Running multiple jobs and convergence issues in TeNeS

[HamidArianZad]

Dear TeNeS Developers,

1. I would like to run multiple jobs simultaneously in TeNeS, but I am encountering an issue where TeNeS only works when a single job is running. When I attempt to start a second job, TeNeS stops entirely, and even the first job halts. Could you please advise on how to run multiple jobs concurrently?

2. Additionally, I am working on a frustrated 2D spin-1/2 lattice. When I increase the virtual bond dimension beyond 3 (D > 3), I am unable to achieve convergence, even with a large number of simple update steps (num_step_table = 4000) and CTM parameters (iteration_max = 500, dimension >= 25). The mode is depicted in following figure:

Since the TeNeS does not support different exchange couplings in this model, I considered J0 = J1 and use modified class square lattice :

class SquareLattice(Lattice):
   def __init__(self, param: Dict[str, Any]):
       super().__init__(param)
       self.type = "square lattice"
       self.zs = [[1, 1, 0], [0, 1, 0], [0, 0, 0]]
       #
       self.L *= 2
       self.W *= 2
       L, W = self.L, self.W
       self.sublattice = [SubLattice([self.vdim] * 4),
                          SubLattice([self.vdim] * 4),
                          SubLattice([self.vdim] * 4),
                          SubLattice([self.vdim] * 4)]

       for source in range(L * W):
           x, y = index2coord(source, L)
           #
           # sublattice A
           #
           if x % 2 == 0 and y % 2 == 0:
               self.sublattice[0].add_site(source)
               self.coords.append(np.array([x, y]))
               # 1st neighbors
               self.bonds[0][0].append(Bond(source, 1, 0))
               self.bonds[0][1].append(Bond(source, 0, 1))
           #
           # sublattice B
           #
           elif x % 2 == 1 and y % 2 == 0:
                 self.sublattice[1].add_site(source)
                 self.coords.append(np.array([x, y]))
                 # 1st neighbors
                 self.bonds[0][1].append(Bond(source, 0, 1))
           #
           # sublattice C
           #
           elif x % 2 == 0 and y % 2 == 1:
                 self.sublattice[2].add_site(source)
                 self.coords.append(np.array([x, y]))
                 # 2nd neighbors
                 self.bonds[1][1].append(Bond(source, 1, -1))
           #
           # sublattice D
           #
           elif x % 2 == 1 and y % 2 == 1:
                 self.sublattice[3].add_site(source)
                 self.coords.append(np.array([x, y]))
                 # 1st neighbors
                 self.bonds[0][0].append(Bond(source, 1, 0))
                 # 2nd neighbors
                 self.bonds[1][1].append(Bond(source, -1, 1))

to identify my lattice. Following inputs in simple.toml file is considered:

[parameter]
[parameter.general]
is_real = true

[parameter.simple_update]
num_step = 200
tau = 0.01

[parameter.full_update]
num_step = 0
tau = 0.01

[parameter.ctm]
iteration_max = 200
dimension = 10

[lattice]
type = "square lattice"
L = 2
W = 2
virtual_dim = 2
initial = "random"

[model]
type = "spin"
J0 = 1.0
J1 = 1.0
"J1'" = 1.0

The code seems work well for D<=3 and L, W<=3.

Any advice on resolving these issues would be greatly appreciated.

Thank you for your support.

[yomichi]

1. Do you use a cluster machine (e.g., supercomputer)? If so, please ask the system administrator how to run jobs (commands) in parallel. In addition, for TeNeS, please make sure that the names of the output directories (output and tensor_save) of each job differs for avoiding overwriting.

(i) to increase the number of steps.
(ii) to specify an initial state moderately. The initial state can be generated by using Hamiltonian including only magnetic field.

[HamidArianZad]

Thank you for reply,

Is it possible to apply a coarse-grained method in TeNeS to locally combine three spin-1/2 particles on the triangles of the lattice shown below into a single site with an effective spin-3/2?

If so, could I then use the class HoneycombLattice to calculate the magnetization of the effective honeycomb model with spin-(1/2, 3/2) spin as a function of the magnetic field?

[yomichi]

Yes, it is possible once you define effective Hamiltonian and observables like Sz.
In this case, the effective spin has 8 states (↑↑↑, ↑↑↓, ..., ↓↓↓), and the bond Hamiltonians on the red bonds become the site Hamiltonian described as an 8x8 matrix.