Efficient continuous-time quantum Monte Carlo method for the ground state of correlated fermions

We present the ground state extension of the efficient continuous-time quantum Monte Carlo algorithm for lattice fermions of M. Iazzi and M. Troyer, Phys. Rev. B 91, 241118 (2015). Based on continuous-time expansion of an imaginary-time projection operator, the algorithm is free of systematic error and scales linearly with projection time and interaction strength. Compared to the conventional quantum Monte Carlo methods for lattice fermions, this approach has greater flexibility and is easier to combine with powerful machinery such as histogram reweighting and extended ensemble simulation techniques. We discuss the implementation of the continuous-time projection in detail using the spinless $t-V$ model as an example and compare the numerical results with exact diagonalization, density matrix renormalization group, and infinite projected entangled-pair states calculations. Finally we use the method to study the fermionic quantum critical point of spinless fermions on a honeycomb lattice and confirm previous results concerning its critical exponents.

Figure 1

A configuration with $k=3$ vertices. We divide the imaginary-time axis into intervals of size $\mathrm{\Delta }$ and sweep through them sequentially. In each interval we propose updates that either insert or remove a vertex. Measurement is performed at the center of the imaginary-time $\tau =\mathrm{\Theta }/2$.

Figure 2

Density-density correlation function of a 32-site chain with periodic boundary condition. Solid lines are DMRG results.

Figure 3

Interaction energy (red dots), ground state energy (yellow squares), and CDW structure factor $M_2$ (blue triangles) of an $N=18$ site honeycomb lattice shown in the inset. Solid lines are exact diagonalization results.

Figure 4

Ground state energy per site of a honeycomb lattice versus inverse system length $1/L$ (QMC) or inverse bond dimension $1/D$ (iPEPS). The QMC results of periodic boundary conditions and antiperiodic boundary conditions approach to the thermodynamic limit value from different sides.

Figure 5

The QMC results for the CDW structure factor compared with the square of CDW order parameter calculated using iPEPS. For $V/t=1$ the CDW order parameter vanishes for bond dimensions $D>8$ in iPEPS. For $V/t=1.4$ we used a linear fit in $1/D$ of the CDW order parameter to obtain an estimate in the infinite $D$ limit (see Ref. [51] for more details).

Figure 6

(a) Scaled CDW structure factor of different system sizes cross at the transition point. (b) Scaled CDW structures factor collapse onto a single curve when plotted against scaled interaction strength.