noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC, we study a planar version of the $S=1/2$ $J$-$Q$ spin Hamiltonian (a quantum XY-model with additional multi-spin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships.

Highlights

A duality in physics is an equivalence of different mathematical descriptions of a system or a state of matter, established through a mapping by change of variables
The easyplane noncompact CP1 model (NCCP1) model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized ground state, while N 1⁄4 2 noncompact quantum electrodynamics (QED) is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator
(3) Building on the tricritical point we identify here within the easy-plane J-Q (EPJQ) spin model, our work suggests other directions in which to expand the web of dualities, by looking for the analogous point within extensions of the fermionic field theory and the bilayer honeycomb (BH) model

Summary

Introduction

A duality in physics is an equivalence of different mathematical descriptions of a system or a state of matter, established through a mapping by change of variables. The low- and high-temperature expansions of the partition function can be related to each other by identifying a one-to-one correspondence between the terms in the two different series, establishing an exact mapping between the ordered and disordered phases and the corresponding collective variables. In this case, the critical point is a self-duality point. Many other examples of dualities have been established, e.g., the well-known equivalence between the 3D O(2) Wilson-Fisher fixed

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Results

Conclusion