I can't figure out how to make a proper thread-safe random number generator

I'm trying to build a thread-safe random number generator, without any luck. I looked for some solutions, but none of them worked for some reason, can you help me figure out why and show me how to do it?. Here is the struct:

struct A{
    std::thread tid;
    std::default_random_engine generator;

    float val_0;
    float val_1;

    void start(float lb, float ub){
        tid = std::thread([&lb, &ub, this](){
                generator.seed(std::random_device{}());

                val_0 = R_0(generator, lb, ub);
                val_1 = R_1(lb, ub);
        });
    }

    void wait(){
        tid.join();
    }

    float R_0(std::default_random_engine& generator, float lower_bound=0.0, float upper_bound=1.0){

        return std::uniform_real_distribution<float>{lower_bound, upper_bound}(generator);
    }

    float R_1(float lower_bound=0.0, float upper_bound=1.0){
        static thread_local std::mt19937 generator(std::random_device{}());
        return std::uniform_real_distribution<float>{lower_bound, upper_bound}(generator);
    }
};

As you can see, I tried two alternatives (R_0, R_1) but both provides garbage values. Here is an output example of 10 start() invokes:

0.502351
-8.97876e-14
0.93787
0.203829
0.0451958
0.118904
0.783515
0.155594
0.649292
-4.22577e-13