Projected Thermal Density Matrix Monte Carlo on the Shastry-Sutherland Model

We present a continuous-time Monte Carlo method for computing the low-lying spectrum of frustrated quantum spin systems defined on finite-dimensional Hilbert spaces. The method projects the thermal density matrix onto a subspace spanned by a chosen set of linearly independent basis states. It works directly with the Hamiltonian, avoids Trotter discretization errors, and provides systematic access to the low-energy sector. While most effective for systems without sign problems, it also yields useful results when sign problems are present. We illustrate the approach using the Shastry–Sutherland model, a paradigmatic example of geometric frustration that exhibits a severe sign problem. The method reproduces exact diagonalization results where available and extends to systems just beyond that reach. We aim to diminish the sign problem by using experimentally motivated projection subspaces and optimizing their dimension to achieve convergence at small inverse temperatures before the sign problem becomes prohibitive. We are also exploring additional observables and expect to use the method to identify phase transitions in the model.