Continuous Easy-Plane Deconfined Phase Transition on the Kagome Lattice

We use large scale quantum Monte Carlo simulations to study an extended Hubbard model of hard core bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at $1/3$ filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. We present a theory in terms of an easy plane noncompact $\mathrm{C}{\mathrm{P}}^1$ gauge theory describing the phase transition at $1/3$ filling. Utilizing large scale quantum Monte Carlo simulations with parallel tempering in the canonical ensemble up to 15552 spins, we provide evidence that the phase transition is continuous at exactly $1/3$ filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality.

Figure 1

Phase diagram of Hamiltonian (1) at $1/3$ filling with a DCP separating a VBS and a superfluid phase. In the VBS phase, resonant processes (colored hexagon) spontaneously break translation symmetry. In contrast, in the superfluid phase, the bosons condense and spontaneously break the $U(1)$ symmetry.

Figure 2

The structure factor (b) and its Binder cumulant (a) vs $t/V$ at $1/3$ filling and $\beta V/L=25/3$ with different $L$. (c) The probability density function (PDF) of kinetic energy at $L=72$ and $\beta V=600$ near the critical point.

Figure 3

Data collapse of (a) superfluid density with logarithmic correction, (b) structure factor, and (c) condensate fraction at $1/3$ filling and $\beta V/L=25/3$.

Figure 4

(a) Off-diagonal correlation function vs distance at $1/3$ filling for $L=18$, $\beta V=300$, and different $t/V$. (b) Off-diagonal and (c) diagonal correlation function vs distance for different system sizes near the critical point at $1/3$ filling, $t/V=0.1303$ and $\beta V/L=25/3$. Inset: FSS of the anomalous exponents from fitting to $C_l(\delta ,r)$. The extracted critical exponents are ${\eta }_{\mathrm{SF}}=0.305(0.020)$ and ${\eta }_{\mathrm{VBS}}=0.313(0.057)$. (d) Spinon correlation function vs distance at $1/3$ filling, near the critical point $t/V=0.1303$ and $\beta V/L=25/3$ for different system sizes. The black line is a fit to a power law decay $r^{-4.02(0.18)}$.

Figure 5

Histogram of [$\mathrm{\Xi }({\mathbf{Q}}_h{)}_x$, $\mathrm{\Xi }({\mathbf{Q}}_h{)}_y$] in (a) VBS phase ($t/V=0.124$), (b) near the critical point ($t/V=0.129$), and (c) the superfluid phase ($t/V=0.131$) at $1/3$ filling, $L=30$ and $\beta V=500$. (d) The $Z_3$ anisotropy parameter $W_3$ at $1/3$ filling and $\beta V/L=25/3$ for different system sizes.