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DQMC demonstration code for spin-fermion model

Getting Started

These instructions will get you a copy of the project up and running on your local machine for development and testing purposes.


FORTRAN Compiler such as Intel or Gfortran. Lapack and Blas libraries needed.


Firstly git clone the project with

git clone


git clone

To compile it, you should choose the right make.sys depends on your compiler. Let's take Gfortran as an example.

Compile lib

cd lib/

cp make.sys.gfortran make.sys


Compile src

cd src/

cp make.sys.gfortran make.sys


Input file format

We use namelist in the input file. The file src/ is an example.

Code Introduction

ftdqmc variables

  • l: System size in terms of primitive cell
  • lq: l^2, Number of primitive cells
  • norb: Number of orbital
  • ndim: Total number of sites namely lq*norb
  • nfam: Checkerboard decomposition families of hopping
  • mu: Chemical potential
  • beta: Inversed temperature
  • ltrot: Number of imaginary time slices
  • dtau: beta/ltrot
  • xmag: z-flux
  • flux_x, flux_y: Twisted boundary condition
  • nwrap: Frequency of numerical stablization
  • nsweep: Number of sweeps of one bin
  • nbin: Number of bins
  • nwarnup: Number of warm up sweeps
  • nsw_stglobal: When set to 1, do the global update
  • rt: nearest neighbor hopping
  • rt2: next nearest neighbor hopping
  • rt3: third nearest neighbor hopping
  • js: exchange coupling of Ising spins
  • hx: transverse field for Ising spins
  • rhub: spin-fermion coupling strength

ftdqmc flags

  • ltau: Whether to do time-displaced measurements
  • lstglobal: Whether to do the global update such as the Wolff update or self-learning
  • llocal: Whether to do the local update
  • lwarnup: Whether to do the warm up

ftdqmc set lattice

  • sli.f90: set lists for lattice
  • sltpf.f90: set up tables for checkboard decomposition
  • generate_neighbor.f90: generate neighbor lists

ftdqmc set hopping matrices

  • sthop.f90: set hopping matrices
  • thop_mag: z_flux and twisted boundary conditions

ftdqmc auxiliary fields related

  • salph.f90: set auxiliary fields related variables
  • inconfc.f90: initial auxiliary fields
  • outconfc.f90: output auxiliary fields

ftdqmc matrix operation subroutines

Subroutines and modules associated with matrix operations in DQMC algorithm.

  • data_tmp : Temporary matrices used in matrix operations
  • mmuur : Right multiply by exp(V) V: Interacting matrix
  • mmuurH: Right multiply by hermitian of exp(V)
  • muurm1: Right division by exp(V)
  • mmuul: Left multiply by exp(V)
  • mmuulm1: Left division by exp(V)
  • mmthr: Right multiply by exp(-dtau*T) T: hopping matrix
  • mmthrH: Right multiply by hermitian of exp(-datu*T)
  • mmthrm1: Right division by exp(-dtau*T)
  • mmthl: Left multiply by exp(-dtau*T)
  • mmthlm1: Right division by exp(-dtau*T)


DQMC sweep

  • ftdqmc_sweep_start_0b: Sweep from 0 -> beta to prepare UDV.
  • ftdqmc_sweep_start_b0: Sweep from beta -> 0 to prepare UDV.
  • ftdqmc_sweep_b0: Sweep from beta -> 0 and doing measurements.
  • ftdqmc_sweep_0b: Sweep from 0 -> beta and doing measurements.
  • Bmat_tau_R: Compute B(tau1, tau2) tau1 > tau2
  • Bmat_tau_RH: Compute B(tau1, tau2) * tau1 > tau2
  • Bmat_tau_L: Compute * B(tau1, tau2) tau1 > tau2
  • Bmatinv_tau_L: Compute * B(tau1, tau2)^-1 tau1 > tau2

Numerical stablization using ASvQRD method

  • ftdqmc_stablize_0b_svd : Numerical stablization during Monte Carlo local update sweep from 0 -> beta
  • ftdqmc_stablize_b0_svd : Numerical stablization during Monte Carlo local update sweep from beta -> 0

Subroutines associated with Green's function (equal time and time displaced).

  • green_equaltime: Calculate G(tau, tau).
  • green_equaltime00: Calculate G(0, 0).
  • green_equaltimebb: Calculate G(beta, beta).
  • green_tau: Calculate g00, gt0, g0t, gtt.

ftdqmc measurements

  • obser.f90: perform measurements
  • preq.f90: mpi reduce equal-time measurements and output
  • prtau.f90: mpi reduce time-displaced measurements and output


Main program.

Running the tests

There are some scripts in example/ that can start a test locally directly or submit jobs on server with a little change according to the server operating system.



  • Zi Yang Meng
  • Gaopei Pan


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