Real-time simulation of large open quantum spin systems driven by dissipation

We consider a large quantum system with spins $\frac{1}{2}$ whose dynamics is driven entirely by measurements of the total spin of spin pairs. This gives rise to a dissipative coupling to the environment. When one averages over the measurement results, the corresponding real-time path integral does not suffer from a sign problem. Using an efficient cluster algorithm, we study the real-time evolution from an initial antiferromagnetic state of the two-dimensional Heisenberg model, which is driven to a disordered phase, not by a Hamiltonian, but by sporadic measurements or by continuous Lindblad evolution.

Figure 1

(a) Real-time evolution of $\langle M_s^2\rangle$ driven by discrete measurements, for $\beta J=0.01$, $0.1$, 1, and 10, for $L=16a$. (b) Inverse equilibration time $1/\left[\gamma \tau \right(p\left)\right]$ as a function of $\left|p\right|$ for $L=16a$, $\beta J=40$, and $L=32a$, $\beta J=80$. (c) Evolution of the Fourier modes $\langle |\tilde{S}\left(p\right){|}^2\rangle$ for the Heisenberg antiferromagnet driven by a continuous Lindblad process.

Figure 2

(a) $\langle M_s^2\rangle /L^4$ and (b) Binder ratio $\langle M_s^4\rangle /{\langle M_s^2\rangle }^2$ as functions of time for $L/a=8,\cdots ,64$, $\beta J=5,\cdots ,40$. Evolution of (c) ${\mathcal{M}}_s\left(t\right)/{\mathcal{M}}_s\left(0\right)$ and (d) $\xi \left(t\right)/\xi \left(0\right)$.