Hamming Distance and the onset of quantum criticality

Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight configurations in the sampling, that is, the sign problem (SP). There have been several recent calculations which exploit the SP to locate underlying critical behavior. Here, utilizing a metric that quantifies phase-space ergodicity in such sampling, the Hamming distance, we suggest a significant advance on these ideas to extract the location of quantum critical points in various fermionic models, in spite of the presence of a severe SP. Combined with other methods, exact diagonalization in our case, it elucidates both the nature of the different phases as well as their location, as we demonstrate explicitly for the honeycomb and triangular Hubbard models, in both their U(1) and SU(2) forms. Our approach charts a path to circumvent inherent limitations imposed by the SP, allowing the exploration of the phase diagram of a variety of fermionic quantum models hitherto considered to be impractical via quantum Monte Carlo simulations.

Thermal and Quantum Fluctuation Effects in Quasiperiodic Systems in External Potentials

We analyze the many-body phases of an ensemble of particles interacting via a Lifshitz–Petrich–Gaussian pair potential in a harmonic confinement. We focus on specific parameter regimes where we expect decagonal quasiperiodic cluster arrangements. Performing classical Monte Carlo as well as path integral quantum Monte Carlo methods, we numerically simulate systems of a few thousand particles including thermal and quantum fluctuations. Our findings indicate that the competition between the intrinsic length scale of the harmonic oscillator and the wavelengths associated to the minima of the pair potential generically lead to a destruction of the quasicrystalline pattern. Extensions of this work are also discussed.