How to get random numbers of particular variance from truncated normal distribution?

I am trying to sample numbers from truncated normal distribution given particular variance and bounds of the resulting numbers, e.g. I need numbers with mean 0 and unit variance, but they must be within some bounds, for example [-2, 2]

I can't figure out how to truncate the distribution while keeping the variance.

import math
import numpy as np
import scipy.stats as stats


truncation = 2
lower, upper = -truncation, truncation
mu, sigma = 0, 1
num_samples = 1000
if truncation:
    n = stats.truncnorm((lower - mu) / sigma, (upper - mu) / sigma, loc=mu, scale=sigma)
    samples = n.rvs(num_samples)
    std_trunc = np.std(samples)

    n = stats.norm(loc=mu, scale=sigma)
    samples = n.rvs(num_samples)
    std_simple = np.std(samples)

print(std_trunc, std_simple, sep='\n')

# outputs 
# 0.859167285015  # I need number close to 1 here
# 1.01735583631  # like here, but here it's not truncated